Question

A man and a boy can complete a piece of work together in 24 days. if for the last six days boy alone does the work then it is completed in 28 days. how long the man will take to complete the work alone?

Answer 1

Hello Dear.

Here is the answer---

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Time taken by the man and the boy to complete the work together = 24 days.

Thus, One Day Work of the man and the boy = 1/24

Number of Days in which Boys and the Man works Together = 28 - 6
= 22 Days.

Thus, the Work done by the man and the boy in 22 days = 22/24
= 11/12 

Remaining work = 1 - (11/12)
 = (12 - 11)/12
 = 1/12 

Boy have to complete the (1/12)th work in 6 days.
Thus, Boy can complete the Total Work in 6 × 12
= 72 Days.

∴ Work done by the boy in one day = 1/72

∴ Work done by man = One day work of man and boy - one day work of boy
= 1/24 - 1/72
= (3 - 1)/72
= 2/72
= 1/36

∴ Number of Days taken by the Boy is 36.


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Hope it helps.

Answer 2

Solution :-

A man and a boy work together to complete the work in 24 days

A man's + a boy's 1 day work = 1/14

For the last 6 days, the boy alone does the work then it is completed in 28 days.

So, man and boy work together for 22 days (i.e. 28 - 6)

Man's and boy's 22 days work = 22*1/24

= 22/24

= 11/12

Remaining work = 1/1 - 11/12

= 1/12

1/12th of the work completed by the boy in 6 days.

So, boy's 1 day work = 1/12*6

= 1/72

1/72 + man's 1 day work = 1/24

Man's 1 day work = 1/24 - 1/72

⇒ (3 - 1)/72

⇒ 2/72

= 1/36

Hence, the man will take 36 days to complete the work alone.

Answer.