A and B start a business by investing Rs 24,000 and Rs 36,000 respectively. After 4 months, C joins with an investment of Rs x. At the end of the year, the profits are divided in the ratio 4 : 6 : 5 among A, B and C respectively. Find C’s investment.

Solution

Time of investment: A: 12 months B: 12 months C: (12 − 4) = 8 months Capital × time: A: 24,000 × 12 = 2,88,000 B: 36,000 × 12 = 4,32,000 C: x × 8 = 8x Profit ∝ capital × time. Given profit ratio A : B : C = 4 : 6 : 5 Actual ratio from capitals: 2,88,000 : 4,32,000 : 8x First simplify A:B: 2,88,000 : 4,32,000 = 2 : 3 So we can write ratio as: 2 : 3 : (8x / 1,44,000) (divide both A and B by 1,44,000) 2 : 3 : 8x/1,44,000 = 2 : 3 : x/18,000 We are told this is proportional to 4 : 6 : 5 Multiply both sides of 2 : 3 : x/18,000 by 2 to match 4 : 6: 4 : 6 : (2x/18,000) corresponds to 4 : 6 : 5 So: 2x / 18,000 = 5 ⇒ 2x = 5 × 18,000 = 90,000 ⇒ x = 45,000 Answer: C’s investment = Rs 45,000.