Question
Ravi and Mohan started a business by investing Rs.
‘X’ and Rs. (X + 600), respectively. 18 months later, Mohan withdrew his entire investment. At the end of 24 months, the total profit from the business was Rs. 6,000, out of which profit share of Mohan was Rs. 1,200 more than that of Ravi. Find the value of ‘X’.Solution
Number of months for which Ravi invested in the business = 18 + 6 = 24 months Let the profit share of Ravi out of the total profit of Rs. 6000 = Rs. ‘Y’ Then, profit share of Mohan out of the total profit of Rs. 6000 = Rs. (Y + 1200) So, Y + Y + 1200 = 6000 Or, Y = (6000 − 1200) ÷ 2 = 2400 So, profit shares of Ravi and Mohan are Rs. 2,400 and Rs. 3,600, respectively. So, respective ratio of profit shares of Ravi and Mohan = (X × 24) : {(X + 600) × 18} = 24X : (18X + 10800) = 2400 : 3600 = 2 : 3 So, 24X × 3 = (18X + 10800) × 2 Or, 72X = 36X + 21600 Or, X = 21600 ÷ 36 = 600 Hence, X = 600
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