If Rs. 21 is the true discount on Rs. 371 for | vedclass

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(D) True Discount $(T.D.)$ is the simple interest on the Present Worth $(P.W.)$.Given $T.D. = Rs. 21$ and Amount $(A)$ = $Rs. 371$.$P.W. = A - T.D. =

Vedclass · Accepted Answer

$39.75$

Vedclass · Answer

(D) True Discount $(T.D.)$ is the simple interest on the Present Worth $(P.W.)$.Given $T.D. = Rs. 21$ and Amount $(A)$ = $Rs. 371$.$P.W. = A - T.D. = 371 - 21 = Rs. 350$.Using the formula $T.D. = \frac{P.W. 	imes R 	imes T}{100}$,we have $21 = \frac{350 	imes R 	imes T}{100}$.Therefore,$R 	imes T = \frac{21 	imes 100}{350} = 6$.Now,for double the time,the new time is $2T$. The rate $R$ remains the same.New $T.D. = \frac{P.W. 	imes R 	imes (2T)}{100} = \frac{350 	imes R 	imes 2T}{100} = \frac{350 	imes 2 	imes (R 	imes T)}{100}$.Substituting $R 	imes T = 6$,we get New $T.D. = \frac{350 	imes 2 	imes 6}{100} = \frac{4200}{100} = Rs. 42$.Wait,re-evaluating the logic: The $P.W.$ changes when the time changes for a fixed amount. Let $P.W. = x$. Then $A = P.W. + T.D. = x + \frac{xRT}{100} = x(1 + \frac{RT}{100})$.For $T_1 = T$,$371 = P.W._1(1 + \frac{R 	imes T}{100}) \Rightarrow 371 = P.W._1(1 + 0.06) = 1.06 P.W._1 \Rightarrow P.W._1 = 350$.For $T_2 = 2T$,$371 = P.W._2(1 + \frac{R 	imes 2T}{100}) = P.W._2(1 + 0.12) = 1.12 P.W._2$.$P.W._2 = \frac{371}{1.12} = 331.25$.$T.D._2 = A - P.W._2 = 371 - 331.25 = Rs. 39.75$.

If $Rs. 21$ is the true discount on $Rs. 371$ for a certain time,what is the true discount on the same amount for double that time,the rate being the same in both the cases? (in $Rs.$)

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