Question:medium

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

Updated On: Jan 13, 2026
  • Statement (1) alone is sufficient to answer the question
  • Statement (2) alone is sufficient to answer the question
  • Both the statements together are needed to answer the question
  • Either statement (1) alone or statement (2) alone is sufficient to answer the question
  • Neither statement (1) nor statement (2) suffices to answer the question
Show Solution

The Correct Option is B

Solution and Explanation

The correct answer is option (B):
Statement (2) alone is sufficient to answer the question

Here's why statement (2) alone is sufficient to answer the question:

The key to solving this type of problem is understanding how profits are divided in a partnership. The profit share is directly proportional to the investment amount and the time for which the investment was made.

Let's denote the time for which A invested as TA (which is equal to the entire duration of the business), and the time for which B invested as TB. Let X be the number of years after which B joined. Since the business has run for a total of TA = 3 years (from statement 1), and B joined X years after A, then TB = TA - X = 3-X.

The profit ratio is given as 2:1 for A and B. We also know the investment amounts: A invested Rs. 4500 and B invested Rs. 3000. The profit share ratio can be expressed as:

(A's Investment * A's Time) / (B's Investment * B's Time) = 2/1

Looking at the statements individually:

Statement 1: Provides information about the business's total run time. However, this alone doesn't tell us when B joined. We still don't know the profit ratio or how long B's investment was active. Not sufficient.

Statement 2: We can work with the profit ratio given in statement 2 and not need statement 1, since the profit sharing ratio is for ONE year only. The statement 2 tells us the profit sharing ratio at the end of the year. Let the investment of A remain active for T years, and the investment of B remain active for (T - X) years. The profit-sharing ratio is:
(4500 * T) / (3000 * (T - X)) = 2/1

Since statement 2 gives the ratio *at the end of one year,* this means that A and B have been invested for 1 year. The time period is 1 year. Then T = 1 year, and TB = (1-X) years. We can rewrite the profit ratio equation as:

(4500 * 1) / (3000 * (1 - X)) = 2 / 1
4500 / 3000(1-X) = 2/1
4500 = 6000(1-X)
4500 = 6000 - 6000X
6000X = 1500
X = 1500/6000
X = 0.25 years

Therefore, from Statement 2 alone, we can find out after how many years B joined.
Statement 2 alone is sufficient.
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