Question

The ages of 3 friends Elan Musk, Bill Gates and Bob Marley are in H.P. The sum of their ages is 37 and the sum of the reciprocals of their ages is 1/4. what is the middle age(in years) among them.
1. 10
2. 12
3. 14
4. 16

Answer 1

Correct Answer - Option 2 : 12

Given∶

The ages are in H.P.

The sum of their ages is 37.

The sum of the reciprocals of their ages is 1/4.

Formula Used∶

Three numbers. in H.P. are taken as,

1/(a - d), 1/a, 1/(a + d)

Calculation∶

Let the ages of Elan, Bill and Bob in H.P. ae taken as 1/(a - d), 1/a, 1/(a + d)

then 1/(a - d) + 1/a + 1/(a + d) = 37      (1)

and a - d + a + a + d = 1/4

a = 1/12

Put a = 1/12 in eq.(1), we get 

⇒ 12/(1 - 12d) + 12 + 12/(1 + 12d) = 37

⇒ 12/(1 - 12d) + 12/(1 + 12d) = 37 - 12 = 25

⇒ 24/(1 - 144d²) = 25

⇒ 1 - 144d² = 24/25

⇒ d² = 1/(25 × 144)

⇒ d = ±1/60

a - d, a, a + d

1/15, 1/12, 1/10 or 1/10, 1/12, 1/15

So, the ages are 15, 12, 10 or 10, 12, 15

∴ Bill Gate is the middle aged one having 12 years age.