Rs. 20 is the true discount on Rs. 260 due af | vedclass

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(B) Let the principal amount be $P$ and the time be $t$. The amount due is $A = P + T.D. = 260$. Given $T.D. = 20$,so $P = 260 - 20 = 240$.Simple Inte

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$10.40$

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(B) Let the principal amount be $P$ and the time be $t$. The amount due is $A = P + T.D. = 260$. Given $T.D. = 20$,so $P = 260 - 20 = 240$.Simple Interest $(S.I.)$ on $P$ for time $t$ is equal to the True Discount $(T.D.)$,so $S.I. = 20$.Since $S.I. = \frac{P 	imes R 	imes t}{100}$,we have $20 = \frac{240 	imes R 	imes t}{100}$,which implies $R 	imes t = \frac{2000}{240} = \frac{25}{3}$.Now,for half the time $(t' = t/2)$,the new $T.D.'$ is the $S.I.$ on the present worth $P'$ for time $t/2$.The present worth $P'$ is calculated as $P' = \frac{A 	imes 100}{100 + (R 	imes t')}$.Substituting $R 	imes t' = \frac{1}{2} 	imes \frac{25}{3} = \frac{25}{6}$,we get $P' = \frac{260 	imes 100}{100 + 25/6} = \frac{260 	imes 600}{625} = \frac{156000}{625} = 249.6$.The new $T.D.' = A - P' = 260 - 249.6 = 10.40$.

$Rs. 20$ is the true discount on $Rs. 260$ due after a certain time. What will be the true discount on the same amount due after half of the earlier time,the rate of interest being the same? (in $Rs.$)

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