Arun invested a sum of money at a certain rat | vedclass

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(D) Let the principal be $P$ and the rate of interest be $R$ percent per annum.In the first case,the time $T_1 = 4$ years. The simple interest $SI_1 =

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Cannot be determined

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(D) Let the principal be $P$ and the rate of interest be $R$ percent per annum.In the first case,the time $T_1 = 4$ years. The simple interest $SI_1 = \frac{P 	imes R 	imes 4}{100}$.In the second case,the time $T_2 = 6$ years. The simple interest $SI_2 = \frac{P 	imes R 	imes 6}{100}$.According to the problem,$SI_2 = SI_1 + 50\% 	ext{ of } SI_1 = 1.5 	imes SI_1$.Substituting the formulas: $\frac{P 	imes R 	imes 6}{100} = 1.5 	imes \frac{P 	imes R 	imes 4}{100}$.Simplifying this: $\frac{6PR}{100} = 1.5 	imes \frac{4PR}{100} \Rightarrow \frac{6PR}{100} = \frac{6PR}{100}$.Since both sides result in the same expression,the variables $P$ and $R$ cancel out,meaning the relationship holds true for any rate of interest $R$. Therefore,the specific rate of interest cannot be determined from the given information.

Arun invested a sum of money at a certain rate of simple interest for a period of $4$ years. Had he invested the same sum for a period of $6$ years,the total interest earned by him would have been $50$ percent more than the earlier interest amount. What was the rate of interest per cent per annum?

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