Rd Sharma 2020 2021 for Class 7 Maths Chapter 12 - Profit And Loss

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Page No 12.10:

Question 10:

A vendor bought lemons at 6 for a rupee and sold them at 4 for a rupee. His gain % is

(a) 50%
(b) 40%
(c) $33 \frac{1}{3} %$
(d) $16 \frac{2}{3} %$

Answer:

Let the total lemons be 12.

CP of 6 lemons = ₹1
then, CP of 12 lemons = ₹2

Also, SP of 4 lemons = ₹1
then, SP of 12 lemons = ₹3

Therefore, SP is more than CP.

So, Gain = SP − CP
= ₹3 − ₹2
= ₹1

$Gain percent = \frac{Gain}{CP} \times 100 = \frac{1}{2} \times 100 = 50 %$

Hence, the correct option is (a).

Page No 12.10:

Question 11:

On selling a pen for ₹48, a shopkeeper loses 20%. In order to gain 20% what should be the selling price?

(a) ₹52
(b) ₹56
(c) ₹68
(d) ₹72

Answer:

Let the CP of a pen be x.

SP of a pen = ₹48
Loss = 20%

Therefore, CP is more than SP.

Now, Loss = CP − SP and Loss = Loss percent × CP

$Thus, CP - SP = Loss percent \times CP \Rightarrow x - 48 = \frac{20}{100} \times x \Rightarrow 100 x - 4800 = 20 x \Rightarrow 100 x - 20 x = 4800 \Rightarrow 80 x = 4800 \Rightarrow x = \frac{4800}{80} \Rightarrow x = 60$

Therefore, CP of the pen = ₹60

Now, in order to gain 20%, let the new SP be y.

Gain = Gain percent × CP
= $\frac{20}{100} \times 60$
= ₹12

SP = CP + Gain
= ₹60 + ₹12
= ₹72

Hence, the correct option is (d).

Page No 12.10:

Question 12:

On selling an article for ₹144 a man loses 10%. At what price should he sell it to gain 10% ?

(a) ₹158.40
(b) ₹172.80
(c) ₹176
(d) ₹192

Answer:

Let the CP of an article be x.

SP of the article = ₹144
Loss = 10%

Therefore, CP is more than SP.

Now, Loss = CP − SP and Loss = Loss percent × CP

$Thus, CP - SP = Loss percent \times CP \Rightarrow x - 144 = \frac{10}{100} \times x \Rightarrow x - 144 = \frac{1}{10} \times x \Rightarrow 10 x - 1440 = x \Rightarrow 10 x - x = 1440 \Rightarrow 9 x = 1440 \Rightarrow x = \frac{1440}{9} \Rightarrow x = 160$

Therefore, CP of the article = ₹160

Now, in order to gain 10%, let the new SP be y.

Gain = Gain percent × CP
= $\frac{10}{100} \times 160$
= ₹16

SP = CP + Gain
= ₹160 + ₹16
= ₹176

Hence, the correct option is (c).

Page No 12.10:

Question 13:

If the cost price of 15 pens is equal to the selling price of 20 pens, then the loss percent is

(a) 25%
(b) 20%
(c) 15%
(d) 18%

Answer:

Let the cost price of one pen be ₹1.
Then, CP of 20 pens = ₹20
and SP of 20 pens = ₹15 (∵ SP of 20 pens = CP of 15 pens)

Therfore, CP is more than SP.

So, Loss = CP − SP
= ₹20 − ₹15
= ₹5

$Loss percent = \frac{Loss}{CP} \times 100 = \frac{5}{20} \times 100 = 25 %$

Hence, the correct option is (a).

Page No 12.10:

Question 14:

If the cost price of 6 pencils is equal to the selling price of 5 pencils, then the gain percent is

(a) 10%
(b) 20%
(c) 15%
(d) 25%

Answer:

Let the cost price of one pencil be ₹1.
Then, CP of 5 pencils = ₹5
and SP of 5 pencils = ₹6 (∵ SP of 5 pencils = CP of 6 pencils)

Therfore, SP is more than CP.

