A bill which is due at the end of 4 text{ yea | vedclass

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(C) Let the rate of interest be $r \%$ per annum.Let the sum of the bill (Present Worth) be $x$.The present worth $P$ is given by the formula $P = \fr

Vedclass · Accepted Answer

$713$

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(C) Let the rate of interest be $r \%$ per annum.Let the sum of the bill (Present Worth) be $x$.The present worth $P$ is given by the formula $P = \frac{100 	imes A}{100 + (r 	imes t)}$,where $A$ is the amount of the bill and $t$ is the time in years.For the first case: $575 = \frac{100x}{100 + 4r} \implies 57500 + 2300r = 100x \implies x = 575 + 23r$ ... $(1)$For the second case: $620 = \frac{100x}{100 + 2.5r} \implies 62000 + 1550r = 100x \implies 620 + 15.5r = x$ ... $(2)$Equating $(1)$ and $(2)$:$575 + 23r = 620 + 15.5r$$23r - 15.5r = 620 - 575$$7.5r = 45$$r = \frac{45}{7.5} = 6$Substituting $r = 6$ in $(1)$:$x = 575 + 23(6) = 575 + 138 = 713$.Thus,the sum of the bill is $Rs. 713$.

$A$ bill which is due at the end of $4 \text{ years}$ is now worth $Rs. 575$,but if it is due in $2 \frac{1}{2} \text{ years}$,it would now be worth $Rs. 620$. The sum of the bill is (in $Rs.$)

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