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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
Solution
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
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