Question

Two persons $X$ and $Y$ lent certain amounts at the same rate of interest for 2 years and 3 years, respectively, under compound interest. If their final amounts are in the ratio of $2: 5$, $Y$ s amount at the end of the first year being $₹ 4000$ and $X$ earned an interest of $₹ 160$ for the first year, then find the ratio of their principals.

• A. $22: 50$
• B. $27: 47$
• C. $35: 61$
• D. $22: 51$

Answer 1

Answer: (A)

$P_1, P_2$ are the principals of $X$ and $Y$.
$\frac{P_1(1+\frac{R}{100})^2}{P_2(1+\frac{R}{100})^3}=\frac{2}{5} $
$\Rightarrow \frac{P_1}{P_2(1+\frac{R}{100})}=\frac{2}{5} \Rightarrow \frac{P_1}{4000}=\frac{2}{5}$
$\Rightarrow P_1=1600 . $
$\Rightarrow \frac{P_1 \times 1 \times R}{100}=400$
$\Rightarrow P_2(1+\frac{R}{100})=4000 . $
$\Rightarrow P_2(1+\frac{10}{100})=4000 \Rightarrow P_2 \times \frac{11}{10}=4000 $
$\Rightarrow P_2=4000 \times \frac{10}{11} . $
$\therefore P_1: P_2=1600: 4000 \times \frac{10}{11} $
$=2: \frac{50}{11}=22: 50 .$