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Mr. Mehta sold his two luxury cars at Rs. 39,10,000 each. On one he gains 15% but on the other, he loses 15%. How much does he gain or lose in the whole transaction?

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#### Solution

Let x, y be the C.P. of two cars.

S.P. of both the cars = 39,10,000 .....…[Given]

∴ One car is sold at a 15% loss

∴ S.P. of the first car = `"x" - 15/100 "x"`

∴ `85/100 "x"` = 39,10,000

∴ x = `(39,10,000 xx 100)/85`

= `(2,30,000 xx100)/5`

= 46,000 × 100

= 46,00,000

Other car is sold at 15% gain

∴ S.P. of second car = `"y" + 15/100 "y"`

∴ `"y" + 15/100 "y" = 39,10,000`

∴ `115/100 "y" = 39,10,000`

∴ y = `(39,10,000 xx 100)/115`

= `(7,82,000 xx 100)/23`

= 34,000 × 100

= 34,00,000

x + y = Total C.P. of two cars

= 46,00,000 + 34,00,000

= 80,00,000

Total S.P. = 39,10,000 + 39,10,000

= 78,20,000

∴ S.P. < C.P.

∴ There is a loss of ₹ (80,00,000 – 78,20,000)

∴ = ₹ 1,80,000

∴ Loss% = `(1,80,000)/(80,00,000) xx 100`

= `18/8`

= `9/4`

= 2.25

∴ Mr. Mehta bears a 2.25% loss in the whole transaction.