A and B started a business by investing Rs.2,400 and Rs. 3,600 respectively. At the end of 4th month from the start, C joined with Rs. x. After 8 months from start of the business, B withdrew Rs. 600. If C's share is Rs. 8,000 in annual profit of Rs. 22,500 then amount invested by Cis:

Correct option is A

Given:

Investment by A = Rs 2400

Investment by B = Rs 3600

After the 4th month, C joined with Rs x.

After 8 months, B withdrew Rs 600 from the business.

Total annual profit = Rs 22,500

C's share = Rs 8000

Formula Used:

Profit Share = Amount Invested × Duration of Investment

Solution:

Total duration for which A invested: 1 year = 12 months

B invested Rs 3600 for 8 months, and then Rs (3600 - 600) = 3000 for 4 months

C invested Rs x for 8 months.

Profit share of A, B, and C in ratio:

(2400×12) : (3600×8 + 3000×4) : (x×8)

Simplify:

A's share: 2400×12 = 28800

B's share: 3600 × 8 + 3000 × 4 = 28800 + 12000 = 40800

C's share: x × 8 = 8x

Total profit = Rs 22,500. C's share:

$$\frac{8x}{28800 + 40800 + 8x} \times 22500 = 8000$$​​

​$$\text{Simplify: } \\\frac{8x}{69600 + 8x} = \frac{8000}{22500} \\\text{Cross multiply: } \\45 \times 8x = 16 \times (69600 + 8x) \\45x = 16 \times 69600 + 16x \\45x - 16x = 1113600 \\29x = 1113600 \\x = \frac{1113600}{29} = 4800 \\\text{C's investment: Rs } 4800$$​​