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(B) Let the principal sum be $P = Rs. x$.Given,Compound Interest $(CI)$ = $Rs. 45.90$,Rate $(R)$ = $4 \%$,Time $(T)$ = $2 	ext{ years}$.Using the for

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$41.67$

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(B) Let the principal sum be $P = Rs. x$.Given,Compound Interest $(CI)$ = $Rs. 45.90$,Rate $(R)$ = $4 \%$,Time $(T)$ = $2 	ext{ years}$.Using the formula $CI = P \left[ (1 + \frac{R}{100})^T - 1 ight]$:$45.90 = x \left[ (1 + \frac{4}{100})^2 - 1 ight]$$45.90 = x \left[ (1.04)^2 - 1 ight] = x [1.0816 - 1] = x(0.0816)$$x = \frac{45.90}{0.0816} = Rs. 562.50$.Now,we need to find the True Discount $(TD)$ on $Rs. 562.50$ for $2 	ext{ years}$ at $4 \%$ simple interest.The formula for True Discount is $TD = \frac{P 	imes R 	imes T}{100 + (R 	imes T)}$.$TD = \frac{562.50 	imes 4 	imes 2}{100 + (4 	imes 2)} = \frac{4500}{108} = Rs. 41.666... \approx Rs. 41.67$.

If the compound interest on a certain sum of money for $2 \text{ years}$ at $4 \%$ per annum is $Rs. 45.90$,the true discount on the same amount of money due $2 \text{ years}$ hence at $4 \%$ per annum simple interest is (in $Rs.$):

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