2 men can complete a piece of work in 6 days. 2 women can complete the same piece of work in 9 days, whereas 3 children can complete the same piece of work in 8 days. 3 women and 4 children worked together for 1 day. If only men were to finish the remaining work in 1 day, how many total men would be required? |
A) 4
B) 8
C) 6
D) Cannot be determined
E) None of the above
Correct Answer: B
Solution :
1 man's one day work \[=\frac{1}{12}\] |
1 woman's one day work \[=\frac{1}{18}\] |
1 child's one day work \[=\frac{1}{24}\] |
1 man can finish the work in 12 days |
1 woman can finish the work in 18 days |
1 child can finish the work in 24 days |
\[\Rightarrow \] 12 men \[\equiv \] 18 women \[\equiv \] 24 children |
\[\Rightarrow \] 2 men \[\equiv \] 3 women \[\equiv \] 4 children |
Now, 3 women + 4 children = 4 men |
Part of work done by 4 men in 1 day \[=\frac{4}{12}=\frac{1}{3}\] |
Remaining work \[=1-\frac{1}{3}=\frac{2}{3}\] |
Remaining \[\frac{2}{3}\]work will be finished by 1 man in |
\[\frac{2}{3}\times 12=8\,days\] |
To finish the work In 1 day we require 8 more men. |
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