Rs Aggarwal 2020 2021 for Class 8 Maths Chapter 10 - Profit And Loss

Answer:

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{CP}=\mathrm{Rs}. 620 \\ \mathrm{SP}=\mathrm{Rs}. 713 \\ \mathrm{Since} \mathrm{SP}> \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{gain}. \\ \mathrm{Gain} =713 - 620 = \mathrm{Rs}. 93 \\ \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100)\% \\ =(\frac{93}{620}\times 100)\% \\ =15\% \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs} 675 \\ \mathrm{SP}=\mathrm{Rs} 630 \\ \mathrm{Since} \mathrm{SP}< \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{loss}. \\ \mathrm{Loss}=675 - 630 = \mathrm{Rs}. 45 \\ \mathrm{Loss} \mathrm{percentage} =(\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{45}{675}\times 100)\% \\ =6\frac{2}{3}\% \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 345 \\ \mathrm{SP}=\mathrm{Rs}. 372.60 \\ \mathrm{Since} \mathrm{SP}> \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{gain}. \\ \mathrm{Gain}=372.60 - 345 = \mathrm{Rs}. 27.6 \\ \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}} \times 100)\% \\ =(\frac{27.6}{345}\times 100)\% \\ =\left(\frac{2760}{345}\right)\% \\ =8\% \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs} 80 \\ \mathrm{SP}=\mathrm{Rs} 76.80 \\ \mathrm{Since} \mathrm{SP}< \mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{loss}. \\ \mathrm{Loss} =80 - 76.80 = \mathrm{Rs}. 3.2 \\ \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}} \times 100)\% \\ =(\frac{3.2}{80}\times 100)\% \\ =(\frac{32}{80}\times 100)\% \\ =4\% \end{gathered}$$

Answer:

(i)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 1650 \\ \mathrm{Gain} \mathrm{percentage}=4\% \\ \mathrm{SP}=\frac{(100+\mathrm{gain} \%)}{100}\times \mathrm{CP} \\ =\frac{(100+4)}{100}\times 1650 \\ =\frac{104\times 1650}{100} \\ =\mathrm{Rs}. 1716 \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 915 \\ \mathrm{Gain} \mathrm{percentage}=6\frac{2}{3}\%=\frac{20}{3}\% \\ \mathrm{SP}=\frac{(100+\mathrm{gain} \%)}{100}\times \mathrm{CP} \\ =\frac{(100+{\displaystyle \frac{20}{3}})}{100}\times 915 \\ =\frac{\left({\displaystyle \frac{320}{3}}\right)}{100}\times 915 \\ =\left(\frac{320}{3}\right)\times \left(\frac{1}{100}\right)\times 915 \\ =\mathrm{Rs}. 976 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 875 \\ \mathrm{Loss} \mathrm{percentage}=12\% \\ \mathrm{SP}=\frac{(100-\mathrm{loss} \%)}{100}\times \mathrm{CP} \\ =\frac{(100-12)}{100}\times 875 \\ =\frac{77000}{100} \\ =\mathrm{Rs}. 770 \end{gathered}$$

(iv)

$$\begin{gathered} \mathrm{CP}=\mathrm{Rs}. 645 \\ \mathrm{Loss} \mathrm{percentage}=13\frac{1}{3}\%=\frac{40}{3}\% \\ \mathrm{SP}=\frac{(100-\mathrm{loss} \%)}{100}\times \mathrm{CP} \\ =\frac{(100-{\displaystyle \frac{40}{3}})}{100}\times 645 \\ =\frac{\left({\displaystyle \frac{300-40}{3}}\right)}{100}\times 645 \\ =\left(\frac{260}{3}\right)\times \left(\frac{1}{100}\right)\times 645 \\ =\mathrm{Rs}. 559 \end{gathered}$$

Answer:

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{SP}=\mathrm{Rs}. 1596 \\ \mathrm{Gain} \mathrm{percentage}=12\% \\ \mathrm{CP}=\frac{100}{(100+\mathrm{gain} \%)}\times \mathrm{SP} \\ =\frac{100}{(100+12)}\times 1596 \\ =\mathrm{Rs}. 1425 \end{gathered}$$

(ii)

$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}. 2431 \\ \mathrm{Loss} \mathrm{percentage}=6\frac{1}{2}\%=\frac{13}{2}\% \\ \mathrm{CP}=\frac{100}{(100-\mathrm{loss} \%)}\times \mathrm{SP} \\ =\frac{100}{(100-{\displaystyle \frac{13}{2}})}\times 2431 \\ =\frac{100\times 2}{187}\times 2431 \\ =\mathrm{Rs}. 2600 \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}. 657.60 \\ \mathrm{Loss} \mathrm{percentage}=4\% \\ \mathrm{CP}=\frac{100}{(100-\mathrm{loss} \%)}\times \mathrm{SP} \\ =\frac{100}{(100-4)}\times 657.60 \\ =\mathrm{Rs}. 685 \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{SP}=\mathrm{Rs}. 34.40 \\ \mathrm{Gain} \mathrm{percentage}=7\frac{1}{2}\%=\frac{15}{2}\% \\ \mathrm{CP}=\frac{100}{(100+\mathrm{gain} \%)}\times \mathrm{SP} \\ =\frac{100}{(100+{\displaystyle \frac{15}{2}})}\times 34.40 \\ =\frac{100\times 2}{215}\times 34.40 \\ =\mathrm{Rs}. 32 \end{gathered}$$

Answer:

CP of the iron safe = ₹12,160
Money spent on transportation = ₹340
Total CP = ₹12,160 + ₹340 = ₹12,500
SP of the iron safe = ₹12,875
Profit = SP − CP = ₹12,875 − ₹12,500 = ₹375
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\%$$=\frac{375}{12500}\times 100\%=3\%$
 

Answer:

$$\begin{gathered} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{car}=\mathrm{Rs}. 73500 \\ \mathrm{Repairs}=\mathrm{Rs}. 10300 \\ \mathrm{Insurance}=\mathrm{Rs}. 2600 \\ \mathrm{Total} \mathrm{CP}=73500+10300+2600=\mathrm{Rs}.86400 \\ \mathrm{SP}=\mathrm{Rs}. 84240 \\ \mathrm{Since} \mathrm{SP}<\mathrm{CP}, \mathrm{Robin} \mathrm{has} \mathrm{a} \mathrm{loss}. \\ \mathrm{Loss}=86400-84240 \\ =\mathrm{Rs}. 2160 \\ \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{total} \mathrm{CP}}\times 100)\% \\ =(\frac{2160}{86400}\times 100)\% \\ =2\frac{1}{2}\% \end{gathered}$$

Answer:

Total cost of rice of 1st variety = ₹36/kg × 20 kg = ₹720
Total cost of rice of 2nd variety = ₹32/kg × 25 kg = ₹800
Total cost of the two rice varieties = ₹720 + ₹800 = ₹1,520
Total quantity of the two rice varieties = 20 kg + 25 kg = 45 kg
Selling price of the mixture of two rice = ₹38/kg × 45 kg = ₹1,710
Gain = SP − CP = ₹1,710 − ₹1,520 = ₹190
Gain% = $\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100\%=\frac{190}{1520}\times 100\%=12\frac{1}{2}\%$

