Rs Aggarwal 2020 2021 for Class 7 Maths Chapter 11 - Profit And Loss

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Page No 157:

Answer:

(i) CP = Rs. 950
Gain = 6%

$SP = {\frac{(100 + G ain %)}{100} \times CP} = {\frac{(100 + 6)}{100} \times 950} = \frac{106}{100} \times 950 = \frac{100700}{100} = Rs . 1007$

(ii) CP = Rs. 9600
Gain = $16 \frac{2}{3} % = \frac{50}{3} %$

$S P = {\frac{(100 + G ain %)}{100} \times CP} = {\frac{(100 + \frac{50}{3})}{100} \times 9600} = \frac{350}{300} \times 9600 = \frac{3360}{3} = Rs . 11200$

(iii) CP = Rs. 1540
Loss = 4%

$S P = {\frac{(100 - L oss %)}{100} \times CP} = {\frac{(100 - 4)}{100} \times 1540} = \frac{96}{100} \times 1540 = \frac{147840}{100} = Rs . 1478.40$

(iv) CP = Rs. 8640
Loss = $12 \frac{1}{2} % = \frac{25}{2} %$

$S P = {\frac{(100 - L oss %)}{100} \times CP} = {\frac{(100 - \frac{25}{2})}{100} \times 8640} = \frac{175}{200} \times 8640 = \frac{1512000}{200} = Rs . 7560$

Page No 157:

Answer:

(i) CP = Rs. 2400
SP = Rs. 2592
Gain = SP - CP = Rs. ( 2592 - 2400) = Rs. 192

Gain% = $(\frac{Gain}{CP} \times 100)$ $= (\frac{192}{2400} \times 100)$ = $8$

(ii) CP = Rs. 1650
SP = Rs. 1452
Loss = CP - SP = ( 1650 - 1452) = Rs. 198

   Loss% = $(\frac{L oss}{CP} \times 100)$ $= (\frac{198}{1650} \times 100) = 12$

(iii) CP = Rs. 12000 and SP = Rs. 12800
Gain = SP - CP = ( 12800 - 12000) = Rs. 800

   Gain% = $(\frac{Gain}{CP} \times 100) =$ $(\frac{800}{12000} \times 100) = 6.66$

(iv) CP = Rs. 1800
SP = Rs. 1611
Loss = CP - SP = ( 1800 - 1611) = Rs. 189

   Loss% = $(\frac{L oss}{CP} \times 100) =$ $(\frac{189}{1800} \times 100) = 10.5$

Page No 157:

Answer:

(i) SP = Rs. 924
Gain = 10%

$CP = {\frac{100}{(100 + G ain %)} \times SP}$

$= {\frac{100}{(100 + 10)} \times 924} = \frac{92400}{110} = Rs . 840$

(ii) SP = Rs. 1755
Gain = $12 \frac{1}{2} % = \frac{25}{2} %$

$CP = {\frac{100}{(100 + G ain %)} \times SP} = {\frac{100}{(100 + \frac{25}{2})} \times 1755} = {\frac{200}{225} \times 1755} = \frac{351000}{225} = Rs . 1560$

(iii) SP = Rs. 8510
Loss = 8%

$CP = {\frac{100}{(100 - L oss %)} \times SP} = {\frac{100}{(100 - 8)} \times 8510} = \frac{851000}{92} = Rs . 9250$

(iv) SP = Rs. 5600
Loss = $6 \frac{2}{3} % = \frac{20}{3} %$

$CP = {\frac{100}{(100 - L oss %)} \times SP} = {\frac{100}{(100 - \frac{20}{3})} \times 5600} = {\frac{300}{280} \times 5600} = \frac{168000}{28} = Rs . 6000$

Page No 157:

Answer:

Cost price of an almirah = Rs. 13600
Transportation cost = Rs. 400
Total cost price = Rs. (13600 + 400) = Rs. 14000
Selling price = Rs. 16800
Now, SP > CP
$Gain = SP - CP =$ ( 16800 - 14000) = Rs. 2800

$Gain % = (\frac{Gain}{CP} \times 100)$ %

$= (\frac{2800}{14000} \times 100)$ %

$= \frac{2800}{140} % = 20 %$

Page No 157:

Answer:

Cost price of the house = Rs. 765000
Cost of repairing the house = Rs. 115000
Total Cost price = (765000 + 115000) = Rs. 880000
Ravi sold it at a gain of 5%.

