Question 25

A mining work can be undertaken only between 9 AM to 6 PM. If A and B work entirely during these hours, they can complete the work alone in 18 days and 22 days respectively. If A and B both start together on 25th Nov at 12 noon, when should B stop doing the work so that the work will be completed exactly on 09th Dec at 12 noon?

Solution

Time taken by A alone to finish the work = 18*9 hrs

Time taken by B alone to finish the work = 22*9 hrs

Let the total work be LCM(18*9, 22*9) = 198*9 units

Work done by A in 1 hour = 11 units

Work done by B in 1 hour = 9 units

Let the number of hours B worked be 'x'

work done by A + work done by B = Total work done

(6)(11)+(13)(9)(11)+(3)(11) + x(9) = 198*9

x = 44 hours

Number of days B worked = 4 days 8 hours

Therefore, B stopped working on 30th Nov at 11 am.

Answer is option C.


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