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A and B can do a piece of work in 6 and 12 days, respectively. They (both) will complete the work in how many days?

#### Options

9 days

18 days

6 days

4 days

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#### Solution

**4 days**

**Explanation:**

A's 1 day's work = `1/6`

B's 1 day's work = `1/12`

(A+ B)'s 1 day's work = `1/6+1/12`

= `(2+1)/12=3/12=1/4`

Hence, both will complete the work in 4 days.

**Second Method**

Here, x = 6

and y = 12

∴ Time taken by (A+ B) = `(xy)/(x+y)`

= `(6xx12)/(12+6)` = 4 days

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