Three times the present age of P exceeds the present age of Q by 23 years. After 7 years, six times Q’s age will be 30 years less than six times P’s age at that time. What is the present age (in years) of Q?
Given:
3P − Q = 23
After 7 years: 6(Q + 7) = 6(P + 7) − 30
Solution:
Let P = p, Q = q.
From statement 1:
3p = q + 23
q = 3p - 23
From statement 2:
6(q + 7) = 6(p + 7) - 30
6q + 42 = 6p + 42 - 30
6q = 6p - 30
q = p - 5
Equate the two expressions for (q):
p - 5 = 3p - 23
18 = 2p
p = 9
Then q = p - 5 = 9 - 5 = 4
Present age of Q = 4 years
Alternate Solution (short trick ):
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