Question:medium

12 men and 8 women can complete a piece of work in 10 days. How many days will it take for 15 men and 4 women to complete the same work
Statement 1: The amount of work done by a woman is three-fourth of the work done by a man in one day.
Statement 2: 15 men can complete the work in 12 days.

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 D

Solution and Explanation

The correct answer is option (D):
Either statement (1) alone or statement (2) alone is sufficient to answer the question

Let's break down this problem and analyze why the correct answer is what it is. The core concept here involves understanding work-rate problems, where we calculate how much work individuals or groups accomplish in a given amount of time.

The question asks for the number of days required for 15 men and 4 women to complete a task. We're given that 12 men and 8 women finish the same task in 10 days.

We have two statements that can give us more information to calculate the amount of work done by each individual and finally, find the solution.

Analyzing Statement 1: "The amount of work done by a woman is three-fourth of the work done by a man in one day."

This statement provides a crucial link between the work rate of a man and a woman. Let's denote the amount of work done by a man in one day as 'm' and the amount of work done by a woman in one day as 'w'. Statement 1 tells us that w = (3/4)m.

Using the information from the original problem (12 men and 8 women in 10 days), we can derive an equation representing the total work. The total work is equal to the number of people * their work rate * the number of days. So, 10 * (12m + 8w) = Total Work.

Substituting w = (3/4)m into this equation, we can express the total work in terms of 'm' only: 10 * (12m + 8 * (3/4)m) = Total Work. Simplifying this gives us the total work in terms of men's work rate.

We can then determine how long it takes for 15 men and 4 women to do the work. We'd use the equation: Days * (15m + 4w) = Total Work. Again substituting w = (3/4)m, we can determine the time required, because we know the "Total Work".

Therefore, with Statement 1 alone, we can solve the problem.

Analyzing Statement 2: "15 men can complete the work in 12 days."

This statement gives us another crucial piece of information: the work rate of 15 men. Using the information in the original question, we can know the amount of work done by 12 men and 8 women in 10 days.

From Statement 2, we know the total work done by the group of 15 men. We can use the information from the question in order to find the amount of work done by a woman by making an assumption that all the men do the work by themselves and then with the help of the information in the question, we can find the amount of work done by the women.

From the question we can create the equation: Total work = 10 * (12 * work done by a man + 8 * work done by a woman). Since we know the work done by the men from the second statement, we can plug in and solve for the total work and the work done by a woman. With the help of the work done by the men and the women, we can solve for the total amount of time required by 15 men and 4 women.

Therefore, with Statement 2 alone, we can also solve the problem.

Conclusion:

Either Statement 1 or Statement 2 alone is sufficient to provide the necessary information to solve the problem. Both are independent of each other and still provide the required information.
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