Question
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. The question consists of three statements numbered “I, II and III'' given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. A. Data in statement I and statement III together are necessary to answer the question. B Data in statement II and statement III together are necessary to answer the question. C Data in statement I and statement III together are necessary to answer the question. D Data in statement I, statement II and statement III together are necessary to answer the question. E Data in statement I or data in statement II or data in statement III alone are sufficient to answer the question.Solution
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.
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