A man invested 1/3 of his capital at 7%, 1/4 at 8% and the remainder at 10%. If his annual income is Rs. 561, the capital is

let the total capital be Rs 12y

capital is invested at 7%, =$$\frac{1}{3}$$ x 12y = 4y

Capital invested at 8% = $$\frac{1}{4}$$ x 12y = 3y

Remaining capital = 12y - 7y = 5y

It is given that remaining capital is invested at 10% per annum

Simple Interest = $$\frac{P \times R \times T}{100}$$

Now , income in year = $$\frac{4y \times 7 \times 1}{100}$$ + $$\frac{3y \times 8 \times 1}{100}$$ + $$\frac{5y \times 10 \times 1}{100}$$ = 561

1.02y = 561

y = Rs 550

So principal amount = 12 y = 12 x 550 = Rs 6600