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