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