Question

This is from comparing quantities chapter

1. A dealer sells a calculator at a loss of 12% . If he had sold it at a profit of 12% he would have gained Rs.288 more . Find the cost price

2. If a person sells an article for Rs 400 gaining 1/4 of its cost price, find the gain percent.

Answer 1

1. A dealer sells a calculator at a loss of 12% . If he had sold it at a profit of 12% he would have gained Rs.288 more . Find the cost price

2. If a person sells an article for Rs 400 gaining 1/4 of its cost price, find the gain percent

Solution :
          1)  Here S.P  = Selling Price
                   C.P = Cost Price 
        A dealer sells a calculator at a loss of 12% , means          
                 S.P = (100 - 12)% C.P
               or S.P = 88%C.P
       If he had sold it at a profit of 12% he would have gained Rs.288 more , means
              (100 + 12 )%C.P =  88%C.P + 288
               112 % C.P = 88%C.P + 288
               112 % C.P -  88 % C.P = 288
                (112 - 88 ) % C.P = 288
               (24) % C.P = 288
             (24/100 )* C.P = 288
             C.P = 288 * 100 /24
                    C.P  = 1200

Hence Cost Price of Calculator (in Rupees)= 1200 .

Hope U Understand the Solution .
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Cheers !!!

2 ) 
2. If a person sells an article for Rs 400 gaining 1/4 of its cost price, find the gain percent          ?


Solution : 
           S.P = 400
     Let The C.P = X
 Gain = 1/4*X
we Know that ,
                  Gain = S.P - C.P
                   1/4*X = 400 - X (Given Gain = 1/4 *X)
                   X/4 = 400 - X
                   X/4 + X = 400
                   (X + 4*X)/4 = 400
                   5X / 4 = 400
                   5X = 4*400
                   5X = 1600
                   X = 1600/5
                   X =320
Hence C.P = 320
         therefore , S.P - C.P = 400 - 320
                         S.P - C.P = 80
Therefore ,
         Gain % = (S.P - C.P) / C.P *100
                     = 80 /320*100
                     = 25 %

Hence gain percent = 25

Hope U understood the Solution !!

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Cheers !!!

Answer 2

1.  Profit and Loss are calculated on the basis of  cost price.
Profit = 12%    Loss = 12%  

Selling price for profit = 100% + 12 % = 112 % of CP
Selling price for loss =  100% - 12 %   =  88% of CP

Difference between the two prices =  112 - 88 = 24 % of CP

  SO   24 /100 * CP = Rs  288    =>  CP = 100 * 288 / 24 = Rs 1, 200.
================
2)
        Gain = 1/4 * CP    
              So   CP = 4 * Gain

        Gain percentage  = Gain * 100 / CP  = Gain * 100 / (4 * Gain )
                                   =  25 %