Rs., 20 is the true discount on Rs., 210 due | vedclass

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(D) Let the sum be $P$,the rate be $R$,and the time be $T$. The true discount $(TD)$ is the simple interest on the present worth $(PW)$.Given $TD = Rs

Vedclass · Accepted Answer

$10.50$

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(D) Let the sum be $P$,the rate be $R$,and the time be $T$. The true discount $(TD)$ is the simple interest on the present worth $(PW)$.Given $TD = Rs.\, 20$ and Amount $(A)$ $= Rs.\, 210$.Present Worth $(PW)$ $= A - TD = 210 - 20 = Rs.\, 190$.Simple Interest on $PW$ $(190)$ for time $T$ at rate $R$ is $20$.Now,we need the true discount on the same sum $(Rs.\, 210)$ for time $T/2$.The new $PW'$ for the amount $210$ at time $T/2$ is given by $PW' = \frac{100 	imes A}{100 + (R 	imes T/2)}$.Since $TD = \frac{P 	imes R 	imes T}{100} = 20$,we have $R 	imes T = \frac{2000}{190} = \frac{200}{19}$.For time $T/2$,the simple interest on $190$ is $10$.Thus,the $TD$ on $Rs.\, 200$ (which is $190 + 10$) is $10$.Therefore,the $TD$ on $Rs.\, 210$ is $\left(\frac{10}{200} 	imes 210ight) = Rs.\, 10.50$.

$Rs.\, 20$ is the true discount on $Rs.\, 210$ due after a certain time. What will be the true discount on the same sum due after half of the former time,the rate of interest being the same? (in $Rs.$)

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