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?
Correct Answer: Description for Correct answer:
Let man's 1 day's work = \( \Large \frac{1}{m} \)
and boy's 1 day's work = \( \Large \frac{1}{n} \)
1 day's work man and boy = \( \Large \frac{1}{24} \)
Man's 6 day's work = \( \Large \frac{6}{m} \)
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,
\( \Large \frac{1}{m}+\frac{1}{n}=\frac{1}{24} \)
=> \( \Large 20 \left(\frac{1}{m}+\frac{1}{n}\right)+\frac{6}{m}=1 \)
=> \( \Large \left(20 \times \frac{1}{24}\right)+\frac{6}{m}=1 \)
\( \Large \frac{6}{m}= \left(1-\frac{20}{24}\right)=\frac{4}{24}=\frac{1}{6} \)
\( \Large \frac{1}{m}=\frac{1}{36} \)
Now from eq. (i)
\( \Large \frac{1}{m}+\frac{1}{n}=\frac{1}{24} \)
\( \Large \frac{1}{36}+\frac{1}{n}=\frac{1}{24} \)
=> \( \Large \frac{1}{n} = \left(\frac{1}{24 }- \frac{1}{36}\right)=\frac{1}{72} \)
Hence, the boy alone can do the work in 72 days.
Part of solved Unitary Method questions and answers :
>> Aptitude >> Unitary Method