Question

A fruiterer has some apples and pears in the ratio of 2:5. He sold 261 pears and bought 261 more apples. After that, he had as many apples and pears. How many apples did he have at first.

Answer 1

The number of apples the fruitier have at first is 348 apples

Explanation:

The given parameters are;

The ration of the apples to pears the fruitier has = 2:5

The number of pears he sold = 261 pears

The number of apples he bought = 261 apples

The new ratio of apples to pears the fruitier then has = 1:1

Let 'x', represent the initial number of apples the fruitier has at first, and let 'y', represent the initial number of pears the fruitier has at first

Therefore, we have; x:y = 2:5

x/y = 2/5

∴ 5·x = 2·y

x = 2·y/5...(1)

(x + 261):(y - 261) = 1:1

∴ (x + 261)/(y - 261) = 1

x + 261 = y - 261...(2)

Substituting the value of 'x' from equation (1) in equation (2), gives;

2·y/5 + 261 = y - 261

261 + 261 = y - 2·y/5 = 3·y/5

522 = 3·y/5

∴ y = 5 × 522/3 = 870

The number of pears the fruitier have at first, y = 870 pears

x = 2·y/5 = 2 × 870/5 = 348

The number of apples the fruitier have at first, x = 348 apples.