Question

A started a business with an investment of Rs. 4,500 and B joined after some period with Rs. 3000. After how many years did B join in the business?
Statement 1: The business has run for 3 years
Statement 2: The ratio of profits shared by A and B at the end of one year is in the ratio 2 : 1

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question

Answer 1

The Correct Option is B

To find out after how many years B joined the business, let's analyze each statement: 

Statement 1: The business has run for 3 years

This statement only provides the total duration for which the business ran but does not specify when B joined. Therefore, this statement alone is not sufficient to determine after how many years B joined the business.

Statement 2: The ratio of profits shared by A and B at the end of one year is in the ratio 2 : 1

The profit-sharing ratio at the end of the year is dependent on both the amount of investment and the duration for which the investment was active. Let's denote:

• The total duration of the business is 3 years (from Statement 1; not directly needed, but useful for overall context).
• Let \( x \) be the number of years B was involved in the business.
• A's total investment period is 3 years.

The profit ratio is given by: \(\frac{4500 \times 3}{3000 \times x} = \frac{2}{1}\)

Solving the equation:

• From the profit-sharing formula, we have: \(4500 \times 3 = 2 \times 3000 \times x\)
• Solving for \( x \) \(4500 \times 3 = 6000x\)
• Simplifies to: \(13500 = 6000x\)
• Calculate \( x \): \(x = \frac{13500}{6000}\) \(x = 2.25\)

 

According to the calculations, B joined 0.75 years (9 months) after the start of the business.

Thus, Statement 2 alone is sufficient to answer the question.

Therefore, the correct option is: Statement (2) alone is sufficient to answer the question.