So, Profit = SP − CP
= ₹6 − ₹5
= ₹1

$Gain percent = \frac{Profit}{CP} \times 100 = \frac{1}{5} \times 100 = 20 %$

Hence, the correct option is (b).

Page No 12.8:

Question 1:

Given the following values, find the unknown values:
(i) C.P. = Rs 1200,      S.P. = Rs 1350,     Profit/Loss = ?
(ii) C.P. = Rs 980,       S.P. = Rs 940,      Profit/Loss = ?
(iii) C.P. = Rs 720,      S.P. = ?,                Profit = Rs 55.50
(iv) C.P. = ?                 S.P. = Rs 1254,     Loss = Rs 32

Answer:

(i) CP = Rs.. 1200, SP = Rs.. 1350
     CP < SP. So, profit.
Profit = Rs. (1350 - 1200) = Rs. 150

(ii) CP = Rs. 980, SP = Rs. 940
     CP > SP. So, loss.
   Loss = Rs. (980 - 940) = Rs. 40

(iii) CP = Rs. 720, SP = ?, profit = Rs. 55.50
   Profit = SP - CP
⇒   Rs. 55.50 = SP - Rs. 720
⇒   SP = Rs. (55.50 + 720) = Rs. 775.50

(iv) CP = ?, SP = Rs. 1254, loss = Rs. 32
⇒ Loss = CP - SP
⇒ Rs. 32 = CP - Rs. 1254
⇒ CP = Rs. (1254 + 32) = Rs. 1286

Page No 12.8:

Question 2:

Fill in the blanks in each of the following:
(i) C.P. = Rs 1265,      S.P. = Rs 1253,    Loss = Rs .....
(ii) C.P. = Rs ....,         S.P. = Rs 450,      Profit = Rs 150
(iii) C.P. = Rs 3355,    S.P. = Rs 7355,    .... = Rs ....
(iv) C.P. = Rs ....,        S.P. = Rs 2390,    Loss = Rs 5.50

Answer:

(i) CP = Rs. 1265, SP = Rs. 1253
Loss = CP - SP = Rs. (1265 - 1253) = Rs. 12

(ii) CP = ?, SP = Rs. 450, profit = Rs. 150
Profit = SP - CP
⇒ Rs. 150 = Rs. 450 - CP
⇒ CP = Rs. (450 - 150) = Rs. 300

(iii) CP = Rs. 3355, SP = Rs. 7355,
Here SP > CP, so profit.
Profit = SP - CP
⇒ Profit = Rs. (7355 - 3355) = Rs. 4000

(iv) CP = ?, SP = Rs. 2390, loss = Rs. 5.50
Loss = CP - SP
⇒ Rs. 5.50 = CP - Rs. 2390
⇒ CP = Rs. (5.50 + 2390) = Rs. 2395.50

Page No 12.8:

Question 3:

Calculate the profit or loss and profit or loss per cent in each of the following cases:
(i) C.P. = Rs 4560, S.P. = Rs 5000
(ii) C.P. = Rs 2600, S.P. = Rs 2470
(iii) C.P. = Rs 332, S.P. = Rs 350
(iv) C.P. = Rs 1500, S.P. = Rs 1500

Answer:

(i) CP = Rs. 4560, SP = Rs. 5000
    Here, SP > CP. So, profit.
Profit = SP - CP = Rs. (5000 - 4560)= Rs. 440
Profit % = {(Profit/CP) × 100}% = {(440/4560) × 100}% = {0.0965 × 100}% = 9.65%

(ii) CP = Rs. 2600, SP = Rs. 2470. Here, CP > SP. So, loss.
Loss = CP - SP = Rs. (2600 - 2470) = Rs. 130
Profit% = {(Profit/CP) × 100}% = {(130/2600) × 100}% = {0.05 × 100}% = 5%

(iii) CP = Rs. 332, SP= Rs. 350. Here, SP > CP. So, profit.
Profit = SP - CP = Rs. (350 - 332) = Rs. 18
Profit% = {(Profit/CP) × 100}% = {(18/332) × 100}% = {0.054  × 100}% = 5.4%

(iv) CP = Rs. 1500, SP = Rs. 1500
SP = CP. So, neither profit nor loss.

