Question

Two numbers are in the ratio 5 : 8. If 10 is subtracted from each number, the ratio becomes 4 : 7. The numbers are ______.

Options

• 80 and 50

• 50 and 80

• 25 and 40

• 40 and 25

Answer 1

Two numbers are in the ratio 5 : 8. If 10 is subtracted from each number, the ratio becomes 4 : 7. The numbers are 50 and 80.

Explanation:

Let the two numbers are 5x and 8x

According to given condition,

5x – 10 : 8x – 10 = 4 : 7

`\implies (5x - 10)/(8x - 10) = 4/7`

`\implies` 7(5x – 10) = 4(8x – 10)

`\implies` 35x – 70 = 32x – 40

`\implies` 35x – 32x = 70 – 40

`\implies` 3x = 30

`\implies` x = 10

Thus, the required numbers are 50 and 80.