| 25 men can reap a field in 20 days. When should 15 men leave the work, if the whole field is to be reaped in \[37\frac{1}{2}\]days after they leave the work? |
A) After 5 days
B) After 10 days
C) After 9 days
D) After 7 days
E) None of these
Correct Answer: A
Solution :
| Let 15 men work for m days. |
| Work done in 1 days \[\frac{m}{20}\] |
| Remaining work \[=\left( 1-\frac{m}{20} \right)\] |
| 25 men's 1 day's work \[=\frac{1}{20}\] |
| 1 man's 1 day's work \[=\frac{1}{20}\times \frac{1}{25}=\frac{1}{500}\] |
| 10 men's 1 day's work \[=\frac{1}{500}\times 10=\frac{1}{50}\] |
| 10 men's \[\frac{75}{2}\]days work \[=\frac{1}{50}\times \frac{75}{2}=\frac{75}{100}=\frac{3}{4}\] |
| \[\therefore \] \[\left( 1-\frac{m}{20} \right)=\frac{3}{4}\]\[\Rightarrow \]\[\frac{m}{20}=\frac{1}{4}\] |
| \[\Rightarrow \] \[m=\frac{1}{4}\times 20=5\] |
| Clearly, 15 men leave after 5 days. |
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