Alok and Kajal started a business by investing Rs. 'X' and Rs. (X + 700), respectively. 20 months later, Kajal withdrew his entire investment. At the end of 24 months, the total profit from the business was Rs. 8,200, out of which profit share of Kajal was Rs. 1,800 more than that of Alok. Find the value of 'X'.

Number of months for which Alok invested in the business = 20 + 4 = 24 months Let the profit share of Alok out of the total profit of Rs. 8200 = Rs. 'Y' Then, profit share of Kajal out of the total profit of Rs. 8200 = Rs. (Y + 1800) So, Y + Y + 1800 = 8200 Or, Y = (8200 - 1800) ÷ 2 = 3200 So, profit shares of Alok and Kajal are Rs. 3,200 and Rs. 5,000, respectively. So, respective ratio of profit shares of Alok and Kajal = (X × 24):{(X + 700) × 20} = 24X:(20X + 14000) = 3200:5000 = 16:25 So, 24X × 25 = (20X + 14000) × 16 Or, 600X = 320X + 224000 Or, X = 224000 ÷ 280 = 800