The simple interest on a certain sum of money | vedclass

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(C) Let the principal sum be $P$.The Simple Interest ($S$.$I$.) for $3$ years at $8 \%$ per annum is given by:$S.I. = \frac{P 	imes 3 	imes 8}{100}

Vedclass · Accepted Answer

$1750$

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(C) Let the principal sum be $P$.The Simple Interest ($S$.$I$.) for $3$ years at $8 \%$ per annum is given by:$S.I. = \frac{P 	imes 3 	imes 8}{100} = \frac{24P}{100} = 0.24P$ (Equation $1$)The Compound Interest ($C$.$I$.) on ₹ $4000$ for $2$ years at $10 \%$ per annum is:$C.I. = 4000 \left(1 + \frac{10}{100}ight)^2 - 4000$$C.I. = 4000 \left(\frac{11}{10}ight)^2 - 4000 = 4000 	imes 1.21 - 4000 = 4840 - 4000 = 840$ (Equation $2$)According to the problem,the simple interest is half of the compound interest:$S.I. = \frac{1}{2} 	imes C.I.$$0.24P = \frac{1}{2} 	imes 840$$0.24P = 420$$P = \frac{420}{0.24} = \frac{42000}{24} = 1750$Thus,the sum placed on simple interest is ₹ $1750$.

The simple interest on a certain sum of money for $3$ years at $8 \%$ per annum is half the compound interest on ₹ $4000$ for $2$ years at $10 \%$ per annum. The sum placed on simple interest (in ₹) is

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