The question below is followed by three statements I, II and III. You have to determine whether the data given is sufficient for answering the question. You should use the data and your knowledge of mathematics to choose the best possible answer. A, B and C are three partner in a business. They invested for x, y and z months. Their investment were in the ratio of 1 : 2 : 3. What is the profit A in the business when the total profit is Rs. 6000 I. x + y + z = 30 II. x, y and z are in the arithmetic progression. III. x > y?

Option 2 : All the statements together are required to answer the question.

The ratio of profit of A, B and C = x : 2y : 3z

Total profit = Rs. 6000

Statement I

x + y + z = 30     ---- (1)

Statement II

x, y and z are in the arithmetic progression.

⇒ 2y = x + z    ---- (2)

Solving equation (1) and (2)

⇒ y = 10

⇒ x + z = 20

But the value of x and z cannot be found.

Statement III

⇒ x > y

∵ x, y and z are in the arithmetic progression

⇒ Combining the statement III, the only possible value of x and z can be 12 and 8 respectively.

∴ Profit of A = x/(x + 2y + 3z) × 7000 = 12/(12 + 20 + 24) × 7000

⇒ 1500