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There are three persons P, Q, and R in a family, their ages arranged in ascending order

There are three persons P, Q, and R in a family, their ages arranged in ascending order

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

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