A takes twice as much time as b and thrice as much time as c to finish a piece of work. Working together they can finish it in 2 days. A can do the work alone in. ??
If
A takes a days,
B takes b days, b = a/2
C takes c days, c = a/3
1/a + 1/b + 1/c = 1/2
1/a + 2/a + 3/a = 1/2
6/a = 1/2
a = 12
Let's break down the problem step by step to find the answer.
1. Let's assume that b can finish the work in x days. This means that a takes twice as much time as b, so a can finish the work in 2x days.
2. Similarly, c takes one-third of the time required by a, so c can finish the work in (2x)/3 days.
Now, let's calculate their individual rates of work:
- A's rate of work: 1/2x (as A completes the work in 2x days)
- B's rate of work: 1/x (as B completes the work in x days)
- C's rate of work: 1/(2x/3) = 3/2x (as C completes the work in 2x/3 days)
According to the given information, when they work together, they can finish the work in 2 days. So, combining their rates of work, we have:
1/2x + 1/x + 3/2x = 1/2
Now, let's solve the equation to find the value of x:
(1 + 2 + 3)/2x = 1/2
(6/2x) = 1/2
6/2x = 1/2
12x = 6
x = 6/12
x = 1/2
Therefore, b can finish the work alone in 1/2 day.