RS Aggarwal 2019,2020 solution class 7 chapter 11 Profit and Loss Exercise 11A

Exercise 11A

Page-157

Question 1:

Find the SP when:

(i) CP = Rs 950, gain = 6%
(ii) CP = Rs 9600, gain = $16\frac{2}{3}\%$
(iii) CP = Rs 1540, loss = 4%
(iv) CP = Rs 8640, loss = $12\frac{1}{2}\%$

Answer 1:

(i) CP = Rs. 950
Gain = 6%
 
  $$\begin{gathered} SP\; =\{\frac{(100 + G\mathrm{ain}\%)}{100}\times \mathrm{CP} \} \\ = \{\frac{(100 + 6)}{100}\times 950\} \\ = \frac{106}{100}\times 950 \\ = \frac{100700}{100} \\ = \mathrm{Rs}. 1007 \end{gathered}$$


   (ii) CP = Rs. 9600
Gain = $16\frac{2}{3}\% = \frac{50 }{3}\%$
   
        $$\begin{gathered} \mathrm{S}\mathrm{P}=\{ \frac{(100 + G\mathrm{ain}\%)}{100}\times \mathrm{CP}\} \\ = \{\frac{(100 + {\displaystyle \frac{50}{3}})}{100}\times 9600\} \\ = \frac{350}{300} \times 9600 \\ = \frac{3360}{3} \\ = \mathrm{Rs}. 11200 \end{gathered}$$


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


(iv) CP = Rs. 8640  
Loss = $12\frac{1}{2}\% = \frac{25}{2}\%$
     
  $$\begin{gathered} \mathrm{S}\mathrm{P}=\{\frac{(100 - L\mathrm{oss}\%)}{100}\times \mathrm{CP}\} \\ = \{\frac{(100 - {\displaystyle \frac{25}{2}})}{100}\times 8640\} \\ = \frac{175}{200}\times 8640 \\ = \frac{1512000}{200} \\ = \mathrm{Rs}. 7560 \end{gathered}$$

Question 2:

Find the gain or loss per cent when:

(i) CP = Rs 2400 and SP = Rs 2592
(ii) CP = Rs 1650 and SP = Rs 1452
(iii) CP = Rs 12000 and SP = Rs 12800
(iv) CP = Rs 1800 and SP = Rs 1611

Answer 2:

(i) CP = Rs. 2400  
SP = Rs. 2592
    Gain = SP - CP = Rs. ( 2592 - 2400) = Rs. 192
 
    Gain%  = $\left(\frac{\mathrm{Gain}}{\mathrm{CP} }\times 100\right)$ $=\left( \frac{192}{2400}\times 100\right)$ = $8$

(ii) CP = Rs. 1650  
SP = Rs. 1452
    Loss = CP - SP = ( 1650 - 1452) = Rs. 198
   
     Loss%  = $\left(\frac{L\mathrm{oss}}{\mathrm{CP}} \times 100\right)$ $=\left(\frac{198}{1650} \times 100\right) = 12$ 

(iii) CP = Rs. 12000   and   SP = Rs. 12800
    Gain = SP - CP = ( 12800 - 12000) = Rs. 800
   
     Gain% = $\left(\frac{\mathrm{Gain}}{\mathrm{CP}} \times 100 \right)=$ $\left(\frac{800}{12000}\times 100\right) = 6.66$


(iv) CP = Rs. 1800  
SP = Rs. 1611
     Loss = CP - SP = ( 1800 - 1611) = Rs. 189
 
       Loss% = $\left(\frac{L\mathrm{oss}}{\mathrm{CP}} \times 100\right) =$$\left(\frac{189}{1800} \times 100 \right)= 10.5$ 

Question 3:

Find the CP when:

(i) SP = Rs 924, gain = 10%
(ii) SP = Rs 1755, gain = $12\frac{1}{2}\%$
(iii) SP = Rs 8510, loss = 8%
(iv) SP = Rs 5600, loss = $6\frac{2}{3}\%$

Answer 3:

(i) SP = Rs. 924  
Gain = 10%
   
   $\mathrm{CP} =\{ \frac{100}{(100 + G\mathrm{ain}\%)}\times \mathrm{SP}\}$

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


(ii) SP = Rs. 1755  
Gain = $12\frac{1}{2}\% =\frac{25}{2}\%$
 
     $$\begin{gathered} \mathrm{CP} = \{\frac{100}{(100 + G\mathrm{ain}\%)}\times \mathrm{SP}\} \\ =\{\frac{100}{(100 + {\displaystyle \frac{25}{2}})}\times 1755\} \\ = \{\frac{200}{225}\times 1755\} \\ = \frac{351000}{225} \\ = \mathrm{Rs}. 1560 \end{gathered}$$

