Three numbers are in the ratio \(\frac{4}{5}:\frac{5}{6}:\frac{9}{10}\). The difference between the smallest and the greatest numbers is 12. Find the number which is NEITHER the smallest NOR the greatest.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 2)

Answer 1

Given

Three numbers are in the ratio \(\frac{4}{5}:\frac{5}{6}:\frac{9}{10}\).

Calculation

⇒ 4/5 × 12 = 9.6

⇒ 5/6 × 12 = 10

⇒ 9/10 × 12 = 10.8

The three numbers are in the ratio = 9.6:10:10.8

Let the numbers be 9.6x, 10x, and 10.8x.

⇒ 10.8x - 9.6x = 12

⇒ 1.2x = 12

⇒ x = 10

The numbers are 96, 100 and 108

The number which is NEITHER the smallest NOR the greatest is 100.

Alternate Method

Calculation:

LCM of 5, 6 and 10 is 30.

4/5 × 30 = 24

5/6 × 30 = 25

9/10 × 30 = 27

⇒ A ∶ B ∶ C = 24x ∶ 25x ∶ 27x

According to the question

⇒ 27x - 24x = 12

⇒ 3x = 12

⇒ x = 4

First number = 24x = 24 × 4 = 96

Second number = 25x = 25 × 4 = 100

Third number = 27x = 27 × 4 = 108

The correct option is 3 i.e. 100