At a given rate,the simple interest and the t | vedclass

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(A) Let the sum be $P$,the time be $t$,and the rate be $r$. Simple Interest $(SI)$ = $\frac{P 	imes r 	imes t}{100} = 24$. True Discount $(TD)$ is t

Vedclass · Accepted Answer

$264$

Vedclass · Answer

(A) Let the sum be $P$,the time be $t$,and the rate be $r$. Simple Interest $(SI)$ = $\frac{P 	imes r 	imes t}{100} = 24$. True Discount $(TD)$ is the interest on the Present Worth $(PW)$. $TD = \frac{PW 	imes r 	imes t}{100} = 22$. We know that $SI - TD = 	ext{Interest on } (P - PW) = 	ext{Interest on } TD$. Thus,$SI - TD = \frac{TD 	imes r 	imes t}{100}$. From the formula,$Sum = \frac{SI 	imes TD}{SI - TD}$. Substituting the given values: $Sum = \frac{24 	imes 22}{24 - 22} = \frac{528}{2} = 264$. Therefore,the sum is $Rs. 264$.

At a given rate,the simple interest and the true discount on a certain sum,for a given time,are $Rs. 24$ and $Rs. 22$ respectively. The sum is (in $Rs.$)

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