Answer:

$$\begin{gathered} \mathrm{Let} 5 \mathrm{kg} \mathrm{of} \mathrm{coffee} \mathrm{be} \mathrm{mixed} \mathrm{with} 2 \mathrm{kg} \mathrm{of} \mathrm{chicory}. \\ \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{mixture}=\mathrm{Rs} (250\times 5+75\times 2) \\ =\mathrm{Rs} (1250+150) \\ =\mathrm{Rs}. 1400 \\ \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{mixture}=\mathrm{Rs} (7\times 230)=\mathrm{Rs}. 1610 \\ \mathrm{Since} \mathrm{SP}>\mathrm{CP}, \mathrm{there} \mathrm{is} \mathrm{a} \mathrm{gain}. \\ \mathrm{Now}, \mathrm{gain}=\mathrm{Rs} (1610-1400) \\ =\mathrm{Rs}. 210 \\ \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{total} \mathrm{CP}}\times 100)\% \\ =(\frac{210}{1400}\times 100)\% \\ =15\% \end{gathered}$$

Answer:

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{each} \mathrm{bottle} \mathrm{and} \mathrm{Rs} y \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{each} \mathrm{bottle}. \\ \mathrm{SP} \mathrm{of} 16 \mathrm{bottles} = \mathrm{CP} \mathrm{of} 17 \mathrm{bottles} \\ \Rightarrow 16\mathrm{x}=17\mathrm{y} \\ \Rightarrow \frac{\mathrm{x}}{\mathrm{y}}=\frac{17}{16} \\ \mathrm{Gain} \mathrm{per} \mathrm{bottle}=\mathrm{SP}-\mathrm{CP} \\ =\mathrm{Rs} (\mathrm{x}-\mathrm{y}) \\ \therefore \mathrm{Gain} \mathrm{percentage}=(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100)\% \\ =(\frac{\mathrm{x}-\mathrm{y}}{\mathrm{y}}\times 100)\% \\ =\left\{\right(\frac{\mathrm{x}}{\mathrm{y}}-1)\times 100\}\% \\ =\left\{\right(\frac{17}{16}-1)\times 100\}\% \\ =(\frac{1}{16}\times 100)\% \\ =6\frac{1}{4}\% \end{gathered}$$

Answer:

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{one} \mathrm{candle} \mathrm{and} \mathrm{Rs}. y \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{one} \mathrm{candle}. \\ \mathrm{Now}, \mathrm{CP} \mathrm{of} 12 \mathrm{candles}=\mathrm{SP} \mathrm{of} 15 \mathrm{candles} \\ \Rightarrow 12x=15y \\ \Rightarrow \frac{y}{x}=\frac{12}{15} \\ \mathrm{Loss} = \mathrm{CP}-\mathrm{SP} \\ =\mathrm{Rs} (x-y) \\ \therefore \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =\left\{\right(\frac{x-y}{x})\times 100\}\% \\ =\left\{\right(1-\frac{y}{x})\times 100\}\% \\ =\left\{\right(1-\frac{12}{15})\times 100\}\% \\ =(\frac{3}{15}\times 100)\% \\ =20\% \end{gathered}$$

Answer:

It is given that,
Gain = SP of 5 cassettes                 .....(1)
Gain = SP of 130 cassettes − CP of 130 cassettes
⇒ SP of 5 cassettes = SP of 130 cassettes − CP of 130 cassettes               [From (1)]
⇒ CP of 130 cassettes = SP of 125 cassettes          .....(2)
Let the CP of 1 cassettte be ₹x.
∴ CP of 125 cassettes = ₹125x
CP of 130 cassettes = ₹130x
SP of 125 cassettes = CP of 130 cassettes                    [From (2)]
⇒ SP of 125 cassettes = ₹130x
Now, gain% $=\frac{\mathrm{SP}-\mathrm{CP}}{\mathrm{CP}}\times 100\%=\frac{\left(130x-125x\right)}{125x}\times 100\%$$=\frac{5x}{125x}\times 100\%=4\%$
Thus, the gain percent is 4%.  

Answer:

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{one} \mathrm{lemon}. \\ \mathrm{SP} \mathrm{of} 45 \mathrm{lemons}=\mathrm{Rs}. 45x \\ \mathrm{Loss}=\mathrm{SP} \mathrm{of} 3 \mathrm{lemons}=\mathrm{Rs}. 3x \\ \mathrm{But} \mathrm{loss}=\mathrm{CP}-\mathrm{SP} \\ \mathrm{CP}=\mathrm{loss}+\mathrm{SP} \\ =3x+45x \\ =\mathrm{Rs}. 48x \\ \therefore \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{3x}{48x}\times 100)\% \\ =6\frac{1}{4}\% \end{gathered}$$

Answer:

LCM of 6 and 4 = 12
Let the number of oranges bought be 12.
CP of 6 oranges = ₹20
So, CP of 1 orange = $\frac{20}{6}=₹\frac{10}{3}$
CP of 12 orange = $12\times \frac{10}{3}=₹40$
SP of 4 oranges = ₹18
SP of 1 orange = $\frac{18}{4}=₹\frac{9}{2}$
SP of 12 oranges = $12\times \frac{9}{2}=₹54$
Here, SP of 12 oranges > CP of 12 oranges.
Profit = SP − CP = ₹54 − ₹40 = ₹14
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\%=\frac{14}{40}\times 100\%=35\%$

Answer:

LCM of 12 and 10 = 60
Let the number of banana bought be 60.
CP of 12 banana = ₹40
∴ CP of 1 banana = $\frac{40}{12}=₹\frac{10}{3}$
⇒ CP of 60 bananas = $60\times \frac{10}{3}=₹200$
SP of 10 bananas = ₹36
∴ SP of 1 banana = $\frac{36}{10}=₹\frac{18}{5}$
⇒ SP of 60 bananas = $60\times \frac{18}{5}=₹216$
Here, SP of 60 bananas > CP of 60 bananas.
Profit = SP − CP = ₹216 − ₹200 = ₹16
∴ Profit% = $\frac{\mathrm{Profit}}{\mathrm{CP}}\times 100\%=\frac{16}{200}\times 100=8\%$

Answer:

LCM of 10 and 12 = 60
Let the number of apples bought be 60.
CP of 10 oranges = ₹75
∴ CP of 1 orange = $₹\frac{75}{10}$
⇒ CP of 60 orange = $60\times \frac{75}{10}=₹450$
SP of 12 oranges = ₹75
∴ SP of 1 orange = $₹\frac{75}{12}$
⇒ SP of 60 oranges = $60\times \frac{75}{12}=₹375$
Here, CP of 60 oranges > SP of 60 oranges.
Loss = CP − SP = ₹450 − ₹375 = ₹75
∴ Loss% = $\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100\%=\frac{75}{450}\times 100\%=16\frac{2}{3}\%$

Answer:

Let the number of eggs purchased be x.
CP of 3 eggs = ₹16
∴ CP of 1 egg = $₹\frac{16}{3}$
⇒ CP of x eggs = $₹\frac{16}{3}x$
SP of 5 eggs = ₹36
∴ SP of 1 egg = $₹\frac{36}{5}$
⇒ SP of x eggs = $₹\frac{36}{5}x$
Gain = SP − CP = ₹168
$$\begin{gathered} \therefore \frac{36}{5}x-\frac{16}{3}x=168 \\ \Rightarrow \frac{28}{15}x=168 \\ \Rightarrow x=\frac{168\times 15}{28} \\ \Rightarrow x=90 \end{gathered}$$
Hence, the man purchased 90 eggs.

