A family has only one kid. The father says “after ‘n’ years, my age will be 4 times the age of my kid.” The mother says “after ‘n’ years, my age will be 3 times that of my kid.” What will be the combined ages of the parents after ‘n’ years?
A. The age difference between the parents is 10 years.
B. After ‘n’ years, the kid is going to be twice as old as she is now.
Answer: A
Let the present age of father = f years
The present age of mother = m years
The present age of the kid = k years
∴ f + n = 4(k + n) …(i)
∴ m + n = 3(k + n) …(ii)
Equation (i) - equation (ii)
∴ f − m = k + n …(iii)
Equation (i) + equation (ii)
∴ f + m + 2n = 7k + 7n = 7(k + n) …(iv)
From statement A,
f − m = 10
Substituting in equation (iii), we get,
k + n = 10
∴ The combined age of the parents after n years
= 7(k + n)
= 7 × 10 = 70 years\
∴ Statement A alone is sufficient.
From statement B,
k + n = 2k
n = k …(v)
Substituting equation (v) in equation (iii), we get,
f − m = 2n
Substituting equation (v) in equation (iv), we get,
f + m = 14n − 2n
f + m = 12n
∵ The value of n is not known .
∴ We cannot find the combined age of parents.
∴ Statement B alone is not sufficient.
Hence, option (a).