Question

Two numbers are in the ratio of 4 ∶ 5. If the first number is increased by 50% and the second number is decreased by 27, the ratio becomes 3 ∶ 4. Find the difference of numbers.
1. 6
2. 7
3. 8
4. 9

Answer 1

Correct Answer - Option 4 : 9

Given:

Ratio of numbers = 4 ∶ 5

Increment in 1^st number = 50%

Decrement in 2^nd number = 27

Concept used:

If X is distributed between A and B in the ratio of a ∶ b, then A = a/(a + b) × X and B = b/(a + b) × X

To convert any ratio to an exact value, we should have to multiply any constant value

Calculation:

Let, numbers be 4x and 5x respectively

Now, 1^st number = 4x + 50% of 4x = 4x + 2x = 6x

2^nd number = 5x - 27

⇒ 6x / (5x - 27) = 3 / 4

⇒ 6x × 4 = (5x - 27) × 3

⇒ 24x = 15x - 81

⇒ 9x = 81

⇒ x = 9

⇒ Numbers are 9 × 4 = 36 and 9 × 5 = 45

The difference of numbers = 45 – 36 = 9

∴ The difference of the numbers is 9.