Answer:

$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{camera}=\mathrm{Rs}. 1080 \\ \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP}. \\ \mathrm{Gain}=\mathrm{Rs}. \frac{1}{8}x ...\left(\mathrm{i}\right) \\ \mathrm{Also}, \mathrm{gain}=\mathrm{SP}-\mathrm{CP} \\ =\mathrm{Rs}. (1080 -x) ...\left(\mathrm{ii}\right) \\ \mathrm{From} \left(\mathrm{i}\right) \mathrm{and} \left(\mathrm{ii}\right), \mathrm{we} \mathrm{have}: \\ \frac{1}{8}x=1080 -x \\ \Rightarrow x=8640-8x \\ \Rightarrow 9x=8640 \\ \Rightarrow \mathrm{x}=960 \\ \therefore \mathrm{CP}=\mathrm{Rs}. 960 \\ \mathrm{Now}, \mathrm{gain} =\frac{1}{8}\mathrm{x} \\ =\frac{960}{8} \\ =\mathrm{Rs}. 120 \\ \therefore \mathrm{Gain} \mathrm{percentage}=(\frac{120}{960}\times 100)\% \\ =12\frac{1}{2}\% \end{gathered}$$

Answer:

$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{pen}=\mathrm{Rs}. 54 \\ \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{pen}. \\ \mathrm{Loss}=\mathrm{Rs}. \frac{x}{10} \\ \mathrm{SP}=\mathrm{CP}-\mathrm{Loss} \\ =x-\frac{x}{10} \\ =\mathrm{Rs}. \frac{9x}{10} \\ \mathrm{Now}, \mathrm{we} \mathrm{have}\frac{9\mathrm{x}}{10}=54 \\ \Rightarrow x=54\times \frac{10}{9} \\ \Rightarrow \mathrm{x}=60 \\ \therefore \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{pen}=\mathrm{Rs}. 60 \\ \mathrm{Now}, \mathrm{loss}=\frac{\mathrm{x}}{10} \\ =\frac{60}{10} \\ =\mathrm{Rs}. 6 \\ \therefore \mathrm{Loss} \mathrm{percentage}=(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100)\% \\ =(\frac{6}{60}\times 100)\% \\ =10\% \end{gathered}$$

Answer:

Let the cost price be ₹x.
Loss = 10% of ₹x = $\frac{10}{100}x=₹\frac{x}{10}$
SP in case of loss = CP − Loss = $x-\frac{x}{10}=₹\frac{9x}{10}$
Gain =10% of ₹x = $\frac{10}{100}x=₹\frac{x}{10}$
SP in case of profit = CP + Profit = $x+\frac{x}{10}=₹\frac{11x}{10}$
It is given that dealer gets ₹940 more if sold at a profit of 10% instead of loss of 10%.
∴ SP in case of profit − SP in case of loss = ₹940
$$\begin{gathered} \Rightarrow \frac{11x}{10}-\frac{9x}{10}=940 \\ \Rightarrow \frac{2x}{10}=940 \\ \Rightarrow x=4700 \end{gathered}$$
Hence, the cost price of the table is ₹4,700.

Answer:

$$\begin{gathered} \mathrm{Let} Rs x be the \mathrm{CP}. \\ {\mathrm{Gain}}_1 \mathrm{percentage}=\left(\frac{{\mathrm{gain}}_1}{\mathrm{CP}}\times 100\right)\% \\ \Rightarrow 15=\frac{{\mathrm{gain}}_1}{x}\times 100 \\ \Rightarrow {\mathrm{Gain}}_1=\mathrm{Rs} \frac{15x}{100} \\ \mathrm{Again}, {\mathrm{gain}}_2 \mathrm{percentage}=\left(\frac{{\mathrm{gain}}_2}{\mathrm{CP}}\times 100\right)\% \\ \Rightarrow 8=\frac{{\mathrm{gain}}_2}{x}\times 100 \\ \Rightarrow {\mathrm{Gain}}_2=\mathrm{Rs} \frac{8x}{100} \\ \mathrm{According} \mathrm{to} \mathrm{the} \mathrm{question}, \mathrm{we} \mathrm{have}: \\ {\mathrm{Gain}}_1-{\mathrm{gain}}_{ 2}= 56 \\ \Rightarrow \frac{15\mathrm{x}}{100} - \frac{8\mathrm{x}}{100}=56 \\ \Rightarrow \frac{7\mathrm{x}}{100}=56 \\ \Rightarrow 7x=5600 \\ \Rightarrow x=800 \\ \mathrm{Hence}, \mathrm{the} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{chair} \mathrm{is} \mathrm{Rs} 800. \end{gathered}$$

Answer:

Let the CP be ₹x.
SP when gain is 10% = $x+\frac{10}{100}x=₹\frac{110}{100}x$
SP when gain is 14% = $x+\frac{14}{100}x=₹\frac{114}{100}x$
Difference in SP = SP when gain is 14% − SP when gain is 10% = ₹260
$$\begin{gathered} \therefore \frac{114x}{100}-\frac{110x}{100}=260 \\ \Rightarrow \frac{4x}{100}=260 \\ \Rightarrow x=6500 \end{gathered}$$
Hence, the CP of the cycle is ₹6,500.

Answer:

40 kg of wheat is bought for ₹12.50/kg.
∴ CP of 40 kg of wheat = 40 × 12.50 = ₹500
30 kg of wheat is bought for ₹14/kg.
∴ CP of 30 kg of wheat = 30 × 14 = ₹420
Total CP = ₹500 + ₹420 = ₹920
Profit = 5% of CP = 5% of ₹920 = $\frac{5}{100}\times 920=₹46$
Let the SP be ₹x.
Profit = SP − CP
⇒ x − 920 = 46
⇒ x = ₹966
SP of 70 kg wheat = ₹966
∴ SP of 1 kg wheat = $\frac{966}{70}=₹13.80$
Thus, the selling price of the mixture is ₹13.80/kg.

Answer:

CP of the first bat = ₹840
Profit% on the first bat = 15%
∴ Profit = 15% of ₹840 = $\frac{15}{100}\times 840=₹126$
SP of the first bat = ₹840 + ₹126 = ₹966
CP of the second bat = ₹360
Loss = 5% of ₹360 = $\frac{5}{100}\times 360=₹18$
SP of the second bat = ₹360 − ₹18 = ₹342
Total CP of two bats = CP of first bat + CP of second bat = ₹840 + ₹360 = ₹1,200
Total SP of two bats = SP of first bat + SP of second bat = ₹966 + ₹342 = ₹1,308
Here, Total SP of two bats > Total CP of two bats.
Gain = Total SP of two bats − Total CP of two bats = ₹1,308 − ₹1,200 = ₹108
∴ Gain% in the whole transaction$=\frac{\mathrm{Gain}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{bats}}\times 100\%$$=\frac{108}{1200}\times 100=9\%$

Answer:

CP of first jeans = ₹1,450
Profit = 8% of CP = $\frac{8}{100}\times 1450=₹116$
SP of first jeans = ₹1,450 + ₹116 = ₹1,566
CP of second jeans = ₹1,450
Loss = 4% of CP = $\frac{4}{100}\times 1450=₹58$
SP of second jeans = ₹1450 − ₹58 = ₹1,392
Total CP of two jeans = CP of first jeans + CP of second jeans = ₹1,450 + ₹1,450 = ₹2,900
Total SP of two jeans = SP of first jeans + SP of second jeans = ₹1,566 + ₹1,392 = ₹2,958
Here, Total SP of two jeans > Total CP of two jeans.
Gain = Total SP of two jeans − Total CP of two jeans = ₹2,958 − ₹2,900 = ₹58
∴ Gain% = $\frac{\mathrm{Gain}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{jeans}}\times 100\%=\frac{58}{2900}\times 100\%=2\%$

