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(B) Let the principal be $P$ and the time be $T$ years.Using the formula for amount in simple interest: $A = P + \frac{P 	imes R 	imes T}{100} = P(1

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$100$

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(B) Let the principal be $P$ and the time be $T$ years.Using the formula for amount in simple interest: $A = P + \frac{P 	imes R 	imes T}{100} = P(1 + \frac{RT}{100})$.For the first case: $450 = P(1 + \frac{7T}{100}) \implies 450 = P + \frac{7PT}{100} \implies \frac{7PT}{100} = 450 - P$  --- $(1)$For the second case: $350 = P(1 + \frac{5T}{100}) \implies 350 = P + \frac{5PT}{100} \implies \frac{5PT}{100} = 350 - P$  --- $(2)$Dividing $(1)$ by $(2)$: $\frac{7PT/100}{5PT/100} = \frac{450 - P}{350 - P} \implies \frac{7}{5} = \frac{450 - P}{350 - P}$.Cross-multiplying: $7(350 - P) = 5(450 - P) \implies 2450 - 7P = 2250 - 5P$.$2450 - 2250 = 7P - 5P \implies 200 = 2P \implies P = 100$.The sum is ₹ $100$.

$A$ certain sum is invested for a certain time. It amounts to ₹ $450$ at $7 \%$ per annum. But when invested at $5 \%$ per annum,it amounts to ₹ $350$. Find the sum (in ₹).

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