$SP = {\frac{(100 + gain %)}{100} \times CP} = {\frac{(100 + 5)}{100} \times 880000} = \frac{105}{100} \times 880000 = Rs . 924000$

He gets Rs. 924000.

Page No 157:

Answer:

CP of 12 lemons (dozen) = Rs. 25
CP of one lemon = Rs. $\frac{25}{12}$

CP of five lemons = 5 × $\frac{25}{12} =$ $\frac{125}{12} = Rs . 10.42$

SP of five lemons = Rs. 12 (given)

Gain = SP - CP = ( 12 - 10.42 ) = Rs 1.58

$Gain % = (\frac{Gain}{CP} \times 100)$ %

$= (\frac{1.58}{10.42} \times 100)$ %

= 15.2%

Page No 157:

Answer:

Let the cost price of the pen be Re 1.
Cost price of 12 pens = Rs 12
SP of 12 pens = CP of 15 pens = Rs 15
Gain = SP - CP = Rs (15 - 12) = Rs 3

$Gain % = (\frac{Gain}{CP} \times 100)$ %

$= (\frac{3}{12} \times 100) % = 25 %$

Gain% = 25%

Page No 157:

Answer:

Let the cost price of one spoon be Re 1.
CP of 16 spoons = Rs 16
SP of 16 spoons = CP of 15 spoons = Rs 15
Loss = CP - SP = (16 - 15) = Re 1

$Loss % = (\frac{Loss}{CP} \times 100) % = (\frac{1}{16} \times 100) % = 6.25 %$

Loss% = 6.25%

Page No 157:

Answer:

Cost price of a video = Rs. 12000
SP of a video at a gain of 10% = ${\frac{(100 + Gain %)}{100} \times CP}$

$= {\frac{(100 + 10)}{100} \times 12000} = {\frac{110}{100} \times 12000} = Rs . 13200$

So, Rahul purchased at a cost price of Rs. 13200.

Rahul sells it at a loss of 5%.

SP of a video at loss of 5% = ${\frac{(100 - Loss %)}{100} \times CP}$

$= {\frac{(100 - 5)}{100} \times 13200} = \frac{95}{100} \times 13200 = Rs . 12540$

∴ Rakesh pays = Rs. 12540

Page No 157:

Answer:

SP of the sofa set = Rs. 21600
Gain% = 8

$CP of the sofa se t = {\frac{100}{(100 + G a i n %)} \times S P} = {\frac{100}{(100 + 8)} \times 21600} = \frac{2160000}{108} = R s . 20000$

He purchased it at the cost of Rs. 20000.

Page No 157:

Answer:

SP of the watch = Rs 11400
Loss% = 5

$CP = {\frac{100}{(100 - Loss %)} \times SP}$

$= {\frac{100}{(100 - 5)} \times 11400} = \frac{11400}{95} = Rs . 12000$

He purchased it at the cost of Rs. 12000.

Page No 157:

Answer:

SP of the calculator = Rs. 1325
Gain % = 6

CP of the calculator = ${\frac{100}{(100 + Gain %)} \times SP}$

$= {\frac{100}{(100 + 6)} \times 1325} = \frac{132500}{106} = Rs . 1250$

$SP of the calculator = {\frac{(100 + Gain %)}{100} \times CP} = {\frac{(100 + 12)}{100} \times 1250} = \frac{140000}{100} = Rs . 1400$

Page No 157:

Answer:

SP of a computer = Rs. 24480
Loss% = 4

$CP of the c omputer = {\frac{100}{(100 - Loss %)} \times SP} = {\frac{100}{(100 - 4)} \times 24480} = \frac{2448000}{96} = Rs . 25500$