Answer:

CP of 1 kg of rice = Rs 25
C.P of 200 kg rice= $\mathrm{Rs} (200\times 25)=\mathrm{Rs} 5000$
CP of 80 kg of rice=$\mathrm{Rs} (25\times 80)=\mathrm{Rs} 2000$

CP of 40 kg of rice =$\mathrm{Rs} (25\times 40)=\mathrm{Rs} 1000$
 
$$\begin{gathered} \mathrm{SP} \mathrm{of} 80 \mathrm{kg} \mathrm{of} \mathrm{rice} = \frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{110}{100}\times 2000 \\ =\mathrm{Rs} 2200 \end{gathered}$$

$$\begin{gathered} \mathrm{SP} \mathrm{of} 40 \mathrm{kg} \mathrm{rice}=\frac{100-\mathrm{loss}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{96}{100}\times 1000 \\ =\mathrm{Rs} 960 \end{gathered}$$

 $$\begin{gathered} \mathrm{SP} \mathrm{of} 200 \mathrm{kg} \mathrm{rice}=\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{108}{100}\times 5000 \\ =\mathrm{Rs} 5400 \end{gathered}$$

Remaining quantity of rice = (200 − 80 + 40) kg = 80 kg

​SP of the remaining rice (80 kg) = Rs (5400 − 2200 − 960)
                                                        = Rs 2240

$\therefore \mathrm{Rate} \mathrm{per} \mathrm{kg} = \mathrm{Rs} \frac{2240}{80}= \mathrm{Rs} 28$

Answer:

Let the CP of the TV set be ₹x.
SP of the TV set = $\frac{6}{5}\mathrm{CP}=₹\frac{6}{5}x$
Gain = SP of the TV set − CP of the TV set = $\frac{6}{5}x-x=₹\frac{x}{5}$
Gain% = $\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100\%=\frac{{\displaystyle \frac{x}{5}}}{x}\times 100\%=\frac{100}{5}\%=20\%$

Answer:

Let the CP of the flower vase set be ₹x.
SP of the flower vase = $\frac{5}{6}\mathrm{CP}=₹\frac{5}{6}x$
Loss = CP − SP = $x-\frac{5}{6}x=₹\frac{x}{6}$
Loss% = $\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100\%=\frac{{\displaystyle \frac{x}{6}}}{x}\times 100\%=\frac{100}{6}\%=\frac{50}{3}\%=16\frac{2}{3}\%$

Answer:

SP of the bouquet = Rs 322
Gain percentage = 15%
$$\begin{gathered} \mathrm{CP} \mathrm{of} \mathrm{the} \mathrm{bouquet} =\left(\frac{100}{100+\mathrm{gain}\%}\right)\times \mathrm{SP} \\ =\mathrm{Rs} \left(\frac{100}{100+15}\right)\times 322 \\ =\mathrm{Rs} \frac{100}{115}\times 322 \\ =\mathrm{Rs} 280 \end{gathered}$$

Now, CP = Rs 128 and desired gain percentage = 25%

$$\begin{gathered} \therefore \mathrm{Desired} \mathrm{S}\mathrm{P}=\left(\frac{100+\mathrm{gain}\%}{100}\right)\times \mathrm{CP} \\ =\mathrm{Rs} \frac{125}{100}\times 280 \\ =\mathrm{Rs} 350 \end{gathered}$$

​Hence, the selling price to obtain the desired gain must be Rs 350.

Answer:

Let the CP of the umbrella be ₹x.
SP of the umbrella = ₹336
Loss = 4% of ₹x = $₹\frac{4}{100}x$
CP − Loss = SP
$$\begin{gathered} \Rightarrow x-\frac{4}{100}x=336 \\ \Rightarrow \frac{96}{100}x=336 \\ \Rightarrow x=₹350 \end{gathered}$$
∴ CP of the umbrella = ₹350
Now, for gain of 4%,
SP = CP + Gain
$$\begin{gathered} \Rightarrow \mathrm{SP}=350+\frac{4}{100}\times 350 \\ \Rightarrow \mathrm{SP}=350+14 \\ \Rightarrow \mathrm{SP}=₹364 \end{gathered}$$
Hence, in order to gain 4%, the umbrella should be sold for ₹364.

Answer:

Let the original price be $x$.
SP = Rs 3120
Now, SP = CP − loss
​$$\begin{gathered} \Rightarrow 3120=x-\frac{4}{{\displaystyle \frac{100}{x}}} \\ \Rightarrow 3120=x-\frac{x}{25} \\ \Rightarrow 3120=\frac{24x}{25} \\ \Rightarrow \frac{3120\times 25}{24}=x \\ \Rightarrow x=3250 \end{gathered}$$

So, the cost price is Rs 3250.

If it is sold for Rs 3445, then its a gain because SP > CP.
Now, gain = SP − CP
= Rs (3445 − 3250)
= Rs 195
$$\begin{gathered} \therefore Gain percentage=\left(\frac{gain}{CP}\times 100\right)\% \\ =\left(\frac{195}{3250}\times 100\right)\% \\ =6\% \end{gathered}$$

Hence, gain percent = 6%

Answer:

SP of first saree = ₹1,980
Loss = 10%
Let the CP of first saree be ₹x.
CP = Loss + SP
$$\begin{gathered} \Rightarrow \frac{10}{100}\times x+1980=x \\ \Rightarrow x-\frac{{\displaystyle 10}}{{\displaystyle 100}}x=1980 \\ \Rightarrow \frac{90}{100}x=1980 \\ \Rightarrow x=2200 \end{gathered}$$
∴ CP of first saree = ₹2,200
SP of second saree = ₹1,980
Gain = 10%
Let the CP of second saree be ₹y.
CP = SP − Gain
$$\begin{gathered} \Rightarrow 1980-\frac{10}{100}\times y=y \\ \Rightarrow 1980-\frac{y}{10}=y \\ \Rightarrow y+\frac{y}{10}=1980 \\ \Rightarrow \frac{11y}{10}=1980 \\ \Rightarrow y=1800 \end{gathered}$$
∴ CP of second saree = ₹1,800
Total CP of two sarees = CP of first saree + CP of second saree = ₹2,200 + ₹1,800 = ₹4,000
Total SP of two sarees = SP of first saree + SP of second saree = ₹1,980 + ₹1,980 = ₹3,960
Here, Total CP of two sarees > Total SP of two sarees
Loss = Total CP of two sarees − Total SP of two sarees = ₹4,000 − ₹3,960 = ₹40
∴ Loss% in the whole transaction$=\frac{\mathrm{Loss}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{sarees}}\times 100\%=\frac{40}{4000}\times 100\%=1\%$

Answer:

