CUET UG 2025 — General Test Arithmetic

Let the total capital be Rs. $x$x

---

First part $= \dfrac{x}{4}$=4x​

Second part $= \dfrac{x}{3}$=3x​

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

Converting to common denominator 12:

$$= \dfrac{12x}{12} - \dfrac{3x}{12} - \dfrac{4x}{12}$$=1212x​−123x​−124x​

$$= \dfrac{5x}{12}$$=125x​

---

Using Simple Interest formula with time = 1 year:

Interest from first part:

$$= \dfrac{x}{4} \times \dfrac{8}{100} \times 1$$=4x​×1008​×1

$$= \dfrac{2x}{100}$$=1002x​

Interest from second part:

$$= \dfrac{x}{3} \times \dfrac{7}{100} \times 1$$=3x​×1007​×1

$$= \dfrac{7x}{300}$$=3007x​

Interest from remaining part:

$$= \dfrac{5x}{12} \times \dfrac{10}{100} \times 1$$=125x​×10010​×1

$$= \dfrac{5x}{120}$$=1205x​

---

Total interest equals Rs. 510:

$$\dfrac{2x}{100} + \dfrac{7x}{300} + \dfrac{5x}{120} = 510$$1002x​+3007x​+1205x​=510

Converting to common denominator 600:

$$\dfrac{12x}{600} + \dfrac{14x}{600} + \dfrac{25x}{600} = 510$$60012x​+60014x​+60025x​=510

$$\dfrac{51x}{600} = 510$$60051x​=510

$$x = 510 \times \dfrac{600}{51}$$x=510×51600​

$$x = \dfrac{306000}{51}$$x=51306000​

$$x = 6000$$x=6000

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