There are five members in a family – P, Q, R, S, and T. one fourth of the sum age of all members (except T) is 29 years

There are five members in a family – P, Q, R, S, and T. one fourth of the sum age of all members (except T) is 29 years. Find the age of T.

Statement I: Ratio of age of R, S, and T is 9:10:5 respectively and 20% of sum of ages of P and Q is 8 years

Statement II: Age of P is 50% more than Q, age of R is 10% less than S, while R is 12 years older than P. Difference between age of S and T is 20 years.

Statement III: Difference between Age of Q and T is 4 years. T is not the youngest person in the family.

A. alone is sufficient to answer

B. Either I or II alone is sufficient to answer

C.II alone is sufficient to answer

D. Either I alone or II and III together is sufficient to answer

E. Any one of them is sufficient

Sol:

(P + Q + R + S) = 29 x 4 = 116 years
From Statement I,
Let respective age of R, S, and T = 9a, 10a and
5a
(P + Q) = 5 x 8 = 40
Also,
(P + Q + R + S) = 116 years
So,
40 + 9a + 10a = 116
Value of a = 4

So, age of T = 5 x 4 = 20 years
This statement alone is sufficient to answer the
question.
From Statement II,
Let age of P and Q = 3a and 2a
Let age of R and S = 9b and 10b
Also, (P + Q + R + S) = 116
So,
3a + 2a + 9b + 10b = 116
5a + 19b = 116……………… (1)
Also,
9b – 3a = 12
3b – a = 4……………… (2)
On solving both equations
34b = 136
Value of b = 4
Value of a = 8
So, age of S = 10 x 4 = 40 years
Age of T = 40 + 20 or 40 – 20 = 60 or 20
This statement alone is not sufficient to answer
the question.
From Statement III,
T – Q = 4
This statement alone is not sufficient to answer
the question.
On combining Statement (II + III),
Age of P = 3a = 24 years
Age of Q = 2a = 2 x 8 = 16
Age of R = 36
Age of S = 40
Age of T = 16 + 4 = 20 years

This combination is sufficient to answer the
question.
Either I alone or II and III together is sufficient to
answer the question.
Hence answer is option D