A person invested 1/3 of his capital at 7%; 1/4 of his capital at 8% and the remainder at 10%. If his total annual income from the investment is Rs. 561, then what is the total investment made by the person?

Correct option is A

Given:
One-third money invested at 7%
One-fourth money invested at 8%
Remainder invested at 10%
Total return = Rs 561
Solution:
Let the money be x
Then money invested at 7% is 1/3rd of x = x/3
Money invested at 8% is 1/4th of x = x/4
Remainder money = x - (x/3 +x/4) = 5x/12
Then:
​$$7\% \text{ of } \frac{x}{3} + 8\% \text{ of } \frac{x}{4} + 10\% \text{ of } \frac{5x}{12} = 561 \\\ \\\left( \frac{7}{3} + \frac{8}{4} + \frac{25}{6} \right)\% \text{ of } x = 561 \\\ \\\left( \frac{28 + 24 + 50}{12} \right)\% \text{ of } x = 561 \\\ \\x = \frac{561 \times 100 \times 12}{102} \\\ \\x = \text{Rs } 6600$$​​