A sum of Rs. 8448 is to be divided between X | vedclass

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(C) Let the shares of $X$ and $Y$ be $Rs. x$ and $Rs. (8448 - x)$ respectively.$X$ is $18$ years old,so the time remaining until age $21$ is $21 - 18

Vedclass · Accepted Answer

$4096$

Vedclass · Answer

(C) Let the shares of $X$ and $Y$ be $Rs. x$ and $Rs. (8448 - x)$ respectively.$X$ is $18$ years old,so the time remaining until age $21$ is $21 - 18 = 3$ years.$Y$ is $19$ years old,so the time remaining until age $21$ is $21 - 19 = 2$ years.The rate of interest $R = 6.25 \% = \frac{6.25}{100} = \frac{1}{16}$.According to the problem,the amounts received by both at age $21$ are equal:$x(1 + \frac{1}{16})^3 = (8448 - x)(1 + \frac{1}{16})^2$Dividing both sides by $(1 + \frac{1}{16})^2$:$x(1 + \frac{1}{16}) = 8448 - x$$x(\frac{17}{16}) = 8448 - x$$17x = 16(8448 - x)$$17x = 135168 - 16x$$33x = 135168$$x = \frac{135168}{33} = 4096$.Thus,the present share of $X$ is $Rs. 4096$.

$A$ 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 $Rs.$)

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