Unitary Method
- 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 ?
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Let man's 1 day's work = 1/m
and boy's 1 day's work = 1/n
1 day's work man and boy = 1/24
Man's 6 day's work = 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,
1/m + 1/n = 1/24Correct Option: A
Let man's 1 day's work = 1/m
and boy's 1 day's work = 1/n
1 day's work man and boy = 1/24
Man's 6 day's work = 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,
1/m + 1/n = 1/24
⇒ 20(1/m + 1/n) + 6/m = 1
⇒ 20 x (1/24) + 6/m = 1
⇒ 6/m = (1 - 20/24) = 4/24 = 1/6
⇒ 1/n = 1/36
Now from eq. (i)
1/m + 1/n = 1/24
1/36 + 1/n = 1/24
⇒ 1/n = (1/24) - (1/36) = 1/72
Hence, the boy alone can do the work in 72 days.
