2.
The age of a father is twice that of the
elder son. Ten years hence the age of
the father will be three times that of
the younger son. If the difference of
ages of the two sons is 15 years, the
age of the father is:
(a) 70 years
(b) 60 years
(c) 55 years
(d) 50 years
Question
Answer:
50 years old
Step-by-step explanation:
Let the age of father be x years, the age of elder son be y years
and the age of younger son be z years.
From the first condition, we have
x=2y …(i)
From the second condition, we have
x+10=3(z+10)
∴x+10=3z+30
∴x−3z=20 …(ii)
From the third condition, we have
y−z=15 …(iii)
Put the value of y from eqn. (i) in (iii) we get
x−2z=30 …(iv)
Solving (ii) and (iv), we get
x=50
∴ the age of the father is 50 years.