Question : A sum of Rs. 120 is divided among p, q, and r in such a way that p gets Rs. 9 more than q and q gets Rs. 6 more than r. What is the ratio of shares of p, q, and r respectively?
Option 1: 18 : 15 : 13
Option 2: 15 : 12 : 10
Option 3: 16 : 13 : 11
Option 4: 11 : 8 : 10
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Correct Answer: 16 : 13 : 11
Solution : Given, A sum of Rs. 120 is divided among p, q, and r. According to the question, p gets Rs. 9 more than q ⇒ p = 9 + q ...............(1) And, q gets Rs. 6 more than r ⇒ q = 6 + r ⇒ r = q – 6 ................(2) Also, p + q + r = 120 Putting values from (1) and (2), we get, ⇒ 9 + q + q + q - 6 = 120 ⇒ 3q + 3 = 120 ⇒ 3q = 117 $\therefore$ q = 39 ⇒ p = 9 + 39 = 48 ⇒ r = 39 – 6 = 33 ⇒ p : q : r = 48 : 39 : 33 = 16 : 13 : 11 Hence, the correct answer is 16 : 13 : 11.
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