Three positive numbers are in ratio 4 : 3 : 2. If the difference between square of the largest and the smallest number is 48, the numbers are;

1. 48, 36 and 24

2. 24, 18 and 12

3. 8, 6 and 2

4. 8, 6 and 4

8, 6 and 4

Reason

It is given that three positive numbers are in ratio 4 : 3 : 2.

Let the numbers be 4x, 3x and 2x.

The difference between square of the largest and the smallest number = 48.

⇒ (4x)² - (2x)² = 48

⇒ 16x² - 4x² = 48

⇒ 12x² = 48

⇒ x² = $\dfrac{48}{12}$

⇒ x² = 4

⇒ x = $\sqrt{4}$

⇒ x = $\pm$ 2

So, the numbers are 4x = 4 x 2 or 4 x (-2) = 8 or -8

3x = 3 x 2 or 3 x (-2) = 6 or -6

2x = 2 x 2 or 2 x (-2) = 4 or -4

The numbers are positive numbers. So, the numbers cannot be -8, -6 and -4.

∴ The numbers are 8, 6 and 4

Hence, option 4 is the correct option.