Question
There are five members P, Q, R, S and T in a family. R is the only child of Q. Four years ago, Q was 50 years old. The present age of the eldest member of the family is 64 years. R is younger than her husband S, and the present age difference between Q and R is 28 years. The ratio of the age of that female member who is not the youngest to the age of the youngest male member of the family is 8 : 5, respectively. S is the son-in-law of T, whose mother-in-law is P. The difference between the average present age of the female members and the average present age of the male members is 4 years (female average minus male average). Q is not anyone’s mother, and S is not older than any of his in-laws. Which of the following statement(s) is/are true?
I. The present age of the eldest member equals 165% of the present age of T.
II. Eight years hence from now, the ratio of ages of S and T will be 11 : 16 respectively.
III. The difference between the present ages of the youngest female and the eldest male is 28 years.
Solution
ATQ, From “4 years ago Q was 50”, Q(now) = 54. Difference Q − R = 28 ⇒ R = 54 − 28 = 26. By the relations, sexes are: Males: Q, S Females: P, T, R R is youngest female (26). Youngest male is S. The given ratio 8 : 5 is between T (a non-youngest female) and S, so T : S = 8 : 5. Using: T : S = 8 : 5 Average(females) − Average(males) = 4 Eldest age = 64 S is not older than his in-laws one gets consistent integer solutions, e.g.: Case 1: P = 64, Q = 54, R = 26, S = 30, T = 48 Case 2: P = 63, Q = 54, R = 26, S = 40, T = 64 In both cases: Youngest female = R = 26 Eldest male = Q = 54 Now check statements: I. Eldest = 64. 165% of T is not 64 in either case ⇒ false. II. Eight years later, S : T is not 11 : 16 in either case ⇒ false. III. Eldest male − youngest female = 54 − 26 = 28 ⇒ true. Answer: Only statement III is true.
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