Age of R after 12 years is 80% more than present age of P, while present age of T is 20% more

Q. Age of R after 12 years is 80% more than present age of P, while present age of T is 20% more than S. Find the present average age of P and Q together

Statement I: Present age of T is 80% more than P, while after 6 years age of Q is 50% as that of S.

Statement II: R is 12 years older than Q, and the respective ratio of age of R and S after 4 years is 14:17.

Statement III: P is 4 years younger than R and 8 years older than Q.

A. Either I alone or II alone is sufficient to answer the question

B. Either I alone or II and III together is sufficient to answer the question

C. III alone is sufficient to answer the question

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

E. None of these

Ans: Either III alone or I and II together is sufficient to answer the question

sol:

(R + 12) / P = 9/5

5R + 60 = 9P

9P – 5R = 60……………… (1)

T/S = 6/5…………… (2)

From Statement I,

T/P = 9/5

So, T:S:P = 18:15:10 [18a, 15a, 10a]

(Q + 6) / (S + 6) = 1/2

2Q + 12 = S + 6

S – 2Q = 6

Q = (S – 6)/2 = (15a – 6)/2

This statement alone is not sufficient to answer

the question

From Statement II,

R = 12 + Q

(R + 4) / (S + 4) = 14/17

17R + 68 = 14S + 56

14S – 17R = 12

This statement alone is not sufficient to answer

the question

From Statement III,

R – P = 4

Also, we have

9P – 5R = 60

On adding both equations, we get

4R = 96
Age of R = 24 years
Age of P = 24 – 4 = 20 years
Age of Q = 20 – 8 = 12 years
Required average = (20 + 12)/2 = 16 years
This statement alone is sufficient to answer the
question
On combining Statement (I + II),
Q = (15a – 6)/2
R = 12 + (15a – 6)/2 = (18 + 15a)/2
S = 15a
Also,
14S – 17R = 12
So,
14 x 15a – 17 x (18 + 15a)/2 = 12
Value of a = 2
So, age of Q = (15 x 2 – 6)/2 = 12
Age of P = 10 x 2 = 20
Required average = (20 + 12)/2 = 16 years
This combination is sufficient to answer the
questions.
Either I and II together or III alone is sufficient to
answer the question.
Hence answer is option D

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