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?

Let the total capital be Rs. $x$

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First part $= \dfrac{x}{4}$

Second part $= \dfrac{x}{3}$

Remaining part $= x - \dfrac{x}{4} - \dfrac{x}{3}$

Converting to common denominator 12:

$= \dfrac{12x}{12} - \dfrac{3x}{12} - \dfrac{4x}{12}$

$= \dfrac{5x}{12}$

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Using Simple Interest formula with time = 1 year:

Interest from first part:

$= \dfrac{x}{4} \times \dfrac{8}{100} \times 1$

$= \dfrac{2x}{100}$

Interest from second part:

$= \dfrac{x}{3} \times \dfrac{7}{100} \times 1$

$= \dfrac{7x}{300}$

Interest from remaining part:

$= \dfrac{5x}{12} \times \dfrac{10}{100} \times 1$

$= \dfrac{5x}{120}$

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Total interest equals Rs. 510:

$\dfrac{2x}{100} + \dfrac{7x}{300} + \dfrac{5x}{120} = 510$

Converting to common denominator 600:

$\dfrac{12x}{600} + \dfrac{14x}{600} + \dfrac{25x}{600} = 510$

$\dfrac{51x}{600} = 510$

$x = 510 \times \dfrac{600}{51}$

$x = \dfrac{306000}{51}$

$x = 6000$

Therefore, the total capital invested by Mr. X is Rs. 6000.