Question

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

विकल्प

• 48, 36, and 24

• 24, 18, and 12

• 8, 6, and 2

• 8, 6, and 4

Answer 1

Three positive numbers are in the ratio 4 : 3 : 2. If the difference between the squares of the largest and smallest numbers is 48, the numbers are 8, 6, and 4.

Explanation:

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 = `48/12`

⇒ x² = 4

⇒ x = `sqrt4`​

⇒ x = ± 2

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

3x = 3 × 2 or 3 × (−2) = 6 or −6

2x = 2 × 2 or 2 × (−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