Mohan and Sohan working separately can dig a trench in 10 days and 12 days respectively. If they work for 1 day alternately, Mohan begins it, in how many days Mohan will dug the trench ?

** Option:**

**A.**22 days

**B.**$16{1/2}$ days

**C.**$11{2/3}$ days

**D.**$10{5/6}$ days

**Answer: D . $10{5/6}$ days**

** Justification:**

Mohan's 1 day's work = $1/10$

Sohan's 1 day's work = $1/12$

Mohan and Sohan's 10 days work (working alternately by)

= $5 × 1/10 + 5 × 1/12 = 11/12$

Remaining work = $1 - 11/12 = 1/12$

Now,$1/10$ work is done by Mohan in = 1 day

$1/12$ work is done by Mohan in = $1/{1/10}$ × $1/12$ = $10/12$ = $5/6$

Hence, number of days to finish the work = 10 + $5/6$ = $10{5/6}$