A man borrows money at 3 % per annum interest | vedclass

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(D) Let the sum borrowed be $₹ x$.Interest to be paid at $3 \%$ per annum simple interest for $1$ year $= x 	imes \frac{3}{100} = ₹ \frac{3x}{100}$.F

Vedclass · Accepted Answer

$16000$

Vedclass · Answer

(D) Let the sum borrowed be $₹ x$.Interest to be paid at $3 \%$ per annum simple interest for $1$ year $= x 	imes \frac{3}{100} = ₹ \frac{3x}{100}$.For the money lent at $5 \%$ compound interest payable half-yearly:Rate $= \frac{5}{2} \% = 2.5 \%$ per half-year.Time $= 2$ half-years.Amount received $= x \left(1 + \frac{2.5}{100}ight)^2 = x \left(1 + \frac{1}{40}ight)^2 = x \left(\frac{41}{40}ight)^2 = x 	imes \frac{1681}{1600}$.Compound Interest earned $= x \left(\frac{1681}{1600} - 1ight) = \frac{81x}{1600}$.Gain $= 	ext{Interest earned} - 	ext{Interest paid} = \frac{81x}{1600} - \frac{3x}{100} = \frac{81x - 48x}{1600} = \frac{33x}{1600}$.Given,gain $= ₹ 330$.$\frac{33x}{1600} = 330 \implies x = \frac{330 	imes 1600}{33} = 10 	imes 1600 = ₹ 16000$.

$A$ man borrows money at $3 \%$ per annum interest payable yearly and lends it immediately at $5 \%$ interest (compound) payable half-yearly and thereby gains ₹ $330$ at the end of the year. The sum borrowed (in ₹) is

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