Question
Two partners, X and Y, invested in a business in the
ratio of 5:8. After 5 months, X increased his capital by 25%, and 2 months later, he increased it again by 12%. Y reduced his capital by 25% after 4 months and then increased it by 25% after 5 more months. If the total profit at the end of the year is Rs. 27,632, what is Y's share of the profit?Solution
Let the investment of X = 5 And investment of Y = 8 So, profit after one year for X will be, = (5 × 5) + (5 × 125/100 × 2) + (5 × 125/100 × 112/100 × 5) = (5 × 5) + (6.25 × 2) + (7 × 5) = 25 + 12.5 + 35 = 72.5 Similarly, profit after one year for Y will be, = (8 × 4) + (8 × 75/100 × 5) + (8 × 75/100 × 125/100 × 3) = (8 × 4) + (6 × 5) + (7.5 × 3) = 32 + 30 + 22.5 = 84.5 So, ratio of profit after one year for X and Y = 72.5 : 84.5 = 145 : 169 Thus, the profit share of Y = 27,632 × 169/314 => Rs. 14,872 Hence, the required answer = Rs. 14,872.
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