In order to gain 4%:
$SP of the c omputer = {\frac{(100 + Gain %)}{100} \times CP} = {\frac{(100 + 4)}{100} \times 25500} = {\frac{104}{100} \times 25500} = \frac{2652000}{100} = Rs . 26520$

Page No 157:

Answer:

Let the CP of the tricycle be Rs. x

SP at 15% gain = ${\frac{(100 + G ain %)}{100} \times CP}$
$= {\frac{(100 + 15)}{100} \times x} = \frac{115}{100} x$

$= Rs . \frac{23}{20} x$

SP at 20% gain = $x \times \frac{120}{100} =$ $Rs . \frac{6}{5} x$

$\frac{6}{5} x - \frac{23}{20} x = 108 \Rightarrow \frac{24 x - 23 x}{20} = 108 \Rightarrow \frac{x}{20} = 108 \Rightarrow x = 2160$

Hence, the cost price of the tricycle is Rs. 2160

Page No 157:

Answer:

Let CP of a television be Rs x.
SP at 8% loss = $\frac{(100 - 8)}{100} \times x = Rs . \frac{92}{100} x$
100
SP at 6% gain = $(\frac{100 + 6)}{100} \times x = Rs . \frac{106}{100} x$

      $\frac{106}{100} x - \frac{92}{100} x = 3360$

⇒ $\frac{14}{100} x = 3360$

⇒ $x = \frac{336000}{14} = 24000$

∴ CP = Rs. 24000
Sandeep bought it at the cost of Rs. 24000.

Page No 157:

Answer:

SP of each cycle = Rs. 2376
He gains 10% in one cycle.
CP = ${\frac{100}{(100 + G ain %)} \times SP}$
$= {\frac{100}{(100 + 10)} \times 2376} = \frac{100}{110} \times 2376 = Rs . 2160$

He looses 10% in the second cycle.
CP = $\frac{100}{(100 - L oss %)} \times SP$

$= \frac{100}{(100 - 10)} \times 2376 = \frac{100}{90} \times 2376 = \frac{23760}{9} = Rs . 2640$

Total CP = $Rs . (2160 + 2640) = Rs . 4800$
Total SP = $Rs . (2376 + 2376) = Rs . 4752$
Loss = CP - SP = $Rs . (4800 - 4752) = Rs . 48$
$Loss %$ = $(\frac{Loss}{CP} \times 100)$ %
$= (\frac{48}{4800} \times 100) % = 1 %$

Page No 157:

Answer:

Let the CP of the exhaust fan be Rs. x.
Gain = $Rs . \frac{x}{6}$

SP = $R s (x + \frac{x}{6})$

SP = Rs. 7350

∴ $x + \frac{x}{6} = 7350$
⇒ $\frac{7}{6} x = 7350$
⇒ $x = \frac{7350 \times 6}{7} = \frac{44100}{7} = 6300$
CP of the fan = Rs. 6300

Page No 157:

Answer:

Mohit sold a watch to Karim at Rs. x.
Mohit sold it at a gain of 10%.
SP of the watch = $110 % o f x$
= $(x + \frac{110}{100}) = Rs . \frac{11}{20} x$
Karim sold it to Rahim at a gain of 4%.
SP of the watch = $104 % o f \frac{11}{10} x = (\frac{104}{100} \times \frac{11}{10} x) = Rs . (\frac{26}{25} \times \frac{11}{10} x)$

But, Rahim pays Rs. 14300.
∴ $\frac{26}{25} \times \frac{11}{10} x = 14300$

$\Rightarrow x = \frac{14300 \times 25 \times 10}{26 \times 11} = \frac{3575000}{286} = 12500$

Mohit purchased it at Rs. 25000.

