A can complete a work in 12 days with a working of 8 hours per day. B can comple

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A can complete a work in 12 days with a working of 8 hours per day. B can complete the same work in 8 days when working 10 hours a day. If A and B work together, working 8 hours a day, the work can be completed in_______days.

Options:

A . 5 5⁄11

B . 4 5⁄11

C . 6 4⁄11

D . 6 5⁄11

Answer: Option A
A CAN COMPLETE THE WORK IN 12 DAYS WORKING 8 HOURS A DAY
=> NUMBER OF HOURS A CAN COMPLETE THE WORK = 12×8 = 96 HOURS
=> WORK DONE BY A IN 1 HOUR = 1/96
B CAN COMPLETE THE WORK IN 8 DAYS WORKING 10 HOURS A DAY
=> NUMBER OF HOURS B CAN COMPLETE THE WORK = 8×10 = 80 HOURS
=> WORK DONE BY B IN 1 HOUR = 1/80
WORK DONE BY A AND B IN 1 HOUR = 1/96 + 1/80 = 11/480
=> A AND B CAN COMPLETE THE WORK IN 480/11 HOURS
A AND B WORKS 8 HOURS A DAY
HENCE TOTAL DAYS TO COMPLETE THE WORK WITH A AND B WORKING TOGETHER
= (480/11)/ (8) = 60/11 DAYS = 5 5⁄11 DAYS

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