SP of first fan = ₹1,140
Gain = 14%
Let the CP of first fan be ₹x.
CP = SP − Gain
$$\begin{gathered} \Rightarrow x=1140-\frac{14}{100}x \\ \Rightarrow x+\frac{14}{100}x=1140 \\ \Rightarrow \frac{114}{100}x=1140 \\ \Rightarrow x=1000 \end{gathered}$$
∴ CP of first fan = ₹1,000
SP of second fan = ₹1,140
Loss = 5%
Let the CP of second fan be ₹y.
CP = Loss + SP
$$\begin{gathered} \Rightarrow y=\frac{5}{100}y+1140 \\ \Rightarrow y-\frac{5}{100}y=1140 \\ \Rightarrow \frac{95}{100}y=1140 \\ \Rightarrow y=1200 \end{gathered}$$
∴ CP of second fan = ₹1,200
Total CP of two fans = CP of first fan + CP of second fan = ₹1,000 + ₹1,200 = ₹2,200
Total SP of two fans = SP of first fan + SP of second fan = ₹1,140 + ₹1,140 = ₹2,280
Here, Total SP of two fans > Total CP of two fans
Gain = Total SP of two fans − Total CP of two fans = ₹2,280 − ₹2,200 = ₹80
∴ Gain% on whole transaction$=\frac{\mathrm{Gain}}{\mathrm{Total} \mathrm{CP} \mathrm{of} \mathrm{two} \mathrm{fans}}\times 100\%=\frac{80}{2200}\times 100\%=3.64\%$

Answer:

Let the CP of the watch for Vinod be ₹x.
SP = Gain + CP
$$\begin{gathered} =12\% \mathrm{of} \mathrm{CP}+x \\ =\frac{12}{100}x+x \\ =₹\frac{112}{100}x \end{gathered}$$
Now,
SP of the water for Vinod will be the CP of the watch for Arun.
SP of the watch for Arun
= CP − Loss
$$\begin{gathered} =\frac{112}{100}x-5\% \mathrm{of} \frac{112}{100}x \\ =\frac{112}{100}x-\frac{5}{100}\left(\frac{112}{100}x\right) \\ =\frac{112}{100}x\left(1-\frac{5}{100}\right) \\ =₹\frac{112}{100}x\left(\frac{95}{100}\right) \end{gathered}$$
SP of the watch for Arun will be the CP of the watch for Manoj.
But, CP of the watch for Manoj = ₹3,990
So,
$\frac{112}{100}x\left(\frac{95}{100}\right)=3990$
$\Rightarrow x=\frac{3990\times 100\times 100}{112\times 95}=3750$
Thus, Vinod paid ₹3,750 for the watch.

Answer:

CP of the plot of land = ₹4,80,000
CP of $\frac{2}{5}$th of the land = $\frac{2}{5}\times 480000=₹1,92,000$
Loss on $\frac{2}{5}$th of the land = 6%
SP of $\frac{2}{5}$th of the land = CP − Loss
$$\begin{gathered} =192000-\frac{6}{100}\times 192000 \\ =₹1,80,480 \end{gathered}$$
CP of $\frac{3}{5}$th of the land = 480000 − 192000 = ₹2,88,000
Total gain% = 10%
Total gain = $\frac{10}{100}\times 480000=₹48,000$
Total SP = CP + Gain = ₹4,80,000 + ₹48,000 = ₹5,28,000
SP of $\frac{3}{5}$th of the land = ₹5,28,000 − ₹1,80,480 = ₹3,47,520
Gain on $\frac{3}{5}$th of the land = SP of $\frac{3}{5}$th land − CP of $\frac{3}{5}$th land
= ₹3,47,520 − ₹2,88,000
= ₹59,520
Gain% on seling the remaining part of the plot = $\frac{\mathrm{Gain}}{\mathrm{CP} \mathrm{of} {\displaystyle \frac{3}{5}}\mathrm{th} \mathrm{land}}\times 100\%=\frac{59520}{288000}\times 100\%=20\frac{2}{3}\%$

Answer:

CP of sugar = Rs 4500
Profit on one-third of the sugar = 10%

CP of one-third of the sugar = Rs $\frac{4500}{3}=\mathrm{Rs}. 1500$

 $$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{one}-\mathrm{third} \mathrm{of} \mathrm{the} \mathrm{sugar} =\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{110}{100}\times 1500 \\ =\mathrm{Rs} 1650 \end{gathered}$$

Now, profit= Rs (1650 − 1500) = Rs 150

At a profit of 12%, we have:
$$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{sugar} =\frac{100+\mathrm{gain}\%}{100}\times \mathrm{CP} \\ =\mathrm{Rs} \frac{112}{100}\times 4500 \\ =\mathrm{Rs} 5040 \end{gathered}$$

∴ Gain= Rs (5040 − 4500) = Rs 5400

Profit on the remaining amount of sugar = Rs (540 − 150) = Rs 390
CP of the remaining sugar = Rs (4500 − 1500) = Rs 3000

 $$\begin{gathered} \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{390}{3000}\times 100\right)\% \\ =13\% \end{gathered}$$

Therefore, the profit on the remaining amount of sugar is 13%.

Answer:

Marked price = $\mathrm{Rs} 4650$ and discount = 18%
Discount = 18% of marked price
              $=18\% of Rs 4650$
             $$\begin{gathered} =Rs \left(4650\times \frac{18}{100}\right) \\ =Rs 837 \end{gathered}$$
Selling price = marked price − discount
                     $$\begin{gathered} =\mathrm{Rs} (4650 - 837) \\ =\mathrm{Rs} 3813 \end{gathered}$$

Therefore, the selling price of the cooler is $\mathrm{Rs} 3813$.

Answer:

Marked Price = Rs 960
Selling Price = Rs 816
Discount = MP − SP
                = Rs (960 − 816)
                  = Rs 144
$\mathrm{Rate} \mathrm{of} discount=144\times \frac{100}{960}=15\%$

Therefore, the discount on the sweater is 15%.

Answer:

SP of the shirt = ₹1,092
Discount = ₹208
MP = SP + Discount = ₹1,092 + ₹208 = ₹1,300
∴ Rate of discount = $\frac{\mathrm{Discount}}{\mathrm{MP}}\times 100\%=\frac{208}{1300}\times 100\%=16\%$

Answer:

Selling Price = Rs 216.20
Rate of discount = 8%
Marked Price = ?
SP = MP − discount
Let the MP be Rs $x$.

$$\begin{gathered} \mathrm{Now}, x-\frac{8}{100}\times x=216.20 \\ \Rightarrow \frac{92x}{100}=216.20 \\ \Rightarrow 92x=21620 \\ \Rightarrow x=\frac{21620}{92} \\ \Rightarrow x=235 \end{gathered}$$

∴ Marked price = $Rs 235$

Answer:

Cost price = Rs 528
Rate of discount = 12%
Marked price = ?
SP= MP − discount
Let the MP be Rs $x$.
$$\begin{gathered} \mathrm{Now}, \frac{x-12}{100\times x}=528 \\ \Rightarrow \frac{88x}{100}=528 \\ \Rightarrow 88x=52800 \\ \Rightarrow x=\frac{52800}{88} \\ \Rightarrow x=\mathrm{Rs} 600 \end{gathered}$$

Therefore, the marked price of tea set is Rs 600.

Answer:

Let Rs 100 be the CP.
Then, marked price = $Rs 135$
Discount = 20% of MP
                $$\begin{gathered} =\frac{20}{100}\times 135 \\ =27 \end{gathered}$$
Selling price = marked price − discount
                     = 135 − 27
                     = Rs 108
Now, gain = SP − CP
                  =108 − 100
                   =Rs 8

$\therefore \mathrm{Gain} \mathrm{percentage}=\frac{\mathrm{gain}}{\mathrm{CP}}\times 100$

                            = $$\begin{gathered} \frac{8}{100}\times 100 \\ = 8\% \end{gathered}$$

Answer:

Let Rs 100 be the CP.
Then, marked price = $Rs 140$
Discount = 30% of MP
                $$\begin{gathered} =\frac{30}{100}\times 140 \\ =42 \end{gathered}$$
Selling Price = marked price − discount
                      = 140 − 42
                      = Rs 98
Now, loss = CP − SP
                 = 100 − 98
                 = Rs 2
$$\begin{gathered} \therefore Loss percentage=\frac{Loss\times 100}{CP} \\ =\frac{2\times 100}{100} \\ =2\% \end{gathered}$$

Therefore, the shopkeeper had a loss of 2%.

