Question : An amount of Rs.12,029 is divided among P, Q, and R such that P's share is 5 times Q's share and R's share is one-third of P's share. what is the share of R?
Option 1: Rs. 2,718
Option 2: Rs. 2,312
Option 3: Rs. 2,615
Option 4: Rs. 2,518
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Correct Answer: Rs. 2,615
Solution :
Total amount = Rs. 12,029
P's share = 5Q
R's share = $\frac{1}{3}$P = $\frac{5}{3}$Q
P's Share + Q's Share + R's Share = 12029
$5\text{Q} + \text{Q} + \frac{5}{3}\text{Q}$ = 12029
⇒ $\frac{15\text{Q} + 3\text{Q} + 5\text{Q}}{3}$ = 12029
⇒ $\frac{23\text{Q}}{3}$ = 12029
⇒ 23Q = 36087
⇒ Q = Rs. 1569
$\therefore$ Share of Q is Rs. 1569
Now, we have to find the share of R.
R = $\frac{5}{3}$Q
⇒ R = $\frac{5}{3}$ × 1569
⇒ R = Rs. 2615
Hence, the correct answer is Rs. 2615.
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