Arjun and Bhavya started a business by investing Rs. 6000 and Rs. 9000 respectively. Bhavya invested for 6 months less than Arjun. If Arjun’s profit share was Rs. 14000 out of the total profit of Rs. 26000, then for how many months did Bhavya invest?

ATQ, In partnership questions, profit is divided in the ratio of capital × time. Let Bhavya invest for X months. According to the question, Bhavya invested for 6 months less than Arjun. So, Arjun invested for (X + 6) months. Arjun’s investment = Rs. 6000 Bhavya’s investment = Rs. 9000 Arjun’s profit share = Rs. 14000 Total profit = Rs. 26000 So, Bhavya’s profit share = 26000 − 14000 = Rs. 12000 Profit ratio of Arjun and Bhavya = 14000 : 12000 Divide both terms by 2000. 14000 ÷ 2000 = 7 12000 ÷ 2000 = 6 So, profit ratio = 7 : 6 Now, profit ratio is equal to the ratio of capital × time. Arjun : Bhavya = 6000 × (X + 6) : 9000 × X So, 6000 × (X + 6) : 9000 × X = 7 : 6 Cross multiply: 6000 × (X + 6) × 6 = 9000 × X × 7 36000(X + 6) = 63000X 36000X + 216000 = 63000X 63000X − 36000X = 216000 27000X = 216000 X = 216000 ÷ 27000 = 8 So, Bhavya invested for 8 months.