Question

The Given question is followed by two statements A and B. You are to determine whether the data given in the statements is sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose between the possible answers.
How many women can complete a piece of work in10 days?
A If the same piece of work is completed by 4 men in 6 days.
B. If the same piece of work is completed by 7 women in 14 days.

• A. The statement A alone is sufficient to answer the question, but the statement B alone is not sufficient.
• B. The statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.
• C. Both statements A and B together are needed to answer the question.
• D. Either the statement A alone or statement B alone is sufficient to answer the question.
• E. Cannot get the answer from the statement A and B together, but need even more data.

Answer 1

The Correct Option is B

We can solve this problem using only statement B.
Using Statement B
7 women complete the work in 14 days.

Let's find the work done by one woman in one day

Work done by 7 women in 1 day = \(\frac{1}{14}\)

Work done by 1 woman in 1 day = \(\frac{\frac{1}{14}}{7} = \frac{1}{98}\)

Now let's find how many women are needed to complete the work in 10 days

• Work done by 1 woman in 10 days = \(\frac{1}{98} \times 10 = \frac{10}{98} = \frac{1}{9.8}\)
• Number of women required to complete the work in 10 days = 9.8.
• Since we can't have fractions of people, we round 9.8 up to the nearest whole number.

Therefore, 10 women are needed to complete the work in 10 days
Final Answer: The statement B alone is sufficient to answer the question, but the statement A alone is not sufficient.
So the correct option is (B)