Answer:

Cost price of the fan = $Rs 1080$
Gain percentage = 25%
$$\begin{gathered} \therefore \mathrm{Selling} \mathrm{price} = \left\{\frac{(100 +\hspace{0.17em}\mathrm{gain} \%)}{100}\times \mathrm{CP}\right\} \\ =\left\{\frac{100+25}{100}\times 1080\right\} \\ =\frac{125}{100}\times 1080 \\ =\mathrm{Rs} 1350 \end{gathered}$$

Let the marked price be Rs $x$.
Discount = 25% of $Rs x$

             $=\frac{25x}{100}$

SP = MP − discount
⇒ 1350 = $X$ − $\frac{25X}{100}$

$$\begin{gathered} \Rightarrow 1350=\frac{100x-25x}{100} \\ \Rightarrow 135000=75x\Rightarrow x=\frac{13500}{75}\Rightarrow x=1800 \end{gathered}$$

Therefore, the marked price of the fan is $Rs 1800$.

Answer:

Cost price of the refrigerator = $Rs 11515$
Gain percentage = 20%.
$$\begin{gathered} \therefore \mathrm{Selling} \mathrm{price\; =}\left\{\frac{(100 +\hspace{0.17em}\mathrm{gain} \%)}{100}\times C.P\right\} \\ =\left\{\frac{100+20}{100}\times 11515\right\} \\ =\frac{120}{100}\times 11515 \\ =\mathrm{Rs} 13818 \end{gathered}$$

Let the marked price be Rs $x$.
Discount = 16% of $Rs x$
                $=\frac{16x}{100}$
S.P = MP − Discount
⇒ 13818 = x − $\frac{16x}{100}$

$$\begin{gathered} \Rightarrow 13818=\frac{100x-16x}{100} \\ \Rightarrow 1381800=84x\Rightarrow x=\frac{1381800}{84}\Rightarrow x=16450 \end{gathered}$$

​Therefore, the marked price of the refrigerator is $Rs 16450$.

Answer:

The cost price of the ring is $Rs 1190$.
Gain percentage = 20%.
$$\begin{gathered} \therefore \mathrm{Selling} \mathrm{price\; =}\left\{\frac{(100 +\hspace{0.17em}gain \%)}{100}\times C.P\right\} \\ =\left\{\frac{100+20}{100}\times 1190\right\} \\ =\frac{120}{100}\times 1190 \\ =\mathrm{Rs} 1428 \end{gathered}$$

Let the marked price be $x$.
Discount = 16% of $Rs x$
               $=\frac{16x}{100}$
SP = MP − Discount

$$\begin{gathered} \Rightarrow 1428=x-\frac{16x}{100} \\ \Rightarrow 1428=\frac{100x-16x}{100} \\ \Rightarrow 142800=84x \\ \Rightarrow \frac{142800}{84}=x \\ \Rightarrow x=1700 \end{gathered}$$

​Therefore, the marked price of the ring is $\mathrm{Rs} 1700$.

Answer:

Let $Rs 100$ be the cost price.
Gain required = 17%
∴ Selling price = $Rs 117$
Let the marked price be $Rs x$.
Then, discount = 10% of x
                        $$\begin{gathered} =\frac{10}{100}\times x \\ =\frac{x}{10} \end{gathered}$$
Selling Price = MP − discount
$$\begin{gathered} \Rightarrow 117=x-\frac{x}{10} \\ \Rightarrow 117=\frac{9x}{10} \end{gathered}$$

$$\begin{gathered} \Rightarrow 9x=1170 \\ \Rightarrow x=\frac{1170}{9} \\ \Rightarrow x=130 \end{gathered}$$

∴ Marked price = $Rs 130$

Hence, the marked price is 30% above the cost price.

Answer:

Let $Rs 100$ be the cost price.
Gain required = 8%
Therefore, the selling price is $Rs 108$.
Let $Rs x$ be the marked price.
Then, discount = 10% of x
                      $$\begin{gathered} =\frac{10}{100}\times x \\ =\frac{x}{10} \end{gathered}$$
Selling Price = MP − discount
$$\begin{gathered} \Rightarrow 117=x-\frac{x}{10} \\ \Rightarrow 117=\frac{9x}{10} \end{gathered}$$

$$\begin{gathered} \Rightarrow 9x=1080 \\ \Rightarrow x=\frac{1080}{9} \\ \Rightarrow x=120 \end{gathered}$$

∴ Marked price = $Rs 120$

Hence, the marked price is 20% above the cost price.

Answer:

Marked price of the TV = Rs 18500
First discount = 20%

$$\begin{gathered} \mathrm{Now}, 20\% of 18500 \\ =\frac{20}{100}\times 18500 \\ =\mathrm{Rs} 3700 \end{gathered}$$

Price after the first discount = Rs (18500 − 3700)= Rs 14800
Second discount = 5% of 14800
                                $$\begin{gathered} =\frac{5}{100}\times 14800 \\ =740 \end{gathered}$$
Price after the second discount = (14800 − 740)
                                                   = Rs 14060
The TV is available for $\mathrm{Rs} 14060.$

Answer:

​Let the marked price of the article be Rs 100.
First discount = 20%
Price after the first discount = (100 − 20) = Rs 80
Second discount = 5% of 80
                            $$\begin{gathered} =\frac{5}{100}\times 80 \\ =\mathrm{Rs} 4 \end{gathered}$$
Price after the second discount = (80 − 4) = Rs 76
Net selling price = Rs 76
∴ Single discount equivalent to the given successive discounts = (100 − 76)% = 24%

Answer:

List price of the refrigerator = Rs 14650
Sales tax = 6% of ​Rs 14650
            $$\begin{gathered} =\mathrm{Rs} \left(14650\times \frac{6}{100}\right) \\ =\mathrm{Rs} 879 \end{gathered}$$

Bill amount$=\mathrm{Rs} \left(14650+879\right)$
                 $=\mathrm{Rs} 15529$
Hence, the cost of the refrigerator is Rs 15,529.

Answer:

(i)
 $\mathrm{Cost} \mathrm{of} \mathrm{the} \mathrm{tie} =\mathrm{Rs}. 250$
$\mathrm{Sales} \mathrm{tax}=6\% \mathrm{of} \mathrm{Rs} 250$
             $$\begin{gathered} =\mathrm{Rs}.\left(250\times \frac{6}{100}\right) \\ =\mathrm{Rs}.15 \end{gathered}$$
$\mathrm{Hence}, \mathrm{bill} \mathrm{amount} = \mathrm{Rs} \left(250+15\right)$
                          $=\mathrm{Rs}.265$

(ii) $\mathrm{Cost} \mathrm{of} \mathrm{the} \mathrm{medicines}=\mathrm{Rs}. 625$
$\mathrm{Sales} \mathrm{tax}=4\% \mathrm{of} \mathrm{Rs}.625$
             $$\begin{gathered} =\mathrm{Rs}.\left(625\times \frac{4}{100}\right) \\ =\mathrm{Rs}.25 \end{gathered}$$
$\mathrm{Hence}, \mathrm{bill} \mathrm{amount} = \mathrm{Rs} \left(625+25\right)$
                           $=\mathrm{Rs} 650$

$$\begin{gathered} \left(\mathrm{iii}\right) \mathrm{Cost} \mathrm{of} \mathrm{the} \mathrm{cosmetics}=\mathrm{Rs} 430 \\ \mathrm{Sales} \mathrm{tax} =10\% \mathrm{of} \mathrm{Rs} 430 \end{gathered}$$
                      $$\begin{gathered} =\mathrm{Rs} \left(430\times \frac{10}{100}\right) \\ =\mathrm{Rs} 43 \end{gathered}$$

