Question

A fruit-seller incurs loss equal to selling price of (x – 6) mangoes by selling (x + 6) mangoes. If the loss percentage incurred is equal to 15%, find the value of x.

1. 9
2. 8.5
3. 7.5
4. 10

Answer 1

Correct Answer - Option 2 : 8.5

Given:

A fruit-seller incurs loss equal to selling price of (x – 6) mangoes by selling (x + 6) mangoes. Loss percentage incurred is equal to 15%.

Concepts used:

Loss % = (Loss/C.P.) × 100 

Loss = C.P. – S.P.

Calculation:

Let S.P. of 1 mango be Rs. y.

A fruit-seller incurs loss equal to selling price of (x – 6) mangoes by selling (x + 6) mangoes.

⇒ Loss on (x + 6) mangoes = y × (x – 6)

⇒ Loss of 1 mango = y × (x – 6)/(x + 6)

C.P. = Loss + S.P.

⇒ C.P. = {y × (x – 6)/(x + 6)} + y

⇒ C.P. = 2xy/(x + 6)

Loss % = 15

⇒ (Loss)/C.P. × 100 = 15

⇒ {(x- 6) × y/(x+ 6)}/{2xy/(x + 6)} × 100 = 15

⇒ x = 8.5 approx.

∴ Value of x is 8.5 mangoes.