Mr. X invested one fourth of his capital at 8%, one third at 7% and the remaining part at 10%. If his annual simple interest on this investment is Rs 510, then the total capital invested by Mr. X is?

Rs. 6000

The correct answer is Option (2) → Rs. 6000

1. Determine the Fractions of Capital

Let the total capital be $C$. The investment is divided into three parts:

• Part 1: $\frac{1}{4}$ of capital at 8%
• Part 2: $\frac{1}{3}$ of capital at 7%
• Part 3: The remaining part at 10%

To find the "remaining part," we subtract the first two fractions from the whole:

$\text{Remaining Part} = 1 - \left(\frac{1}{4} + \frac{1}{3}\right)$

To add the fractions, find a common denominator (12):

$1 - \left(\frac{3}{12} + \frac{4}{12}\right) = 1 - \frac{7}{12} = \frac{5}{12}$

2. Set Up the Simple Interest Equation

The formula for annual simple interest is $\text{Interest} = \text{Principal} \times \text{Rate}$. The sum of the interest from all three parts equals Rs. 510:

$\left( \frac{1}{4}C \times \frac{8}{100} \right) + \left( \frac{1}{3}C \times \frac{7}{100} \right) + \left( \frac{5}{12}C \times \frac{10}{100} \right) = 510$

Simplify each term:

• $\frac{8C}{400} = \frac{2C}{100}$
• $\frac{7C}{300}$
• $\frac{50C}{1200} = \frac{5C}{120}$

To make calculations easier, let's use a common denominator of 1200 for all terms:

$\frac{24C}{1200} + \frac{28C}{1200} + \frac{50C}{1200} = 510$

$\frac{102C}{1200} = 510$

3. Solve for Total Capital ($C$)

$102C = 510 \times 1200$

$C = \frac{510 \times 1200}{102}$

Since $510 \div 102 = 5$:

$C = 5 \times 1200$

$C = 6000$

Conclusion:

The total capital invested by Mr. X is Rs. 6000.

Correct Option: Rs. 6000