Question

The questions below consists of a question and three statements numbered I, II and II given below it. You have to study the questions and decide that the data in which of the statements are sufficient to answer the questions.
In how many days can 10 women finish a work?
I. 10 men can complete the work in 6 days.
II. 10 men and 10 women together can complete the work in 3 \(\frac{3}{7}\) days.
III. If 10 men work for 3 days and thereafter 10 women replace them, the remaining work is completed in 4 days.

• A. Only I and III
• B. 8 days
• C. Only I and II
• D. Only II and III

Answer 1

The Correct Option is B

According to the question, we need to find the work done by 10 women and time taken by men and women and men alone to do the same work is given.
Now, work done by 10 women in one day is \(\frac{7}{24}-\frac{1}{6}=\frac{1}{8}\)
Therefore, 10 women can complete the work in 8 days.
Now, by using second and third condition, let 10 men can finish work in x days and 10 women can finish work in y days then 
⇒ \(\frac{1}{x}+\frac{1}{y}=\frac{7}{24}\) and from second and third condition, \(\frac{3}{x}+\frac{4}{y}=1\) and we know x is 6 days.
Therefore, \(\frac{4}{y}=\frac{1}{2}\)
⇒ \(y=8\)
Hence, the time taken by 10 women to complete the work is 8 days.
The correct option is (B): 8 days