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### Question

A, B and C complete a work in 19, 14 and 7 days respectively. All three of them start the work together, but A leaves the work after 1 days. In how many days will the work be completed?

**A**

$4{8/19}$ days.

**B**

$5{8/19}$ days.

**C**

$6{8/19}$ days.

**D**

$7{8/19}$ 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, the work is completed in ${yz}/{y + z}$ × $(1 - n/x)$ days. Putting the various values x = 19, y = 14, z = 7, n = 1, and simplifying, we get ${84/19}$, which is same as: $4{8/19}$.