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.

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