Page No 12.8:

Question 4:

Find the gain or loss per cent, when:
(i) C.P. = Rs 4000 and gain = Rs 40.
(ii) S.P. = Rs 1272 and loss = Rs 328
(iii) S.P. = Rs 1820 and gain = Rs 420.

Answer:

(i) CP = Rs. 4000, gain = Rs. 40
Gain % = {(Gain/CP) × 100}% = {(40/4000) × 100}% = (0.01 × 100)% = 1%

(ii) SP = Rs. 1272, loss = Rs. 328
      Loss = CP - SP
      Hence, CP = Loss+ SP = Rs. 328 + Rs. 1272 = Rs. 1600
Loss % = {(Loss/CP) × 100}% = {(328/1600) × 100% = 20.5%

(iii) SP = Rs. 1820, gain = Rs. 420
       Gain = SP - CP
       CP = 1820 - 420 = Rs. 1400
  Gain % = {(Gain/CP) × 100}% = {(420/1400) × 100% = 30%

Page No 12.8:

Question 5:

Find the gain or loss per cent, when:
(i) C.P. = Rs 2300, Overhead expenses = Rs 300 and gain = Rs 260.
(ii) C.P. = Rs 3500, Overhead expenses = Rs 150 and loss = Rs 146

Answer:

(i) CP = Rs. 2300, overhead expenses = Rs. 300, gain = Rs. 260
Gain % = {(Gain/(CP + overhead expenses)} × 100 = {260/(2300 + 300} × 100 = {260/2600} × 100 = 10%

(ii) CP = Rs. 3500, overhead expenses = Rs. 150, loss = Rs. 146

Loss % = {( Loss/(CP + overhead expenses)} × 100 = {146/(3500+ 150)} × 100
= {146/3650} × 100
= 14600/3650 = 4%

Page No 12.8:

Question 6:

A grain merchant sold 600 quintals of rice at a profit of 7%. If a quintal of rice cost him Rs 250 and his total overhead charges for transportation, etc. were Rs 1000 find his total profit and the selling price of 600 quintals of rice.

Answer:

Cost of 1 quintal of rice = Rs. 250
Cost of 600 quintals of rice = 600 × 250 = Rs. 150000
Overhead expenses = Rs. 1000
Total CP = Rs. (150000 + 1000) = Rs. 151000
Profit % = (Profit/CP) × 100
7 = (P/151000) × 100
P = 1510 × 7 = Rs. 10570
Profit = Rs. 10570
SP = CP + profit = Rs. (151000 + 10570) = Rs. 161570

Page No 12.8:

Question 7:

Naresh bought 4 dozen pencils at Rs 10.80 a dozen and sold them for 80 paise each. Find his gain or loss percent.

Answer:

Cost of 1 dozen pencils = Rs. 10.80
Cost of 4 dozen pencils = 4 × 10.80 = Rs. 43.2

Selling price of each pencil = 80 paise
Total number of pencils = 12 × 4 = 48
SP of 48 pencils = 48 × 80 paise = 3840 paise = Rs. 38.40

Here, SP < CP.
Loss = CP - SP = Rs. (43.2 - 38.4) = Rs. 4.8
Loss % = (Loss/CP) × 100 = (4.8/43.2) × 100 = 480/43.2 = 11.11%

Page No 12.8:

Question 8:

A vendor buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13. Find his gain per cent.

