There are three persons P, Q, and R in a family, their ages arranged in ascending order (P < Q < R). Difference between the present age of P and Q is the same as that of Q and R, while the difference between the ages of P and Q is more than 2. Product of their ages is 400% more than the sum of their ages. Find unit digit of (R – P) 13579. Ages of all three numbers are integers.
A.6
B.1
C.9
D.4
E. None of these
Ans: 4
Sol:
According to question,
Q – P = R – Q
2Q = P + R………………………. (1)
That means P, Q, and R in increasing AP.
P x Q x R = 500% x (P + Q + R)
P x Q x R = 5 x (P + Q +
R)………………………..(2)
Put 2Q = P + R
So,
P x Q x R = 5 x (2Q + Q)
P x Q x R = 15Q
P x R = 15
15 = 3 x 5
15 = 1 x 15
Difference between P and Q is more than 2, that
means difference between P and R is surely
more than difference between P and Q
So, P = 1, and R = 15
(R – P) = 14
1413579 = 4
41 = 4
42 = 6
43 = 4
So on odd powers of 4, we get unit digit 4
Hence answer is option D
