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Muks Kumar

· started a discussion

· 1 Months ago

Explain (Question:118071.0)

Explain please

Question:

A and B can complete the work individually in 24 days and 30 days respectively, working 10 hours a day. Work is to be done in two shifts. Morning shift lasts for 6 hours and evening shift lasts for 4 hours. On the first day A works in the morning shift while B works in the evening shift. Next day A works in the evening shift while B works in the morning shift and so on. It means they work alternatively with respect to their shifts. Thus they work on this pattern till the work is completed. On which day the work got completed?

Options:
A) 26th day 
B) 27th day     
C) 28th day  
D) 29th day
Solution:

Ans: (b) Working 10 hrs a day, A’s 1 day work = \(\cfrac{1}{24}\)

Working 10 hrs a day, B’s 1 day work = \(\cfrac{1}{30}\)

Now, A’s 1st day work = 6 hr.

B’s 1st day work = 4 hr.

B’s 2nd day work = 6 hr.

A’s 2nd  day work = 4 hr.

And so on 

In 2 days A and B work for 10 hrs separately,

∴ 2 days work of A = \(\cfrac{1}{24}\)

2 days work of B = \(\cfrac{1}{30}\)

∴ 2 days work of A+B = \(\cfrac{1}{24}+\cfrac{1}{30}\)

= \(\cfrac{5+4}{120}\)

= \(\cfrac{9}{120}\)

∴ 1 days work of A+B =  \(\cfrac{9}{240}\)

∴ Work will be completed in \(\cfrac{240}{9}\)

= \(26\cfrac{6}{9}\) days

∴ work will be completed on 27th day.

Knowledge Expert

· commented

· 1 Months ago

Dear student,
Please go though the given answer solution.

Regards
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