$\mathrm{Hence}, \mathrm{bill} \mathrm{amount}=\mathrm{Rs} \left(430+43\right)$
                          $=\mathrm{Rs}.473$

$$\begin{gathered} \left(\mathrm{iv}\right) \mathrm{Cost} \mathrm{of} \mathrm{clothes}=\mathrm{Rs} 1175 \\ \mathrm{Sales} \mathrm{tax}=8\% \mathrm{of} \mathrm{Rs} 1175 \end{gathered}$$
                 $$\begin{gathered} =\mathrm{Rs} \left(1175\times \frac{8}{100}\right) \\ =\mathrm{Rs} 94 \end{gathered}$$
$\mathrm{Hence}, \mathrm{bill} \mathrm{amount}=\mathrm{Rs} \left(1175+94\right)$
                          $=\mathrm{Rs}.1269$
$\mathrm{Therefore}, \mathrm{total} \mathrm{amount} \mathrm{to} \mathrm{be} \mathrm{paid} \mathrm{by} \mathrm{Reena} = \mathrm{bill} \mathrm{amount} \mathrm{of} \mathrm{all} \mathrm{the} \mathrm{four} \mathrm{items}$
                                                              $$\begin{gathered} =\mathrm{Rs} \left(265+650+473+1269\right) \\ =\mathrm{Rs} 2657 \end{gathered}$$

Answer:

Let the original price of the watch be Rs x.
VAT = 10% of Rs x
       $$\begin{gathered} =\mathrm{Rs} \left(x\times \frac{10}{100}\right) \\ =\mathrm{Rs} \frac{10x}{100} \end{gathered}$$
∴ Price including VAT = $\mathrm{Rs} \left(x+\frac{x}{10}\right)$
                                     $=\mathrm{Rs} \frac{11x}{10}$
Now, $\frac{11x}{10}=1980$
      $$\begin{gathered} \Rightarrow x=\left(1980\times \frac{10}{11}\right) \\ =1800 \end{gathered}$$

Hence, the original price of the watch is Rs 1,800.

Answer:

​​Let the original price of the shirt be Rs x.
VAT = 7% of Rs x
       $$\begin{gathered} =\mathrm{Rs}.\left(x\times \frac{7}{100}\right) \\ =\mathrm{Rs}.\frac{7x}{100} \end{gathered}$$
∴ Price including VAT = $\mathrm{Rs}.\left(x+\frac{7x}{100}\right)$
                                     $=\mathrm{Rs}.\frac{107x}{100}$
Now, $\frac{107x}{100}=1337.50$
         $$\begin{gathered} \Rightarrow x=\mathrm{Rs} \left(1337.50\times \frac{100}{107}\right) \\ =\mathrm{Rs} 1250 \end{gathered}$$

Hence, the original price of the shirt is Rs 1,250.

Answer:

Let the price of 10 g of gold be Rs x.
$$\begin{gathered} \mathrm{VAT}=1\% \mathrm{of} \mathrm{Rs} x \\ =\mathrm{Rs} \left(x\times \frac{1}{100}\right) \\ =\mathrm{Rs} \frac{x}{100} \end{gathered}$$
∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{x}{100}\right)$
                                     $=\mathrm{Rs} \frac{101x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{101x}{100}=15756 \\ \Rightarrow x= \mathrm{Rs} \left(15756\times \frac{100}{101}\right) \\ = \mathrm{Rs} 15600 \end{gathered}$$

Hence, the price of 10 g of gold is Rs 15,600.

Answer:

Let the original price of the computer be Rs x.
$$\begin{gathered} \mathrm{VAT}=4\% \mathrm{of} \mathrm{Rs}.x \\ =\mathrm{Rs}.\left(x\times \frac{4}{100}\right) \\ =\mathrm{Rs}.\frac{4x}{100} \end{gathered}$$
∴ Price including VAT$=\mathrm{Rs}.\left(x+\frac{4x}{100}\right)$
                                    $=\mathrm{Rs}.\frac{104x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{104x}{100}= 37960 \\ \Rightarrow x=\left(37960\times \frac{100}{104}\right) \\ = 36500 \end{gathered}$$

∴ The original price of the computer is Rs 36,500

Answer:

​Let the original cost of the spare parts be Rs x.
$$\begin{gathered} \mathrm{VAT}=12\% \mathrm{of} \mathrm{Rs}.x \\ =\mathrm{Rs}.\left(x\times \frac{12}{100}\right) \\ =\mathrm{Rs}.\frac{12x}{100} \end{gathered}$$
∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{12x}{100}\right)$
                                      $=\mathrm{Rs}.\frac{112x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{112x}{100}=20776 \\ \Rightarrow x=\left(20776\times \frac{100}{112}\right) \\ =18550 \end{gathered}$$

Hence, ​the original cost of the spare parts is Rs 18,550.

Answer:

​Let the list price of the TV set be Rs x.
$$\begin{gathered} \mathrm{VAT}=8\% \mathrm{of} \mathrm{Rs}.x \\ =\mathrm{Rs}.\left(x\times \frac{8}{100}\right) \\ =\mathrm{Rs}.\frac{8x}{100} \end{gathered}$$
∴ Price including VAT $=\mathrm{Rs}.\left(x+\frac{8x}{100}\right)$
                                     $=\mathrm{Rs}.\frac{108x}{100}$
$$\begin{gathered} \mathrm{Now}, \frac{108x}{100}=27000 \\ \Rightarrow x=\left(27000\times \frac{100}{108}\right) \\ =25000 \end{gathered}$$

Hence, the list price of the TV set is Rs 25,000.

Answer:

Let the rate of VAT be x%. Then, we have:

$$\begin{gathered} 840+x\% of 840=882 \\ \Rightarrow \left(\frac{x}{100}\times 840\right)=882-840 \\ \Rightarrow \frac{84x}{10}=42 \\ \Rightarrow x=\left(42\times \frac{10}{84}\right) \\ =5 \end{gathered}$$

∴ The rate of VAT is 5%.

Answer:

Let the rate of VAT be x%. Then, we have:

   $$\begin{gathered} 18500+x\% of 18500=19980 \\ \Rightarrow \left(\frac{x}{100}\times 18500\right)=19980-18500 \\ \Rightarrow 185x=1480 \\ \Rightarrow x=\frac{1480}{185} \\ =8 \end{gathered}$$

∴ The rate of VAT is 8%.

Answer:

Let the rate of VAT be x%. Then, we have:

$$\begin{gathered} 34000+x\% of 34000=382500 \\ \Rightarrow \left(\frac{x}{100}\times 340000\right)=382500-340000 \\ \Rightarrow 3400x=42500 \\ \Rightarrow x=\frac{42500}{3400} \\ =12.5 \end{gathered}$$

∴ The rate of VAT is 12.5%.

