Question

A fruit vendor bought some mangoes of which 10% were rotten. He sold `33 1/3%` of the rest. Find the total number of mangoes bought by him initially, if he still has 240 mangoes with him

Answer 1

Let the number of mangoes bought by fruit seller initially be x.

Given that 10% or mangoes were rotten

∴ Number of rotten mangoes = `10/100 xx x`

Number of good mangoes = x – no. of rotten mangoes

= `x - 10/100 x`

= `(100x - 10x)/100`

= `90/100 x` ...(1)

Number of mangoes sold = `33 1/3%` of good mangoes 

= `100/3%`

∴ Mangoes sold = `100/3 xx 90/100 xx 1/100`

= `30/100 x`  ...(2)

Number of mangoes remaining = No. of good mangoes – No. of mangoes sold

From (1) and (2)

∴  `90/100 x - 30/100 x` = 240

⇒ `(90x - 30x)/100` = 240

∴ `(60x)/100` = 240

∴ x = `(240 xx 100)/60`

x = 400

∴ Intially he had 400 mangoes