If the difference between the C.I. compounded | vedclass

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(C) Let the principal sum be $P$.Given time $T = 1 	ext{ year}$ and rate $R = 10 \% 	ext{ per annum}$.For simple interest $(SI)$: $SI = \frac{P 	im

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$10000$

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(C) Let the principal sum be $P$.Given time $T = 1 	ext{ year}$ and rate $R = 10 \% 	ext{ per annum}$.For simple interest $(SI)$: $SI = \frac{P 	imes R 	imes T}{100} = \frac{P 	imes 10 	imes 1}{100} = 0.1P$.For compound interest $(CI)$ compounded half-yearly: The rate becomes $R' = \frac{10}{2} = 5 \% 	ext{ per half-year}$ and time $n = 2 	ext{ half-years}$.$CI = P(1 + \frac{R'}{100})^n - P = P(1 + \frac{5}{100})^2 - P = P(1.05)^2 - P = P(1.1025) - P = 0.1025P$.The difference between $CI$ and $SI$ is $0.1025P - 0.1P = 0.0025P$.Given $0.0025P = 25$.$P = \frac{25}{0.0025} = \frac{250000}{25} = 10000$.Thus,the sum is $Rs. 10000$.

If the difference between the $C.I.$ compounded half-yearly and simple interest on a sum at $10 \%$ per annum for one year is $Rs. 25$,the sum (in $Rs.$) is:

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