Assuming that, the present age of A = x
the present age of B = y
the present age of F = z
the present age of S = t
It’s understood from the question that,
A is elder to b by 2 years. ⇒ x = y + 2
F is twice as old as A. ⇒ z = 2x
B is twice as old as S. ⇒ y = 2t
Also given that the ages of F and S is differing by 40 years.
⇒ z – t = 40.
So, the four equations are:
x = y + 2 … (i)
z = 2x … (ii)
y = 2t … (iii)
z – t = 40 …(iv)
It’s clearly seen from the equations obtained that x, y, z and t are unknowns.
And we have to find the value of x.
So, by using equation (iii) in (i),
(i) Becomes x = 2t + 2
From (iv), we have t = z – 40
Hence, we get
x = 2(z – 40) + 2
= 2z – 80 + 2
= 2z – 78
Using the equation (ii), we have
x = 2 x 2x – 78
⇒ x = 4x − 78
⇒ 4x – x = 78
⇒ 3x = 78
⇒ x = \(\frac{78}{3}\)
⇒ x = 26
Hence, the age of A is 26 years.