                                 
(iii) SP = Rs. 8510  
Loss = 8%
       
      $$\begin{gathered} \mathrm{CP} = \{\frac{100}{(100 - L\mathrm{oss}\%)}\times \mathrm{SP}\} \\ = \{\frac{100}{(100 - 8 )}\times 8510\} \\ = \frac{851000}{92} \\ = \mathrm{Rs}. 9250 \end{gathered}$$
 

(iv) SP = Rs. 5600  
Loss = $6\frac{2}{3}\% = \frac{20}{3}\%$
     
     $$\begin{gathered} \mathrm{CP} = \{\frac{100}{(100 - L\mathrm{oss}\%)}\times \mathrm{SP}\} \\ = \{\frac{100}{(100 - {\displaystyle \frac{20}{3}})}\times 5600\} \\ = \{\frac{300}{280}\times 5600\} \\ = \frac{168000}{28} \\ = \mathrm{Rs}. 6000 \end{gathered}$$

Question 4:

Sudhir bought an almirah for Rs 13600 and spent Rs 400 on its transportation. He sold it for Rs 16800. Find his gain per cent.

Answer 4:

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
$\mathrm{Gain} = \mathrm{SP} - \mathrm{CP} =$ ( 16800 - 14000) = Rs. 2800

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

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

$$\begin{gathered} =\frac{2800}{140}\% \\ = 20\% \end{gathered}$$

Question 5:

Ravi purchased an old house for Rs 765000 and spent Rs 115000 on its repairs. Then, he sold it at a gain of 5%. How much did he get?

Answer 5:

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%.

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

 He gets Rs. 924000.

Question 6:

A vendor busy lemons at Rs 25 per dozen and sells them at the rate of 5 for Rs 12. Find his gain or loss per cent.

Answer 6:

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} = \mathrm{Rs}. 10.42$

SP of five lemons = Rs. 12            (given)

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

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

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

= 15.2%

Question 7:

The selling price of 12 pens is equal to the cost price of 15 pens. Find the gain per cent.

Answer 7:

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

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

$$\begin{gathered} =\left(\frac{3}{12}\times 100 \right)\% \\ = 25\% \end{gathered}$$

Gain% = 25%

Question 8:

The selling price of 16 spoons is equal to the cost price of 15 spoons. Find the loss per cent.

Answer 8:

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

$$\begin{gathered} \mathrm{Loss}\% = \left(\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100\right)\% \\ = \left(\frac{1}{16}\times 100 \right)\% \\ =6.25\% \end{gathered}$$

Loss% = 6.25%

Question 9:

Manoj purchased a video for Rs 12000. He sold it to Rahul at a gain of 10%. If Rahul sells it to Rakesh at a loss of 5%, what did Rakesh pay for it?

Answer 9:

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

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

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

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

∴ Rakesh pays = Rs. 12540

Question 10:

On selling a sofa-set for Rs 21600, a dealer gains 8%. For how much did he purchase it?

Answer 10:

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

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

He purchased it at the cost of Rs. 20000.

Question 11:

On selling a watch for Rs 11400, a shopkeeper loss 5%. For how much did the purchase it?

Answer 11:

SP of the watch = Rs 11400
Loss% = 5

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

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

 He purchased it at the cost of Rs. 12000.

Question 12:

On selling a calculator for Rs 1325, a man gains 6%. For how much should he sell it to gain 12%?

Answer 12:

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

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

$$\begin{gathered} =\{\frac{100}{(100 + 6)}\times 1325\} \\ = \frac{132500}{106} \\ = \mathrm{Rs}. 1250 \end{gathered}$$
             
 $$\begin{gathered} \mathrm{SP} \mathrm{of} \mathrm{the} \mathrm{calculator}= \{\frac{(100 + \mathrm{Gain}\%)}{100}\times \mathrm{CP}\} \\ = \{\frac{(100 + 12)}{100}\times 1250\} \\ = \frac{140000}{100} \\ = \mathrm{Rs}.1400 \end{gathered}$$

Question 13:

On selling a computer for Rs 24480, a dealer loses 4%. For how much should he sell it to gain 4%?

Answer 13:

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

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

Question 14:

A tricycle is sold at a gain of 15%. Had it been sold for Rs 108 more, the profit would have been 20%. Find its cost price.

Answer 14:

Let the CP of the tricycle be Rs. x

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

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

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



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

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

Question 15:

Sandeep sold a television at a loss of 8%. If he had sold it for Rs 3360 more, he would have gained 6%. For how much did Sandeep buy it?

Answer 15:

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

      $\frac{106}{100}x - \frac{92}{100}x = 3360$                                                                                       
 
                       ⇒$\frac{14}{100}x = 3360$                                                                                             
                                                                          
                        ⇒         $x = \frac{336000}{14} = 24000$                                                                 

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

Question 16:

Pankaj sells two cycles for Rs 2376 each. On one he gains 10% and on the other he loss 10%. Find his gain or loss per cent.

