An amount of ₹ 70,000 was lent at 6 % per ann | vedclass

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(B) Let the total sum be $P = ₹ 70,000$. The total simple interest $SI = ₹ 16,000$ for $T = 5 	ext{ years}$.First,calculate the effective annual rate

Vedclass · Accepted Answer

$20$

Vedclass · Answer

(B) Let the total sum be $P = ₹ 70,000$. The total simple interest $SI = ₹ 16,000$ for $T = 5 	ext{ years}$.First,calculate the effective annual rate of interest for the total sum:$SI = \frac{P 	imes R 	imes T}{100} \implies 16,000 = \frac{70,000 	imes R 	imes 5}{100}$$16,000 = 3,500 	imes R \implies R = \frac{16,000}{3,500} = \frac{160}{35} = \frac{32}{7} \%$.Using the method of alligation:Rate $1$: $6 \% = \frac{42}{7} \%$Rate $2$: $4 \% = \frac{28}{7} \%$Mean Rate: $\frac{32}{7} \%$Difference $1$ (between Mean and Rate $2$): $\frac{32}{7} - \frac{28}{7} = \frac{4}{7}$Difference $2$ (between Rate $1$ and Mean): $\frac{42}{7} - \frac{32}{7} = \frac{10}{7}$Ratio of amounts = $\frac{4}{7} : \frac{10}{7} = 4 : 10 = 2 : 5$.Sum lent at $6 \% = \frac{2}{2+5} 	imes 70,000 = \frac{2}{7} 	imes 70,000 = ₹ 20,000$.

An amount of ₹ $70,000$ was lent at $6 \%$ per annum and the remaining at $4 \%$ per annum. If the total simple interest from both the fractions in $5 \text{ years}$ was ₹ $16,000$,the sum lent at $6 \%$ per annum was (in ₹). (in $,000$)

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