Amit and Sumit started a business by investing Rs. ‘X’ and Rs. (X + 400), respectively. 16 months later, Sumit withdrew his entire investment. At the end of 20 months, the total profit from the business was Rs. 5,600, out of which profit share of Sumit was Rs. 1,600 more than that of Amit. Find the value of ‘X’.

Number of months for which Amit invested in the business = 16 + 4 = 20 months Let the profit share of Amit out of the total profit of Rs. 5600 = Rs. ‘Y’ Then, profit share of Sumit out of the total profit of Rs. 5600 = Rs. (Y + 1600) So, Y + Y + 1600 = 5600 Or, Y = (5600 − 1600) ÷ 2 = 2000 So, profit shares of Amit and Sumit are Rs. 2,000 and Rs. 3,600, respectively. So, respective ratio of profit shares of Amit and Sumit = (X × 20) : {(X + 400) × 16} = 20X : (16X + 6400) = 2000 : 3600 = 5 : 9 So, 20X × 9 = (16X + 6400) × 5 Or, 180X = 80X + 32000 Or, X = 32000 ÷ 100 = 320 Hence, X = 320