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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
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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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