This question was previously asked in

PGCIL DT Civil 2018 Official Paper

- 14
- 27
- 21
- 18

Option 3 : 21

Given:

The ratio of two numbers = 7 : 9

New ratio = 11 : 4

Calculation:

Let the numbers be a and b

a : b = 7 : 9

b = 9a/7 ----(1)

a + 12 : b - 15 = 11 : 4 ----(2)

Substituting value of equation (1) and (2)

4(a + 12) = 11(9a/7 - 15)

4a + 48 = 99a/7 - 165

99a/7 - 4a = 165 + 48 = 213

71a/7 = 213

a = 21

**∴ The first number is 21**

** Alternate Method**The ratio of first number to second number be 7a : 9a

According to the question,

⇒ (7a + 12)/(9a - 15) = 11 : 4

⇒ 28a + 48 = 99a - 165

⇒ 71a = 213

⇒ a = 3

First number = 7a = 7 × 3 = 21

∴ The first number is 21

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