A, B, and C can complete a work in 4 days, 8 days, and 16 days respectively. If all three work on alternate days such that A works on first day, B works on second day, C works on third day and A works on fourth day and so on, then find the number of days in which 175% of the work is done.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 12 days.
A, B, and C can complete a work in 4 days, 8 days, and 16 days respectively
L.C.M(4, 8, and 16) = 16
The efficiency of A = 16/4 = 4 units
The efficiency of B = 16/8 = 2 units
The efficiency of C = 16/16 = 1 units
175% of total work = 175% of 16 = 28
Work done by A on the first day = 4 units
Work done by B on the second day = 2 units
Work done by C on the third day = 1 unit
Total work done in 3 days = 7 units
Then, total work done in 9 days = 21 units
Remaining work = 28 - 21 = 7 units
Work done by A on the tenth day = 4 units
Remaining work = 28 - 25 = 3 units
Work done by B on eleventh day = 2 units
Remaining work = 28 - 27 = 1 unit
Work done by C on twelfth day = 1 unit
Hence, 175% of the total work will be completed in 12 days