Two numbers are in the ratio of 4 ∶ 5. If the first number is increa

1.	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. 62. 73. 84. 9
Answer» 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.

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. 62. 73. 84. 9

Answer» 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.

Discussion

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