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### Question

A, B and C can independently complete a work in 5, 15 and 13 days respectively. B and C start the work together, but A joins them after 2 days. In how many days will the work be completed?

**A**

$4{5/67}$ days.

**B**

$5{5/67}$ days.

**C**

$6{5/67}$ days.

**D**

$7{5/67}$ 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 joins after n days, the work is completed in ${xyz}/{xy + yz + zx}$ × $(1 + n/x)$ days. Putting the various values x = 5, y = 15, z = 13, n = 2, and simplifying, we get ${273/67}$, which is same as: $4{5/67}$.