Question
A invests Rs. 60,000 in a business, and B invests Rs.
80,000. After 6 months, C joins with an investment of Rs. P. At the end of the year, the total profit is Rs. 1,29,600, of which C’s share is Rs. 28,800. What is the value of P?Solution
ATQ, Capital × time: A: 60,000 × 12 = 7,20,000 B: 80,000 × 12 = 9,60,000 C: P × 6 = 6P Divide all by 24,000 to simplify the ratio: A : B : C = 7,20,000/24,000 : 9,60,000/24,000 : 6P/24,000 = 30 : 40 : (P/4000). Let x = P/4000. Then ratio is 30 : 40 : x. Total ratio = 70 + x. C’s share of profit: x / (70 + x) × 1,29,600 = 28,800 So, x / (70 + x) = 28,800 / 1,29,600 = 2/9 => 9x = 2(70 + x) => 9x = 140 + 2x => 7x = 140 => x = 20 Thus P = 4000 × 20 = Rs. 80,000
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