A man invests a certain sum of money at 6 % p | vedclass

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(C) Let the two sums be $P_1$ and $P_2$. Given $R_1 = 6 \%$,$R_2 = 7 \%$,and $T = 2 	ext{ years}$.The total interest is given by: $\frac{P_1 	imes 6

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$2700$

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(C) Let the two sums be $P_1$ and $P_2$. Given $R_1 = 6 \%$,$R_2 = 7 \%$,and $T = 2 	ext{ years}$.The total interest is given by: $\frac{P_1 	imes 6 	imes 2}{100} + \frac{P_2 	imes 7 	imes 2}{100} = 354$.Simplifying this: $\frac{12P_1 + 14P_2}{100} = 354 \Rightarrow 12P_1 + 14P_2 = 35400 \Rightarrow 6P_1 + 7P_2 = 17700$ (Equation $1$).Given that one-fourth of the first sum is equal to one-fifth of the second sum: $\frac{P_1}{4} = \frac{P_2}{5} \Rightarrow P_2 = \frac{5P_1}{4}$ (Equation $2$).Substituting Equation $2$ into Equation $1$: $6P_1 + 7(\frac{5P_1}{4}) = 17700$.Multiply by $4$: $24P_1 + 35P_1 = 70800 \Rightarrow 59P_1 = 70800 \Rightarrow P_1 = 1200$.Then $P_2 = \frac{5 	imes 1200}{4} = 1500$.Total sum invested $= P_1 + P_2 = 1200 + 1500 = 2700$.

$A$ man invests a certain sum of money at $6 \%$ $p.a.$ simple interest and another sum at $7 \%$ $p.a.$ simple interest. His income from interest after $2$ $years$ was $Rs. 354$. One-fourth of the first sum is equal to one-fifth of the second sum. Find the total sum (in $Rs.$) he invested.

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