Answer:

CP of 1 dozen oranges = Rs. 26
CP of 1 orange = 26/12 = Rs. 2.16
CP of 5 oranges = 2.16 × 5 = Rs. 10.8

Now, SP of 5 oranges = Rs. 13

Gain = SP - CP = Rs. (13 - 10.8) = Rs. 2.2
Gain % = (Gain/CP) × 100 = (2.2/10.8) × 100 = 20.3%

Page No 12.8:

Question 9:

Mr Virmani purchased a house for Rs 365000 and spent Rs 135000 on its repairs. If he sold it for Rs 550000, find his gain percent.

Answer:

Amount Mr. Virmani paid to purchase the house = Rs. 365000
Amount he spent on repair = Rs. 135000
Total amount he spent on the house (CP) = Rs. (365000 + 135000) = Rs. 500000
SP of the house = Rs. 550000
Gain = SP - CP = Rs. (550000 - 500000) = Rs. 50000

Gain % = (Gain/CP) × 100 = (50000/500000) × 100 = 5000000/500000 = 10%

Page No 12.8:

Question 10:

Shikha purchased a wrist watch for Rs 840 and sold it to her friend Vidhi for Rs 910. Find her gain percent.

Answer:

The cost price of the wristwatch that Shikha purchased, CP = Rs. 840
The price at which she sold it, SP = Rs. 910
Gain = SP - CP
= (910 - 840) = Rs. 70

Gain % = (Gain/CP) × 100 = (70/840) × 100 = 7000/840 = 8.3%

Page No 12.8:

Question 11:

A business man makes a 10% profit by selling a toy costing him Rs 120. What is the selling price?

Answer:

CP = Rs. 12
Profit % = 10
We now that

SP = {(100 + profit %)/100} × CP
= {(100+ 10)/100} × 120
= {(110/100)} × 120 = 1.1 × 120 = Rs. 132

Page No 12.8:

Question 12:

Harish purchased 50 dozen bananas for Rs 135. Five dozen bananas could not be sold because they were rotten. At what price per dozen should Harish sell the remaining bananas so that he makes a profit of 20%?

Answer:

Cost price of 50 dozens bananas that Harish purchased, CP = Rs. 135

Bananas left after removing 5 dozen rotten bananas = 45 dozens

Effective CP of one dozen bananas = Rs. 135/45 = Rs. 3

Calculating the price at which Harish should sell each dozen bananas to make a profit of 20% (or 1/5), we get
Profit = Gain/CP = (SP - CP)/CP
$\frac{1}{5} = \frac{SP - 3}{3} SP = Rs . 3.60$

Harish should sell the bananas at Rs. 3.60 a dozen in order to make a profit of 20%.

Page No 12.8:

Question 13:

A woman bought 50 dozen eggs at Rs 6.40 a dozen. Out of these 20 eggs were found to be broken. She sold the remaining eggs at 55 paise per egg. Find her gain or loss percent.

Answer:

Cost of one dozen eggs = Rs. 6.40
Cost of 50 dozen eggs = 50 × 6.40 = Rs. 320

Total number of eggs = 50 × 12 = 600
Number of eggs left after removing the broken ones = 600 - 20 = 580

SP of 1 egg = 55 paise
So, SP of 580 eggs = 580 × 55 = 31900 paise = Rs. 31900/100 = Rs. 319

Loss = CP - SP = Rs. (320-319) = Re. 1
Loss % = (Loss/CP) × 100 = (1/320) × 100 = 0.31%

Page No 12.8:

Question 14:

Jyotsana bought 400 eggs at Rs 8.40 a dozen. At what price per hundred must she sell them so as to earn a profit of 15%?

Answer:

Cost of eggs per dozen = Rs. 8.40
Cost of 1 egg = 8.40/12 = Rs. 0.7
Cost of 400 eggs = 400 × 0.7 = Rs. 280
Calculating the price at which Jyotsana should sell the eggs to earn a profit of 15%, we get
15% of 280 + 280
= {(15/100) × 280} + 280 = {4200/100} + 280 = 42 + 280 = Rs. 322

So, Jyotsana must sell the 400 eggs for Rs. 322 in order to earn a profit of 15%.
Therefore, the SP per one hundred eggs = Rs. 322/4 = Rs. 80.50.

