# Discussion of Question with ID = 041 under Time-and-Work

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### Question

A, B and C complete a work in 6, 4 and 5 days respectively. All three of them start the work together, but A leaves the work after 2 days, and B leaves the work after 1 days. In how many days will the work be completed?

A

\$2{1/12}\$ days.

B

\$3{1/12}\$ days.

C

\$4{1/12}\$ days.

D

\$5{1/12}\$ days.

Soln.
Ans: a

Use the shortcut formula. If A, B, C can independently complete the job in x, y and z days, and A leaves after n days, and B after m days, the work is completed in z × \$(1 - n/x - m/y)\$ days. Putting the various values x = 6, y = 4, z = 5, n = 2, m = 1, and simplifying, we get \${25/12}\$, which is same as: \$2{1/12}\$.