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

original number --- x
number of good mangos = .9x
33 1/3% is exactly 1/3
so he still have 2/3 of the .9x mangoes left, that is
(2/3)(9/10)x = 240
(3/5)x = 240
x = 400

so he bought 400 mangoes.

check:
40 were rotten, so he had 360 to sell
he sold 1/3 or 120 of that, leaving him with 240

my answer is correct

Answer 2

Let the total no. of mangoes be x.
10% of the mangoes were rotten.
∴ remaining mangoes = x - 10x/100 = 90/100
The fruit vendor sold 33 1/3% of the remaining.
∴ mangoes still remaining with him
= 90x/100 - 3 * 100 * 90x
= 90x/100 - 90x/300
= (270x - 90x)/300
= 3x/5
By the problem,
3x/5 = 240
=> x = 80 * 5
=> x = 400
The fruit vendor bought 400 mangoes.