CAT 2003 Slot 2 — DILR Question 4
Choose 1, if the question can be answered by using statement A alone but not by using B alone.
Choose 2, if the question can be answered by using statement B alone but not by using A alone.
Choose 3, if the question can be answered by using either statement alone.
Choose 4, if the question can be answered by using both the statements together but not by either statement.
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 & solution
1
- B
2
- C
3
- D
4
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
âµ The value of n is not known .
∴ We cannot find the combined age of parents.
∴ Statement B alone is not sufficient.
Hence, option (a).