A man invested frac{1}{3} of his capital at 7 | vedclass

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(C) Let the total capital invested be $₹ x$.The capital is divided into three parts:Part $1 = \frac{1}{3}x$ at $7 \%$ interest.Part $2 = \frac{1}{4}x$

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$6600$

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(C) Let the total capital invested be $₹ x$.The capital is divided into three parts:Part $1 = \frac{1}{3}x$ at $7 \%$ interest.Part $2 = \frac{1}{4}x$ at $8 \%$ interest.Part $3 = \left(1 - \frac{1}{3} - \frac{1}{4}ight)x = \left(\frac{12-4-3}{12}ight)x = \frac{5}{12}x$ at $10 \%$ interest.The total annual interest is given by:$	ext{Interest} = \left(\frac{\frac{1}{3}x 	imes 7}{100}ight) + \left(\frac{\frac{1}{4}x 	imes 8}{100}ight) + \left(\frac{\frac{5}{12}x 	imes 10}{100}ight) = 561$$\frac{7x}{300} + \frac{8x}{400} + \frac{50x}{1200} = 561$Finding a common denominator $(1200)$:$\frac{28x + 24x + 50x}{1200} = 561$$\frac{102x}{1200} = 561$$x = \frac{561 	imes 1200}{102} = 5.5 	imes 1200 = 6600$Thus,the total capital invested is ₹ $6600$.

$A$ man invested $\frac{1}{3}$ of his capital at $7 \%$,$\frac{1}{4}$ at $8 \%$,and the remaining at $10 \%$ rate of simple interest. If his annual income from interests is ₹ $561$,then the total capital invested (in ₹) was:

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