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The ratio of the present ages of P and Q is 5:7, and six years ago, the age of R was equal to the age of Q four years hence. If the difference between P’s age after nine years and Q’s present age is seven years, then find the average of the present ages of P, Q, and R.

1. 19 years
2. 29/3 years
3. 25/3 years
4. 12 years

Correct answer: 29/3 years

Solution

Let present ages of P and Q be \(5x\) and \(7x\). Since P’s age after 9 years exceeds Q’s present age by 7, \(5x+9-7x=7\), giving \(x=1\), so P=5 and Q=7. Also, R six years ago equals Q four years hence, so \(R-6=11\), hence R=17. Average = \((5+7+17)/3 = 29/3\).

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