Question

B is 2 times as younger than C as he is older than A. If the sum of the ages of A and C is 37 years and that of A and B is 31 years, what is the difference of
he ages of C and A?
12
6
9
15​

Answer 1

Solution:

Let,

age of B = b yrs

age of C = c yrs

age of A = a yrs

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B is younger than C by 2x years

so,

c = b + 2x ...... eqn(1)

B is older than A by x years

so,

b = a + x ....... eqn(2)

Sum of ages of A and C is 37

so,

a + c = 37

c = 37 - a ..... eqn(3)

Sum of ages of A and B is 31

so,

a + b = 31 ..... eqn (4)

Now,

substituting eqn(3) in eqn(1)

we will get,

37 - a = b + 2x

a + b = 37 - 2x ...... eqn(5)

By eqn(4) and eqn(5) we will get

31 = 37 - 2x

2x = 6

x = 3

substituting value of x in eqn (2)

we get

b = 3 + a ..... eqn(6)

Substituting eqn(6) in eqn(1) and using x =3

we get,

c = (3 + a) + 2 ( 3)

c = 3 + a + 6

c - a = 9

Therefore, the difference b/w ages of C and A is 9 yrs.