Page No 157:

Answer:

Let the production cost of a washing machine be Rs. x.
Profit of the manufacturer = 10%
SP of the manufacturer = $110 % o f x$
= $(x + \frac{110}{100}) = \frac{110}{100} x = Rs . \frac{11}{10}$
Profit of the wholesale dealer = 15%
SP of the wholesale dealer = $115 % o f R s \frac{11}{10} x$
= $R s (\frac{11}{10} x \times \frac{115}{100}) = R s (\frac{11}{10} x \times \frac{23}{20})$

Profit of the retailer = 25%
SP of the retailer = $125 % o f R s (\frac{11}{10} x \times \frac{23}{20})$

= $Rs . (\frac{11}{10} x \times \frac{23}{20} \times \frac{125}{100}) = Rs . (\frac{11}{10} x \times \frac{23}{20} \times \frac{5}{4})$

Given:
Retail price = Rs. 37950
∴ $(\frac{11}{10} x \times \frac{23}{20} \times \frac{5}{4}) = 37950$

$\Rightarrow x = \frac{37950 \times 10 \times 20 \times 4}{11 \times 23 \times 5}$
=> x= $\frac{30360000}{1265} = 24000$

∴ Production cost of a washing machine = Rs. 24000

Page No 157:

Answer:

Mr. Mehta purchased a video at the cost of Rs. 20000.
Mr. Mehta purchased a television at the cost of Rs. 30000.
Total cost = Rs. (20000 + 30000) = Rs. 50000

He lost 5% on the video.

$SP = \frac{(100 - L oss %)}{100} \times CP = \frac{100 - 5}{100} \times 20000 = \frac{95}{100} \times 20000 = Rs . 19000$

He gained 8% on the television.

$SP = \frac{(100 + G ain %)}{100} \times CP = \frac{100 + 8}{100} \times 30000 = \frac{108}{100} \times 30000 = Rs . 32400$

Total SP = $Rs . (190000 + 32400) = Rs . 51400$

Total CP = Rs. 50000
Total Gain = SP - CP = $Rs . (51400 - 50000) = Rs . 1400$
$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{1400}{50000} \times 100) % = 2.8 %$

Page No 158:

Answer:

Let the CP of 1 orange be Rs. x.
∴ CP of 36 oranges = Rs. 36x
Let SP of orange be Rs. y.
∴ SP of 36 oranges = Rs. 36y

Loss = SP of 4 oranges = $4 y$      (given)

We know:
Loss = CP - SP
⇒    $4 y = 36 x - 36 y$
⇒ $4 y + 36 y = 36 x$
  ⇒    $40 y = 36 x$
⇒ $10 y = 9 x$
⇒ $y = \frac{9}{10} x$

$Loss % = (\frac{Loss}{CP} \times 100)$ %

$= (\frac{4 y}{36 x} \times 100)$ %

$= (\frac{4 \times 9 x}{36 x \times 10} \times 100) % = 10 %$

Loss% = 10%

Page No 158:

Answer:

Let the CP of one pencil be Rs. x.
Therefore, the CP of 96 pencils will be Rs. 96x.
Let SP of one pencil be Rs. y.
∴ SP of 96 pencils = Rs. 96y
Gain= SP of one dozen pencil = Rs.12y           (given)

Gain = SP - CP

   $\Rightarrow 12 y = 96 y - 96 x \Rightarrow 96 x = 96 y - 12 y \Rightarrow 96 x = 84 y \Rightarrow x = \frac{84 y}{96}$

$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{12 y}{96 x} \times 100) % = (\frac{12 y \times 96}{96 \times 84 y} \times 100) % = 14.28 %$

Page No 158:

Answer:

(b) 25%

CP of the book = Rs. 80
SP of the book = Rs. 100
Gain = SP - CP = Rs. (100 - 80) = Rs. 20
$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Page No 158:

Answer:

(a) $12 \frac{1}{2} %$

CP of a football = Rs. 120
SP of a football = Rs. 105

CP>SP
∴ Loss = CP - SP = Rs. ( 120 - 105 ) = Rs. 15
$Loss % = (\frac{Loss}{CP} \times 100) % = (\frac{15}{120} \times 100) % = \frac{25}{2} % = 12 \frac{1}{2} %$

Page No 158:

Answer:

(b) 25%

SP of the bat = Rs. 100
Gain = Rs. 20

Gain = SP - CP
⇒ 20 = 100 - CP
⇒ CP = 100 - 20 = Rs. 80

$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{20}{80} \times 100) % = 25 %$

Page No 158:

Answer:

