‘X’ and ‘Y’ started a business with an initial investment of Rs. 5000 and Rs. 8000, respectively. After ‘Q’ months, ‘X’ withdrew 30% of his initial investment and ‘Y’ withdrew 40% of his initial investment while ‘Z’ entered into the business investing Rs. 10000. If total profit earned at the end of 2 years is Rs. 90000 and profit share of ‘X’ is Rs. 18000, then find the profit share of ‘Z’.
ATQ, Ratio of profit share of ‘X’, ‘Y’ and ‘Z’, respectively = [5000 × Q + 0.70 × 5000 × (24 – Q)]:[8000 × Q + 0.60 × 8000 × (24 – Q)]:[10000 × (24 – Q)] = [35Q + 8400]:[128Q + 7680]:[240000 – 10000Q] According to question; (35Q + 8400)/(128Q + 7680) = 18000/90000 = 1/5 Or, 175Q + 42000 = 128Q + 7680 Or, 47Q = -34320 Or, Q = 12 Profit share of ‘X’, ‘Y’ and ‘Z’, respectively = [35 × 12 + 8400]:[128 × 12 + 7680]:[ 240000 – 10000 × 12] = 8820:2304:108000 = 49:128:600 Profit share of 'Z' = (600/777) × 90000 = Rs.69300
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