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.