Time & Work

A is thrice as good as B and can finish a work in 60 days less than that of B. If they work together, in how many days work will be completed ?

** Option:**

**A.**45 days

**B.**30 days

**C.**$22{1/2}$ days

**D.**$17{1/2}$ days

**Answer: C . $22{1/2}$ days**

** Justification:**

Suppose B takes $x$ days to finish a certain work.

B's day's work = $1/x$

A's day's work = $3/x$

By hypothesis,

$x - x/3 = 60$

or ${2/3}x = 60$

or $x$ = 90

Now, (A + B)'s 1 day's work

=$1/x + 3/x = 4/x = 4/90 = 2/45$

Hence, A and B can together finish the work in $45/2 = 22{1/2}$ days.