(a) Rs. 180

SP of the racket = Rs. 198
Gain% = 10

$CP of the r acket = {\frac{100}{(100 + Gain %)} \times 100} = {\frac{100}{(100 + 10)} \times 198} = \frac{100}{110} \times 198 = Rs . 180$

Page No 158:

Answer:

Let the cost price be Rs. x.
Loss = $Rs . \frac{x}{7}$
∴ SP = $(x - \frac{x}{7}) = Rs . \frac{6}{7} x$

Given:
SP = Rs. 144

∴   $\frac{6}{7} x = 144$
⇒ $x = \frac{144 \times 7}{6} = Rs . 168$

∴ CP = Rs. 168
SP = Rs. 144

New SP = Rs. 189
Gain = SP - CP = $Rs . (189 - 168) = Rs . 21$

$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{21}{168} \times 100) % = 12.5 %$

The correct answer is 12.5%.
All the given options are wrong.

Page No 158:

Answer:

(d) Rs. 72

SP of the pen = Rs. 48
Loses = 20%
Then , $CP = {\frac{100}{(100 - Loss %)} \times SP}$
$= {\frac{100}{(100 - 20)} \times 48} = Rs . 60$

In order to gain 20%:

$SP = {\frac{(100 + Gain %)}{100} \times CP} = {\frac{(100 + 20)}{100} \times 60} = \frac{120}{100} \times 60 = Rs . 72$

Page No 158:

Answer:

(a) 20%

Let the cost price of each pencil be Rs.1
Cost of 15 pencils = Rs 15
SP of 15 pencil = CP of 12 pencil = Rs 12
∴ CP = Rs 15
SP = Rs 12

Loss = CP - SP = $Rs (15 - 12) = Rs 3$

$Los s % = (\frac{Loss}{CP} \times 100) % = (\frac{3}{15} \times 100) % = \frac{300}{15} % = 20 %$

Page No 158:

Answer:

(d) $33 \frac{1}{3} %$

Let the cost price of each toffee be Rs. 1
Cost price of three toffees = Rs 3
SP of three toffees = CP of four toffees = Rs 4

CP = Rs 3
SP = Rs 4

Gain = SP - CP = $Rs (4 - 3) = Re 1$
$G a i n % = (\frac{G a i n}{C P} \times 100) % = (\frac{1}{3} \times 100) % = \frac{100}{3} % = 33 \frac{1}{3} %$

Page No 158:

Answer:

(c) Rs. 176

SP of an article = Rs. 144
Loss% = 10
$C P = {\frac{100}{(100 - Loss %)} \times S P} = {\frac{100}{(100 - 10)} \times 144} = \frac{100}{90} \times 144 = \frac{1440}{9} = Rs . 160$

In order to gain 10%:

$S . P . = \frac{(100 + Gain %)}{100} \times C P = \frac{(100 + 10)}{100} \times 160 = \frac{110}{100} \times 160 = Rs . 176$

Page No 159:

Answer:

(a) 50%

CP of six lemons = Re 1
CP of one lemon = $Rs \frac{1}{6}$

CP of four lemon = $Rs \frac{4}{6}$
SP of four lemon = Re 1

Gain = $1 - \frac{4}{6} = \frac{2}{6} = Rs \frac{1}{3}$
$Gain % = (\frac{Gain}{C P} \times 100) = (\frac{3}{2 \times 3} \times 100) = \frac{100}{2} = 50$

Page No 159:

Answer:

(d)Rs. 600

SP of the chair = Rs 720
Gain% = 20

$C . P . = {\frac{100}{(100 + Profit percentage)} \times S . P .} = {\frac{100}{120} \times 720} = \frac{7200}{12} = Rs . 600$

Page No 159:

Answer:

(c) Rs. 700

SP of a stool = Rs 630
Loss% = 10
$C P = {\frac{100}{(100 - L oss %)} \times S P} = {\frac{100}{(100 - 10)} \times 630} = \frac{100}{90} \times 630 = Rs 700$

Page No 160:

Answer:

SP of the chair = Rs 1375
Gain% = 10

$CP of the c hair = {\frac{100}{(100 + Gain %)} \times SP}$

$= {\frac{100}{(100 + 10)} \times 1375} = \frac{137500}{110} = Rs . 1250$

Page No 160:

