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Two numbers are respectively 40% and 60% more than the third number. The ratio of the first two numbers when the first number is increased by 4 becomes 9 ∶ 8. Find the ratio of the first two numbers when the second number is increased by 5.

Two numbers are respectively 40% and 60% more than the third number. The ratio of the first two numbers when the first number is increased by 4 becomes 9 ∶ 8. Find the ratio of the first two numbers when the second number is increased by 5. Correct Answer 2 ∶ 3

Given:

Two numbers are respectively 40% and 60% more than the third number.

The ratio of the two numbers when the first is increased by 4 becomes 9 : 8.

Formula:

If the ratio of A and B is a ∶ b, assume A = ak and B = bk

where k is a constant.

Calculation:

Let the third number be x.

First number = (140/100) of x = 7x/5

Second number = (160/100) of x = 8x/5

According to the question

Ratio = ((7x/5) + 4))/(8x/5) = 9/8

⇒ (7x + 20)/(8x) = 9/8

⇒ 2x = 20

⇒ x = 10

First number = 7x/5 = 14

Second number = 8x/5 = 16

The ratio of the two numbers when the second number is increased by 5

⇒ (14)/(16 + 5)

⇒ 14/21 = 2/3

∴ The ratio of the two numbers when the second number is increased by 5 is 2 ∶ 3

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