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(D) Let the original rate of interest be $R \%$. Then,the new rate of interest is $(2R) \%$.The first sum of $Rs. 725$ is lent for $1$ year ($12$ mont

Vedclass · Accepted Answer

$3.46$

Vedclass · Answer

(D) Let the original rate of interest be $R \%$. Then,the new rate of interest is $(2R) \%$.The first sum of $Rs. 725$ is lent for $1$ year ($12$ months).The second sum of $Rs. 362.50$ is lent for $4$ months (since it was lent after $8$ months,the remaining time in the year is $12 - 8 = 4$ months,which is $4/12 = 1/3$ of a year).Using the simple interest formula $SI = (P 	imes R 	imes T) / 100$:Interest from the first loan $= (725 	imes R 	imes 1) / 100$Interest from the second loan $= (362.50 	imes 2R 	imes 1/3) / 100$Total interest $= 33.50$$(725R / 100) + (725R / 300) = 33.50$Multiply the entire equation by $300$ to clear the denominators:$3(725R) + 725R = 33.50 	imes 300$$2175R + 725R = 10050$$2900R = 10050$$R = 10050 / 2900 \approx 3.4655 \%$Rounding to the nearest provided option,the original rate is $3.46 \%$.

$A$ sum of $Rs. 725$ is lent in the beginning of a year at a certain rate of interest. After $8$ months,a sum of $Rs. 362.50$ more is lent but at the rate twice the former. At the end of the year,$Rs. 33.50$ is earned as interest from both the loans. What was the original rate (in $\%$) of interest?

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