Answer:

Let the cost of each pen be Rs. 1
CP of 10 pens = Rs. 10
SP of 10 pens = CP of 14 pens = Rs. 14
Gain = SP - CP = 14-10= Rs. 4
$Gain % = (\frac{Gain}{CP} \times 100) % = (\frac{4}{10} \times 100) % = 40 %$

Page No 160:

Answer:

Let the cost price of the fan be Rs. x.
Gain = $Rs . \frac{x}{10}$
SP of the fan = $(x + \frac{x}{10}) = Rs . \frac{11}{10} x$
SP of the fan = $Rs . 2585$
∴ $\frac{11}{10} x = 2585$
⇒ $11 x = 25850$
⇒ $x = \frac{25850}{11} = 2350$

So, CP of the fan is Rs. 2350.

Page No 160:

Answer:

Cost price of six lemons = Rs. 10
Cost price of one lemon = $Rs . \frac{10}{6}$
Cost price of eight lemons = $8 \times \frac{10}{6} = Rs . \frac{80}{6} = Rs . 13.33$
Selling price of eight lemons = Rs. 15

$Gain = S P - C P = Rs . (15 - 13.33) = Rs . 1.67$

Gain% = $(\frac{Gain}{C . P .} \times 100)$ %
$= (\frac{1.67}{13.33} \times 100)$ %
$= 12.5$ %

Page No 160:

Answer:

SP of the bat = Rs 486
Loss = 10%
CP of the bat = ${\frac{100}{(100 - Loss %)} \times S P}$
$= {\frac{100}{(100 - 10)} \times 486} = \frac{48600}{90} = Rs 540$

CP of the bat = Rs 540

Page No 160:

Answer:

(b) Rs 85

SP of a football = Rs 100
Gain = Rs 15
Gain = SP - CP
⇒ 15 = 100 - CP
⇒ CP = Rs (100 - 15)
⇒ CP= Rs 85

Page No 160:

Answer:

(c) 15.2%

Cost price of 12 bananas = Rs. 25
Cost price of one banana = $Rs . \frac{25}{12}$
$Cost price of five banana s = Rs . 5 \times \frac{25}{12} = Rs . \frac{125}{12} = Rs . 10.42$

He sells five bananas at the cost (SP) of Rs. 12.
Gain = SP - CP

= $= Rs . (12 - 10.42) = Rs . 1.58$

$Gain % = (\frac{Gain}{C P} \times 100) % = (\frac{1.58}{10.4} \times 100) % = 15.2 %$

Page No 160:

Answer:

(c) Rs. 196

Let the cost price of the jug be Rs. x.
Loss = $Rs . \frac{x}{7}$
SP of the jug = CP - Loss
$= Rs . (x - \frac{x}{7}) = Rs . \frac{6}{7} x$

SP of the jug = $R s 168$ (given)

∴ $\frac{6}{7} x = 168$
$\Rightarrow = \frac{168 \times 7}{6} \Rightarrow x = \frac{1176}{6} \Rightarrow x = 196$

∴ CP of the jug = $Rs . 196$

Page No 160:

Answer:

(c) $66 \frac{2}{3} %$

Let the cost price of each banana be Re 1.
Cost price of three bananas = Rs. 3
SP of three bananas = CP of five bananas = Rs. 5
Gain = SP - CP = $Rs . (5 - 3) = Rs . 2$

$Gain % = (\frac{Gain}{C P} \times 100) % = (\frac{2}{3} \times 100) % = (\frac{200}{3}) % = 66 \frac{2}{3} %$

Page No 160:

Answer:

(i) Loss = (CP) - (SP)

(ii) CP = $\frac{100 \times S P}{(100 + Gain %)}$

(iii) Profit or loss is always reckoned on the cost price.
(iv) $\frac{100 \times SP}{(100 - loss %)}$ = CP

Page No 160:

Answer:

(i) False
Gain or loss is always reckoned on the cost price.

(ii) True
(iii) True
(iv) True

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