# The sums of ages of two of them at a time are 4 years, 6 years and 8 years

There are three brothers. The sums of ages of two of them at a time are 4 years, 6 years and 8 years. The age difference between the eldest and the youngest is
(a) 3 years
(b) 4 years
(c) 5 years
(d)( 6 years

Anurag Mishra Professor Asked on 19th February 2016 in

Solution:-
Lat the three brothers be A, B and C

The sum of two of them at a time are 4 years, 6 years and 8 years.
Then,  A + B = 4  ……………………….. (1)
B + C = 6 ……………………………………… (2)
C + A = 8 …………………………………..(3)

From equation (1),
A = 4 – B

Put the value of A = 4 – B in equation (3),
Then,  C + 4 – B = 8
C – B = 8 – 4
C – B = 4 ………………………………(4)

B + C + C – B = 6 + 4
2 C = 10
C = 10/2
C = 5 years

Put the value of C in equation (2),
Then, B +5 = 8
B = 8 – 5
B = 3 years

Put the value of A in equation (1),
Then, 3 + A = 4
A = 4 – 3
A = 1 years

Thus, the ages of the three brothers are 1 years, 3 years and 5 years.

So, the age difference between the eldest and smallest = 5 – 1
= 4 years.

Hence, the correct answer is option (b) 4 years.

Anurag Mishra Professor Answered on 19th February 2016.