Question : Rs. 2,60,200 is divided between Ram and Shyam so the amount that Ram receives in 4 years is the same as that Shyam receives in 6 years. If the interest is compounded annually at the rate of 4% per annum, then Ram's share is:
Option 1: Rs. 1,25,000
Option 2: Rs. 1,35,200
Option 3: Rs. 1,52,000
Option 4: Rs. 1,08,200
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Correct Answer: Rs. 1,35,200
Solution :
Let Ram's share be $x$ and Shyam's share be $y$.
$R=4$%
We know that $\text{Total amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
According to the given condition,
⇒ $x(1+\frac{4}{100})^{4}=y(1+\frac{4}{100})^{6}$
⇒ $\frac{x}{y}=\frac{(1+\frac{4}{100})^{6}}{(1+\frac{4}{100})^{4}}$
⇒ $\frac{x}{y}=(\frac{26}{25})^{2}$
⇒ $x:y=676:625$
$\therefore$ Ram's share $=\frac{676}{1301}×260200=135200$
Hence, the correct answer is Rs. 1,35,200.
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