Page No 12.9:

Question 15:

A shopkeeper makes a profit of 15% by selling a book for Rs 230. What is the C.P. and the actual profit?

Answer:

Given that the SP of a book = Rs. 230
Profit % = 15
Since
CP = (SP × 100) ÷ (100 + profit %)
CP = (230× 100) ÷ (100 + 15)
CP = 23000 ÷ 115 = Rs. 200
Also,
Profit = SP - CP = Rs. (230 - 200) = Rs. 30
Actual profit = Rs. 30

Page No 12.9:

Question 16:

A bookseller sells all his books at a profit of 10%. If he buys a book from the distributor at Rs 200, how much does he sell it for?

Answer:

Given
Profit % = 10%
CP = Rs. 200
Since
SP = {(100 + profit %)/100} × CP
= {(100 + 10)/100} × 200
= {110/100} × 200
= Rs. 220

The bookseller sells the book for Rs. 220.

Page No 12.9:

Question 17:

A flowerist buys 100 dozen roses at Rs 2 a dozen. By the time the flowers are delivered, 20 dozen roses are multilated and are thrown away. At what price should he sell the rest if he needs to make a 20% profit on his purchase?

Answer:

Cost of 1 dozen roses = Rs. 2
Number of roses bought by the florist = 100 dozens
Thus, cost price of 100 dozen roses = 2 × 100 = Rs. 200

Roses left after discarding the mutilated ones = 80 dozens

Calculating the price at which the florist should sell the 80 dozen roses in order to make a profit of 20%, we have

$\frac{Profit %}{100} = \frac{SP - CP}{CP} \frac{20}{100} = \frac{SP - 200}{200} SP = Rs . 240$

Therefore, the SP of the roses should be Rs. 240/80 = Rs. 3 per dozen.

Page No 12.9:

Question 18:

By selling an article for Rs 240, a man makes a profit of 20%. What is his C.P.? What would his profit percent be if he sold the article for Rs 275?

Answer:

Let CP = Rs. x
SP = Rs. 240
Let profit be Rs. P.

Now, profit % = 20%
Since
Profit % = (Profit/CP) × 100
⇒ 20 = (P/x) × 100
⇒ P = 20x/100 = x/5

Profit = SP - CP = 240 - x
⇒ P = 240 - x
⇒ x/5 = 240 - x
⇒ 240 = x + x/5
⇒ 240 = 6x/5
⇒ x = 1200/6 = 200
So, CP = Rs. 200

New SP = Rs. 275 and CP = Rs. 200
Profit % = {(SP - CP)/CP} × 100 = {(275 - 200)/200} × 100 = (75/200) × 100
= 7500/200 = 37.5%

Page No 12.9:

Question 1:

If CP = ₹200 and SP = ₹250, then the profit or loss is equal to

(a) ₹50 loss
(b) ₹50 profit
(c) ₹25 profit
(d) ₹25 loss

Answer:

Since, SP is more than CP.

Therefore, profit = SP − CP
= ₹250 − ₹200
= ₹50

Hence, the correct option is (b).

Page No 12.9:

Question 2:

If CP = ₹120 and SP = ₹80, then profit or loss is equal to

(a) ₹40 loss
(b) ₹60 loss
(c) ₹40 profit
(d) ₹60 profit

Answer:

Since, CP is more than SP.

Therefore, loss = CP − SP
= ₹120 − ₹80
= ₹40

Hence, the correct option is (a).

Page No 12.9:

Question 3:

A trader purchased a bicycle for ₹2500 and sold at ₹2700. His profit percentage is

(a) 8%
(b) 10%
(c) 6%
(d) 4%

Answer:

CP = ₹2500
SP = ₹2700

Since, SP is more than CP.

Therefore, Profit = SP − CP
= ₹2700 − ₹2500
= ₹200

$Profit Percent = \frac{Profit}{CP} \times 100 = \frac{200}{2500} \times 100 = 8 %$

Hence, the correct option is (a).

