If the simple interest on a certain sum for s | vedclass

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Question

(A) Let the sum be $P$,time be $T$ years,and rate be $R$. Simple Interest $(SI)$ at $6 \% = \frac{P 	imes T 	imes 6}{100} = 180$. True Discount $(TD

Vedclass · Accepted Answer

$2100$ and $1 \frac{3}{7}$

Vedclass · Answer

(A) Let the sum be $P$,time be $T$ years,and rate be $R$. Simple Interest $(SI)$ at $6 \% = \frac{P 	imes T 	imes 6}{100} = 180$. True Discount $(TD)$ at $5 \% = \frac{P 	imes T 	imes 5}{100 + (5 	imes T)} = 140$. From the first equation,$P 	imes T = \frac{180 	imes 100}{6} = 3000$. Substitute $P 	imes T = 3000$ into the second equation: $\frac{3000 	imes 5}{100 + 5T} = 140$. $15000 = 140(100 + 5T)$. $15000 = 14000 + 700T$. $1000 = 700T \implies T = \frac{10}{7} = 1 \frac{3}{7}$ years. Now,$P 	imes \frac{10}{7} = 3000 \implies P = 3000 	imes \frac{7}{10} = 2100$. Thus,the sum is $Rs. 2100$ and the time is $1 \frac{3}{7}$ years.

If the simple interest on a certain sum for some years at $6 \%$ is $Rs. 180$,and the true discount at $5 \%$ on the same amount for the same time is $Rs. 140$,find the sum (in $Rs.$) and the time (in $years$).

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