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
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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