Page No 12.9:

Question 4:

If CP = ₹950 and gain 6%, then SP =

(a) ₹1100
(b) ₹1117
(c) ₹1107
(d) ₹1170

Disclaimer: There is a misprint in the options. Option (c) must be equal to ₹1007.

Answer:

Let the SP be x.

CP = ₹950
Gain = 6%

Therfore, SP is more than CP.

Now,
$Gain = 6 % of CP = \frac{6}{100} \times 950 = 3 \times 19 = 57$

Thus, SP = CP + gain
= ₹950 + ₹57
= ₹1007

Hence, the correct option is (c).

Page No 12.9:

Question 5:

If SP = ₹924 and gain = 10%, then CP =

(a) ₹480
(b) ₹804
(c) ₹408
(d) ₹840

Disclaimer: There is a misprint in the question. CP should be ask instead of SP.

Answer:

Let the CP be x.

SP = ₹924
Gain = 10%

Therfore, SP is more than CP.

Now,
$Gain = 10 % of CP$ and SP = CP + gain

$So, SP = CP + 10 % of CP \Rightarrow 924 = x + \frac{10}{100} \times x \Rightarrow 924 = (1 + \frac{1}{10}) x \Rightarrow 924 = \frac{11}{10} x \Rightarrow x = 924 \times \frac{10}{11} \Rightarrow x = 840$

Thus, CP = ₹840

Hence, the correct option is (d).

Page No 12.9:

Question 6:

On selling a pen for ₹100, a shopkeeper gains ₹15. The cost price of the pen is

(a) ₹115
(b) ₹85
(c) ₹70
(d) ₹130

Answer:

Let the CP be x.

SP = ₹100
Profit = ₹15

Therfore, SP is more than CP.

Now,
CP = SP − Profit
= ₹100 − ₹15
= ₹85

Thus, CP = ₹85

Hence, the correct option is (b).

Page No 12.9:

Question 7:

On selling a plastic chair for ₹630, a man loses 10%, the cost price of the chair is

(a) ₹567
(b) ₹693
(c) ₹700
(d) ₹730

Answer:

Let the CP be x.

SP = ₹630
Loss = 10%

Therfore, CP is more than SP.

Now,
$Loss = 10 % of CP$ and SP = CP − loss

$So, SP = CP - 10 % of CP \Rightarrow 630 = x - \frac{10}{100} \times x \Rightarrow 630 = (1 - \frac{1}{10}) x \Rightarrow 630 = \frac{9}{10} x \Rightarrow x = 630 \times \frac{10}{9} \Rightarrow x = 700$

Thus, CP = ₹700

Hence, the correct option is (c).

Page No 12.9:

Question 8:

The CP of a chair is ₹3300. If it is sold at a loss of 10%, then SP is

(a) ₹3000
(b) ₹3070
(c) ₹2790
(d) ₹2970

Answer:

Let the SP be x.

CP = ₹3300
Loss = 10%

Therfore, CP is more than SP.

Now,
$Loss = 10 % of CP$ and SP = CP − loss

$So, SP = CP - 10 % of CP \Rightarrow x = 3300 - \frac{10}{100} \times 3300 \Rightarrow x = 3300 - 330 \Rightarrow x = 2970$

Thus, SP = ₹2970

Hence, the correct option is (d).

Page No 12.9:

Question 9:

If the cost price of 15 pens is equal to the selling price of 20 pens, then the loss percent is

(a) 25%
(b) 20%
(c) 15%
(d) 10%

Answer:

Let the cost price of one pen be ₹1.
Then, CP of 20 pens = ₹20
and SP of 20 pens = ₹15 (∵ SP of 20 pens = CP of 15 pens)

Therefore, CP is more than SP.

So, Loss = CP − SP
= ₹20 − ₹15
= ₹5

$Loss percent = \frac{Loss}{CP} \times 100 = \frac{5}{20} \times 100 = 25 %$

Hence, the correct option is (a).

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