| A man and. a boy working together can complete a work in 24 days. If for the last 6 days, the man alone does the work, then it is completed in 26 days. How long will the boy take to complete the work alone? |
A) 72 days
B) 73 days
C) 49 days
D) 62 days
Correct Answer: A
Solution :
| Let man's 1 day's work \[=\frac{1}{m}\] |
| and boy's 1 day's work \[=\frac{1}{n}\] |
| 1 day's work of man and boy \[=\frac{1}{24}\] |
| Man's 6 days' work \[=\frac{6}{m}\] |
| Now, for 20 days, both man and boy do the work and for last 6 days, only man does the work. |
| According to the question, |
| \[\frac{1}{m}+\frac{1}{n}=\frac{1}{24}\] (i) |
| \[\Rightarrow \]\[20\left( \frac{1}{m}+\frac{1}{n} \right)+\frac{6}{m}=1\] |
| \[\Rightarrow \]\[\left( 20\times \frac{1}{24} \right)+\frac{6}{m}=1\] [from Eq. (i)] |
| \[\Rightarrow \]\[\frac{6}{m}=\left( 1-\frac{20}{24} \right)=\frac{4}{24}=\frac{1}{6}\]\[\Rightarrow \]\[\frac{1}{m}=\frac{1}{36}\] |
| Now from Eq. (i) \[\frac{1}{m}+\frac{1}{n}=\frac{1}{24}\] |
| \[\Rightarrow \]\[\frac{1}{36}+\frac{1}{n}=\frac{1}{24}\]\[\Rightarrow \]\[\frac{1}{n}=\left( \frac{1}{24}-\frac{1}{36} \right)=\frac{1}{72}\] |
| Hence, the boy alone can do the work in 72 days. |
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