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### Question

A, B and C can independently complete a work in 5, 15 and 16 days respectively. First C starts the work, then A joined after 7 days, and B after 6 days. In how many days was the work completed?

**A**

$8{40/79}$ days.

**B**

$9{40/79}$ days.

**C**

$10{40/79}$ days.

**D**

$11{40/79}$ 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, and B joins after m days, the work is completed in ${xyz}/{xy + yz + zx}$ × $(1 + n/x + m/y)$ days. Putting the various values x = 5, y = 15, z = 16, n = 7, m = 6, and simplifying, we get ${672/79}$, which is same as: $8{40/79}$.