Answer 16:

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

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

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

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

Question 17:

On selling an exhaust fan for Rs 7350, a man gains $\frac{1}{6}$ of its cost price. Find the cost price of the fan.

Answer 17:

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

​SP =  $Rs ( x + \frac{x}{6})$  
     
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

Question 18:

Mohit sold a watch to Karim at a gain of 10% and Karim sold it to Rahim at a gain of 4%. If Rahim pays Rs 14300 for it, for how much did Mohit purchase it?

Answer 18:

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

Question 19:

If the manufacturer gains 10%, the wholesale dealer 15%, and the retailer 25% then what is the production cost of a washing machine whose retail price is Rs 37950?

Answer 19:

Let the production cost of a washing machine be Rs. x.
Profit of the manufacturer  = 10%
SP of the manufacturer = $110\% of x$
                                    =  $(x + \frac{110}{100}) = \frac{110}{100}x = \mathrm{Rs}. \frac{11}{10}$                                                             
Profit of the wholesale dealer = 15%
SP of the wholesale dealer =   $115\% of Rs \frac{11}{10}x$                                           
                                        = $Rs (\frac{11}{10}x \times \frac{115}{100}) = Rs (\frac{11}{10}x \times \frac{23}{20})$
                                           
Profit of the retailer = 25%
SP of the retailer = $125\% of Rs (\frac{11}{10}x \times \frac{23}{20})$     
                          
                          = $\mathrm{Rs}. ( \frac{11}{10}x \times \frac{23}{20}\times \frac{125}{100}) = \mathrm{Rs}. (\frac{11}{10}x \times \frac{23}{20}\times \frac{5}{4})$
                                
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

Question 20:

Mr Mehta purchased a video for Rs 20000 and a television for Rs 30000. On the video he lost 5% and on the television he gained 8%. Find his total gain or loss per cent.

Answer 20:

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.

$$\begin{gathered} \mathrm{SP}= \frac{(100-L\mathrm{oss}\%)}{100}\times \mathrm{CP} \\ =\frac{100-5}{100}\times 20000 \\ =\frac{95}{100}\times 20000 \\ =\mathrm{Rs}. 19000 \end{gathered}$$   
                                                 
He gained 8% on the television.

$$\begin{gathered} \mathrm{SP}= \frac{(100+G\mathrm{ain}\%)}{100}\times \mathrm{CP} \\ =\frac{100+8}{100}\times 30000 \\ =\frac{108}{100}\times 30000 \\ =\mathrm{Rs}. 32400 \end{gathered}$$
                                                                                 
Total SP =  $\mathrm{Rs}. ( 190000 + 32400 ) = \mathrm{Rs}. 51400$     
                                                                                
Total CP = Rs. 50000
Total Gain = SP - CP = $\mathrm{Rs}. ( 51400 - 50000 ) = \mathrm{Rs}. 1400$                                                     
$$\begin{gathered} \mathrm{Gain}\% = \left(\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100 \right)\% \\ = \left(\frac{ 1400}{50000} \times 100\right)\% \\ = 2.8\% \end{gathered}$$

page-158

Question 21:

By selling 36 oranges, a vendor suffers a loss equal to the selling price of 4 oranges. Find his loss per cent.

Answer 21:

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 = $4y$      (given)

We know:
Loss = CP - SP 
         ⇒            $4y = 36x - 36y$
        ⇒            $4y + 36y = 36x$  
        ⇒                      $40y = 36x$
        ⇒                         $10y = 9x$
​        ⇒                             $y = \frac{9}{10}x$ 
                              
 $\mathrm{Loss}\% = \left(\frac{\mathrm{Loss}}{\mathrm{CP}}\times 100 \right)$%

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

$$\begin{gathered} =\left(\frac{4 \times 9x}{36x\times 10}\times 100\right)\% \\ = 10\% \end{gathered}$$
  
​Loss% = 10%

Question 22:

By selling 8 dozen pencils, a shopkeeper gains the selling price of one dozen pencils. Find his gain per cent.

Answer 22:

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 

       $$\begin{gathered} \Rightarrow 12y=96y-96x \\ \Rightarrow 96x=96y-12y \\ \Rightarrow 96x=84y \\ \Rightarrow x=\frac{84y}{96} \end{gathered}$$
                              
 $$\begin{gathered} \mathrm{Gain}\% = \left(\frac{\mathrm{Gain}}{\mathrm{CP}}\times 100 \right)\% \\ =\left(\frac{12y}{96x}\times 100\right)\% \\ =\left(\frac{12y\times 96}{96\times 84y}\times 100\right)\% \\ =14.28\% \end{gathered}$$