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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: $2{1/12}$.