Question

A,b,c can do a piece of work in 2,3,4 days respectively. A and b started and after working for two days c replaces



b. The rest of the work is completed in _______days.

Answer 1

Solution:

Time taken by a,b and c to accomplish work = 2, 3,4 days respectively

Let total amount of work = X

For a,

X work = 2 days

1 day= $\frac{x}{2}$ work

For b

X work = 3 days

1 day= $\frac{x}{3}$ work

X work = 4 days

1 day= $\frac{x}{4}$ work

Statement which describes this problem :

a and b started and after working for two days c replaces  b.

a and b one day's work = $\frac{x}{2} +\frac{x}{3}=\frac{5 x}{6}$

a and b two day's work= $\frac{2 \times 5 x}{6}=\frac{5 x}{3}$=x + $\frac{2x}{3}$ which exceeds x amount of work that is , $\frac{5 x}{3}$ work > x work.

So,there is no need of c to join a and b after 2 days.The job gets completed before 2 days.