'A' and 'B' together started a business where 'B' invested Rs. 600 more than 'A'. 6 months later, 'A' increased his investment by 80%. Out of the total annual profit of Rs. 9,000, if the profit shares of 'A' was Rs. 700 more than that of 'B', then find the investment made by 'B'.

Solution

ATQ, Let the amount invested by 'A', initially = Rs. 'Y' Then, amount invested by 'B', initially = Rs. (Y + 600) Let the annual profit share of 'B' = Rs. 'K' Then, annual profit share of 'A' = Rs. (K + 700) ATQ: K + K + 700 = 9,000 Or, 2K + 700 = 9,000 So, 'K' = (9,000 - 700) ÷ 2 = 4,150 So, ratio of profit shares of 'A' and 'B' respectively = (4,150 + 700):(4,150) = 15:14 Also, ratio of profit shares of 'A' and 'B' respectively: = {(Y × 6) + (Y × 1.8 × 6)}:{(Y + 600) × 12} So, 15Y:(12Y + 7,200) = 15:14 Or, 210Y = 168Y + 100,800 So, 'Y' = 100,800 ÷ 42 = 2,400 Therefore, investment made by 'B' = 2,400 + 600 = Rs. 3,000