Answer:

$$\begin{gathered} \left(\mathrm{c}\right) 33\frac{1}{3}\% \\ \mathrm{SP}=\mathrm{Rs} 100 \\ \mathrm{Gain}=\mathrm{Rs} \left(100-75\right) \\ =\mathrm{Rs} 25 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{25}{75}\times 100\right)\% \\ =33\frac{1}{3}\% \end{gathered}$$

Answer:

   $$\begin{gathered} \left(\mathrm{b}\right)12\frac{1}{2}\% \\ \mathrm{CP}=\mathrm{Rs} 120 \\ \mathrm{SP}=\mathrm{Rs} 105 \\ \mathrm{Loss}=\mathrm{Rs} \left(120-105\right) \\ =\mathrm{Rs} 15 \\ \therefore \mathrm{Loss} \mathrm{percentage}=\left(\frac{\mathrm{loss}}{\mathrm{CP}}\times 100\right) \\ =\left(\frac{15}{120}\times 100\right) \\ =12\frac{1}{2}\% \end{gathered}$$

Answer:

 $$\begin{gathered} \left(\mathrm{b}\right) 25\% \\ \mathrm{CP}=\mathrm{SP}-\mathrm{Gain} \\ =\mathrm{Rs} \left(100-20\right) \\ =\mathrm{Rs} 80 \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{20}{80}\times 100\right)\% \\ =25\% \end{gathered}$$

Answer:

 $$\begin{gathered} \left(\mathrm{d}\right) \mathrm{Rs} 72 \\ \mathrm{SP}=\mathrm{Rs} 48 \\ \mathrm{Loss}=20\% \\ \mathrm{Now}, \mathrm{CP}=\frac{100}{100-\mathrm{loss}\%}\times \mathrm{SP} \\ =\mathrm{Rs} \left(\frac{100}{\left(100-\mathrm{loss}\%\right)}\times \mathrm{SP}\right) \\ =\mathrm{Rs} \left(\frac{100}{\left(100-20\right)}\times 48\right) \\ =\mathrm{Rs} \left(\frac{100}{80}\times 48\right) \\ =\mathrm{Rs} 60 \end{gathered}$$

$\therefore \mathrm{Desired} \mathrm{SP}=\left\{\frac{\left(100+\mathrm{gain}\%\right)}{100}\times \mathrm{CP}\right\}$

                   $$\begin{gathered} =\left\{\frac{\left(100+20\right)}{100}\times 60\right\} \\ =\mathrm{Rs} \left(\frac{12}{10}\times 60\right) \\ =\mathrm{Rs} 72 \end{gathered}$$

Answer:

(c) 120%

Let the SP and CP of the article be Rs x and y, respectively.
Gain percentage = 10%
⇒ 10 = $\frac{x-y}{y}\times 100$
⇒ y = $\frac{10x}{11}$

According to the question, we have:

SP = Rs 2x
∴ Gain percentage = $\frac{\mathrm{gain}}{\mathrm{CP}}\times 100$

                                $$\begin{gathered} =\frac{2x-{\displaystyle \frac{10x}{11}}}{{\displaystyle \frac{10x}{11}}}\times 100 \\ =\frac{12}{10}\times 100 \\ =120\% \end{gathered}$$

Answer:

(d) 125%
$$\begin{gathered} \mathrm{Cost} \mathrm{price} \mathrm{of} \mathrm{a} \mathrm{banana}=\mathrm{Rs} \frac{2}{3} \\ \mathrm{Selling} \mathrm{price} \mathrm{of} \mathrm{a} \mathrm{banana}=\mathrm{Rs} \frac{3}{2} \\ \mathrm{Now}, \mathrm{profit} = \mathrm{Rs} (\frac{3}{2}-\frac{2}{3})=\mathrm{Rs} \frac{9-4}{6}=\mathrm{Rs} \frac{5}{6} \\ \therefore \mathrm{Gain} \mathrm{percentage} = \frac{\mathrm{gain}}{\mathrm{CP}}\times 100 \\ =\frac{\left({\displaystyle \frac{5}{6}}\right)}{\left({\displaystyle \frac{2}{3}}\right)}\times 100 \\ =\frac{5}{6}\times \frac{3}{2}\times 100 \\ = \frac{5}{4}\times 100 \\ =5\times 25 \\ =125\% \end{gathered}$$

Answer:

 (c) 20%    

$$\begin{gathered} \mathrm{Let} \mathrm{Rs} x \mathrm{be} \mathrm{the} \mathrm{SP} \mathrm{of} \mathrm{each} \mathrm{pen}. \\ \mathrm{SP} \mathrm{of} 10 \mathrm{pens}=\mathrm{CP} \mathrm{of} 12 \mathrm{pens}=\mathrm{Rs} 12x \\ \mathrm{CP} \mathrm{of} 10 \mathrm{pens}=\mathrm{Rs} 10x \\ \mathrm{Now}, \mathrm{gain}=\mathrm{Rs} \left(12\mathrm{x}-10\mathrm{x}\right) \\ =\mathrm{Rs} 2x \\ \therefore \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \end{gathered}$$
                            $$\begin{gathered} =\left(\frac{2x}{10x}\times 100\right)\% \\ =20\% \end{gathered}$$

Answer:

    (b) 25%

  $$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{SP} \mathrm{of} 100 \mathrm{pens} \mathrm{be} \mathrm{Rs} x. \\ \mathrm{SP} \mathrm{of} 1 \mathrm{pen}=\mathrm{Rs} \frac{x}{100} \\ \mathrm{Profit}=\mathrm{Rs} \frac{20x}{100} \\ =\mathrm{Rs} \frac{x}{5} \\ \mathrm{Now}, \mathrm{CP}=x-\frac{x}{5} \\ =\frac{4x}{5} \\ \therefore \mathrm{Gain} \mathrm{percentage}=\frac{{\displaystyle \frac{x}{5}}}{{\displaystyle \frac{4x}{5}}}\times 100 \\ =25\% \end{gathered}$$

Answer:

(d) 150%     

 ​ $$\begin{gathered} \mathrm{L}.\mathrm{C}.\mathrm{M} \mathrm{of} 5 \mathrm{and} 2=\left(5\times 1\times 2\right)=10 \\ \mathrm{Let} 10 \mathrm{be} \mathrm{the} \mathrm{number} \mathrm{of} \mathrm{toffees} \mathrm{bought}. \\ \mathrm{CP} \mathrm{of} 5 \mathrm{toffees}=\mathrm{Rs} 1 \\ \mathrm{CP} \mathrm{of} 1 \mathrm{toffee}=\mathrm{Rs} \left(\frac{1}{5}\right) \\ \therefore \mathrm{CP} \mathrm{of} 10 \mathrm{toffees}=\mathrm{Rs} \left(\frac{1}{5}\times 10\right) \\ =\mathrm{Rs} 2 \\ \mathrm{SP} \mathrm{of} 2 \mathrm{toffees}= \mathrm{Rs} 1 \\ \mathrm{SP} \mathrm{of} 1 \mathrm{toffee}=\mathrm{Rs} \left(\frac{1}{2}\right) \\ \therefore \mathrm{SP} \mathrm{of} 10 \mathrm{toffees}=\mathrm{Rs} \left(\frac{1}{2}\times 10\right) \end{gathered}$$
                                $=Rs.5$
  $$\begin{gathered} \mathrm{Gain}=\mathrm{Rs} \left(5-2\right) \\ =\mathrm{Rs} 3 \\ \mathrm{Gain} \mathrm{percentage}=\left(\frac{\mathrm{gain}}{\mathrm{CP}}\times 100\right)\% \\ =\left(\frac{3}{2}\times 100\right)\% \\ =150\% \end{gathered}$$