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6.Interest
hard
A sum of $Rs. 8448$ is to be divided between $X$ and $Y$ who are respectively $18$ and $19 \,yr$ old, in such a way that if their shares be invested at $6.25 \%$ per annum at compound interest, they will receive equal amounts on attaining the age of $21 \,yr$. The present share of $X$ is (In $Rs.$)
A
$4225$
B
$4352$
C
$4096$
D
$4000$
Solution
Let shares of $X$ and $Y$ be $R$ s. $x$ and $R s .(8448-x),$ respectively. Amount got by $X$ after 3 years $=$ Amount got by $Y$ after 2 years
$x\left(1+\frac{6.25}{100}\right)^{3}=(8448-x) \times\left(1+\frac{6.25}{100}\right)^{2}$
$\Rightarrow 1+\frac{6.25}{100}=\frac{8448-x}{x} \Rightarrow 1+\frac{1}{16}=\frac{8448-x}{x}$
$\Rightarrow \frac{17}{16}=\frac{8448-x}{x} \Rightarrow 17 x=135168-16 x \Rightarrow$
$x=$ Rs. 4096
Standard 13
Quantitative Aptitude
