Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: · Marks: · Difficulty:
Instead of dividing ₹ 117 among $P, Q, R$ in the ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$, by mistake it was divided in the ratio 2 : 3 : 4. Who gained in the transaction?
(a)Only $P$
(b)Only $Q$
(c)Only $R$
(d)Both $Q$ and $R$
Answer
Answer (as printed): D
Explanation
When money is divided in ratio of $\frac{\mathrm{1}}{\mathrm{2}}: \frac{\mathrm{1}}{\mathrm{3}}: \frac{\mathrm{1}}{\mathrm{4}}$ Ratio of shares $=\frac{1}{2}: \frac{1}{3}: \frac{1}{4}=6: 4: 3$. $P$ 's share $=₹\left(117 \times \frac{6}{13}\right)=₹ 54$; $Q$ 's share $=₹\left(117 \times \frac{4}{13}\right)=₹ 36 ;$ R's share $=₹\left(117 \times \frac{3}{13}\right)=₹ 27$. When money is divided in ratio of 2 : 3 : 4 $P$ 's share $=₹\left(117 \times \frac{2}{9}\right)=₹ 26$; $Q$ 's share $=₹\left(117 \times \frac{3}{9}\right)=₹ 39 ;$ R's share $=₹\left(117 \times \frac{4}{9}\right)=₹ 52$. Clearly, both $Q$ and $R$ gained in the transaction.