Question

Three men, four women, and six children can complete a work in seven days. A woman does double the work a man does and a child does half the work a man does. How many women alone can complete this work in 7 days?
(A) 7
(B) 8
(C) cannot be determined
(D) None of these

Answer 1

Hint: A woman does double the work a man does so, the work done by a woman is equal to the work done by two men, Work done by 2 men = Work done by 1 woman. Similarly, a child does half the work a man does so, the work done by two children is equal to the work done by one man, Work done by 2 children = Work done by 1 man. Now, calculate the work done by 1 man and 1 child in terms of work done by the woman. Now, use the information provided that three men, four women, and six children can complete a work in seven days. Solve it further and get the required answer.

Complete step-by-step answer:
According to the question, we are given that
Three men, four women, and six children can complete a work in seven days ……………………………………(1)
It is also given that a woman does double the work a man does and a child does half the work a man does.
Since a woman does double the work a man does so, we can say that the work done by a woman is equal to the work done by two men.
\[\Rightarrow \] Work done by 2 men = Work done by 1 woman
\[\Rightarrow \] Work done by 1 man = Work done by \[\dfrac{1}{2}\] woman ……………………………………………(2)
In the question, we have 3 men so,
 \[\Rightarrow \] Work done by 3 men = Work done by \[\dfrac{3}{2}\] woman ………………………………………………….(3)
Since a child does half the work a man does so, we can say that the work done by two children is equal to the work done by one man.
\[\Rightarrow \] Work done by 2 children = Work done by 1 man
\[\Rightarrow \] Work done by 1 child = Work done by \[\dfrac{1}{2}\] man …………………………………………….(4)
Now, from equation (2) and equation (4), we get
\[\Rightarrow \] Work done by 1 child = Work done by \[\dfrac{1}{2}\times \dfrac{1}{2}\] woman
\[\Rightarrow \] Work done by 1 child = Work done by \[\dfrac{1}{4}\] woman ……………………………………………………..(5)
In the question, we have six children,
\[\Rightarrow \] Work done by 6 children = Work done by \[6\times \dfrac{1}{4}\] women
\[\Rightarrow \] Work done by 6 children = Work done by \[\dfrac{6}{4}\] women ………………………………………….(6)
Now, from equation (1), equation (3), and equation (6), we get
\[\Rightarrow \] Work done by 3 men + Work done by 4 women + Work done by 6 children = 7 days
\[\Rightarrow \] Work done by \[\dfrac{3}{2}\] women + Work done by 4 women + Work done by \[\dfrac{6}{4}\] women = 7 days
\[\Rightarrow \] Work done by \[\left( \dfrac{3}{2}+4+\dfrac{6}{4} \right)\,\] women = 7 days
\[\Rightarrow \] Work done by 7 women = 7 days ………………………………………………..(7)
So, the time taken by 7 women to finish the work is 7 days.

So, the correct answer is “Option A”.

Note: The best way to solve this type of question, is to compare the work done by man, and child with respect to the woman. By doing this, we can express the work done by the man and the child in terms of a woman which makes the calculation simpler to be solved.