Question

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.

• 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 D

To solve the problem, let's first denote the amount of work done by one man in one day as \(M\) and the work done by one woman in one day as \(W\). We are given that 12 men and 8 women can complete a piece of work in 10 days. This means the total work can be expressed as:

\((12M + 8W) \times 10 = \text{Total Work}\) (Equation 1) 

Now let's use the given statements:

1. Statement 1: The amount of work done by a woman is three-fourth of the work done by a man in one day, i.e., \(W = \frac{3}{4}M\).
2. Statement 2: 15 men can complete the work in 12 days. This implies:

\(15M \times 12 = \text{Total Work}\) (Equation 2)

Let's see how each statement helps:

Using Statement 1:

Substitute \(W = \frac{3}{4}M\) into Equation 1:

\((12M + 8 \times \frac{3}{4}M) \times 10 = \text{Total Work}\)

Simplifying,

\((12M + 6M) \times 10 = 180M = \text{Total Work}\)

Now, for 15 men and 4 women:

\(15M + 4 \times \frac{3}{4}M = 15M + 3M = 18M\)

Number of days required:

\(\frac{\text{Total Work}}{18M} = \frac{180M}{18M} = 10 \text{ days}\)

Using Statement 2:

From Equation 2:

\(180M = \text{Total Work}\)

Using this Total Work, the calculation for 15 men and 4 women remains the same,

Number of days required:

\(\frac{\text{Total Work}}{18M} = \frac{180M}{18M} = 10 \text{ days}\)

Both statements alone lead to the answer that it will take 10 days for 15 men and 4 women to complete the work.

Conclusion: Either statement (1) alone or statement (2) alone is sufficient to answer the question. Thus, the correct answer is: Either statement (1) alone or statement (2) alone is sufficient to answer the question.