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A basket of fruits had a total of 70 fruits comprising of apples and pears. The fruits were divided between Aman and Amit, such that Aman got 60% of the apples, while Amit got 80% of the pears. If Aman got 10 fruits less than Amit, then how many apples and pears were there in the basket?

A basket of fruits had a total of 70 fruits comprising of apples and pears. The fruits were divided between Aman and Amit, such that Aman got 60% of the apples, while Amit got 80% of the pears. If Aman got 10 fruits less than Amit, then how many apples and pears were there in the basket? Correct Answer 40, 30

Let there be ‘x’ apples and ‘y’ pears in the basket

Total no. of fruits = x + y = 70      ----(1)

Fruits received by Aman = 60% of apples + 20% of pears = 3x/5 + y/5 = (3x + y)/5

Fruits received by Amit = 40% of apples + 80% of pears = 2x/5 + 4y/5 = (2x + 4y)/5

But, Aman received 10 fruits less than Amit,

⇒ (2x + 4y)/5 – (3x + y)/5 = 10

⇒ 2x + 4y – 3x – y = 50

⇒ -x + 3y = 50      ----(2)

Adding (1) and (2), we get,

⇒ 4y = 120

⇒ y = 120/4 = 30

Substituting in (1),

⇒ x = 70 – 30 = 40

∴ There were 40 apples & 30 pears in the basket

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