A person has ₹ 5000. He invests a part of it | vedclass

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(D) Let the total sum be ₹ $5000$. The total interest earned in $3$ years is ₹ $750$.The average annual rate of interest is calculated as:$	ext{Avera

Vedclass · Accepted Answer

$3000, 2000$

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(D) Let the total sum be ₹ $5000$. The total interest earned in $3$ years is ₹ $750$.The average annual rate of interest is calculated as:$	ext{Average Rate} = \frac{	ext{Total Interest} 	imes 100}{	ext{Principal} 	imes 	ext{Time}} = \frac{750 	imes 100}{5000 	imes 3} = 5 \% 	ext{ per annum}$.Using the method of alligation:- Rate $1 = 3 \%$- Rate $2 = 8 \%$- Mean Rate = $5 \%$Difference between Rate $2$ and Mean Rate = $|8 - 5| = 3$Difference between Mean Rate and Rate $1$ = $|5 - 3| = 2$The ratio of the sums invested at $3 \%$ and $8 \%$ is $3 : 2$.Sum invested at $3 \% = \frac{3}{3+2} 	imes 5000 = \frac{3}{5} 	imes 5000 = ₹ 3000$.Sum invested at $8 \% = \frac{2}{3+2} 	imes 5000 = \frac{2}{5} 	imes 5000 = ₹ 2000$.

$A$ person has ₹ $5000$. He invests a part of it at $3 \%$ per annum and the remainder at $8 \%$ per annum simple interest. His total income in $3$ years is ₹ $750$. Find the sum invested at different rates of interest (in ₹).

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