Question
Amit, Bhanu, and Chintu started a
business where Bhanu invested Rs. 1,500 more and Chintu invested Rs. 200 less than Amit. The task is to determine the amount initially invested by Amit. Statement I: The ratio of the time periods for which Amit, Bhanu, and Chintu invested is 3:4:5, respectively. Also, the combined profit share of Amit and Chintu is equal to 70% of Bhanu's profit share. Statement II: Amit withdrew his investment 6 months after starting the business, while Bhanu and Chintu withdrew their investments 2 months and 4 months after Amit, respectively. If Amit had invested 60% more and Bhanu had invested Rs. 450 less, Chintu's profit share would have remained unchanged. The question consists of two statements numbered "l and II" given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.Solution
ATQ, Let the investment of ‘Amit’ = Rs. ‘y’ Then investment of ‘Bhanu’ = Rs. (y + 1500) Investment of ‘Chintu’ = Rs. (y – 200) Statement I: Ratio of profit shares of ‘Amit’, ‘Bhanu’ and ‘Chintu’, respectively = (y × 3):{(y + 1500) × 4}:{(y – 200) × 5} = (3y):(4y + 6000):(5y – 1000) We have, (3y + 5y – 1000) = (4y + 6000) × 0.7 Or, 8y – 1000 = 2.8y + 4200 Or, 5.2y = 5200 So, y = (5200/5.2) = 1000 So initial investment made by ‘Amit’ = y = Rs 1000 So, data in statement I alone is sufficient to answer the question. Statement II: Time period of investment of ‘Bhanu’ and ‘Chintu’ = (6 + 2) and (6 + 4) i.e. 8 months and 10 months, respectively Increased investment of ‘Amit’ = y × 1.6 = Rs. ‘1.6y’ Decreased investment of ‘Bhanu’ = y + 1500 – 450 = Rs. (y + 1050) According to the statement, (1.6y × 6) + (y + 1050) × 8 = (y × 6) + (y + 1500) × 8 (Since investment and time period of investment of ‘Chintu’ does not change) Or, 9.6y + 8y + 8400 = 6y + 8y + 12000 Or, 17.6y + 8400 = 14y + 12000 So, y = 3600 ÷ 3.6 = 1000
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