Question

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 1

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?
Solution:-
             Gain = 15
           Let the Cost Price of tricycle (in Rupees) = x
               and the Selling Price = y
           therefore ,
                 gain % = y - x /x *100
                       15   =100(y-x)/x
                        15x = 100y - 100x
                         15x + 100x = 100y
                        115x = 100y
                       or y = 1.15x .........................(1st)
                 condition 2nd :
                 selling price = y+108
                 gain % = 20
                   ( y+108 - x /x)*100 = 20
                   or (y+108 -x ) = 20 *x/100
                       y+108 -x = x/5
                       y + 108 = x+x/5
                       y+108 = 5x+x /5
                       y+108 = 6x/5
                       y+108 = 1.2x
                 using y = 1.15x , we get
                 1.15x +108 = 1.2x
                 or 1.2x = 1.15x+108
                      1.2 x - 1.15x = 108
                   .05x = 108
                     5x/100=108
                    x/20 = 108
                   x = 108*20
                      x=2160
Hence the Cost Price of Tricycle is (Rupees) 2160.

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Answer 2

Let cost price = x

If it is sold at 15% gain,
15% of x = x × 15/100 = 0.15x
selling price = x + 0.15x = 1.15x

If it is sold at 20% gain,
20% of x = x × 20/100 = 0.2x
selling price = x + 0.2x = 1.2x

Given that
1.2x - 1.15 x = 108
⇒0.05x = 108
⇒ x = 108/0.05
⇒x = Rs. 2160

Cost price is Rs. 2160