Aman and Aamandeep started a Factory together with an investment of Rs.(x + 500) and Rs.(x+1100) respectively. After 3 months, Akshay joined them with an investment of Rs.(x – 100). After a year they received a total profit of Rs. 22750 where it is decided that Amandeep will be given 20% of the profit for managing the Factory equipments.What will be the total profit share of Amandeep? Statement-I: Profit share of Aman is Rs.6500. Statement-II: If Akshay would have joined after 6 months of the start of the factory, his profit share out of the total profit will be Rs.2800. Statement-III: The difference of profit share of Aman and Akshay is Rs.2600.

ATQ, Ratio of profit share: Aman: Amandeep: Akshay = (x + 500) × 12: (x + 1100) × 12: (x – 100) × 9 = 4(x + 500):4(x + 1100): 3(x – 100) Profit share of Amandeep for managing the business = 0.2 × 22750 = Rs. 4550 Therefore, remaining profit = 22750 – 4550 = Rs.18200 Statement-I: ATQ, 4(x + 500)/ [4(x + 500) + 4(x + 1100) + 3(x – 100)] = 6500/18200 After solving we will get x = 2500 Therefore, ratio of the profit share: Aman: Amandeep: Akshay = 4(x + 500): 4(x + 1100): 3(x – 100) = 4(3000): 4(3600): 3(2400) = 5: 6: 3 So, profit share of Amandeep = [6/ (5 + 6 + 3)] × 18200 + 4550 = Rs. 12350 Hence, the question can be solved using statement-I alone. Statement-II: Ratio of profit share:Aman: Amandeep: Akshay = (x+500) ×12: (x+1100) × 12: (x–100) × 6 = 2(x + 500): 2(x + 1100): (x – 100) ATQ, (x – 100)/ [2(x + 500) + 2(x + 1100) + (x – 100)] = 2800/18200 After solving above we will get x = 2500 Therefore, ratio of the profit share: Ashutosh: Aakash: Aditya = 5: 6: 3 So, profit share of Aakash = [6/ (5 + 6 + 3)] × 18200 + 4550 = Rs. 12350 Hence, the question can be solved using statement-II alone. Statement-III: ATQ, [4(x + 500) – 3(x – 100)]/ [4(x + 500) + 4(x + 1100) + 3(x – 100)] = 2600/18200 After solving above we will get, x= 2500 Therefore, ratio of the profit share: Aman: Amandeep: Akshay = 4(x + 500): 4(x + 1100): 3(x – 100) = 4(3000): 4(3600): 3(2400) = 5: 6: 3 So, profit share of Aakash = [6/ (5 + 6 + 3)] × 18200 + 4550 = Rs. 12350 Hence, the question can be solved using statement-III alone. Hence, option e.