Question

9. A, B and C together can do a piece of work in 6 days. If A and B together can do the
same work in 10 days, how long will it take for C to finish the work alone?​

Answer 1

Step-by-step explanation:

If A and B can do a piece of work in 6 days and B and C can do the same work in 10 days, in how many days can A, B, and C do the same work?

Let’s say A can do the work in ‘a’ days, B in ‘b’ days and C in ‘c’ days all by themselves.

We know that A and B together can do the work in 6 days, therefore

1 / ( (1/a)+(1/b)) = 6

Similarly, we know that B and C together can do the work in 10 days, therefore

1 / ((1/b)+(1/c)) = 10

There are 3 variables and only 2 virtue of there being only 2 equations for 3 variables, it would not possible to uniquely determine ‘a’, ‘b’ and ‘c’ as there would be infinite answers.

However, by considering certain value for ‘a’, values of ‘b’ and ‘c’ could be determined, thereby giving us one answer for A, B and C together to finish the work.

So, let’s go:

Let A be doing the work in 10 days. Since A and B together do the work in 6 days, B alone can do the work in 1 / ((1/6) - (1/10)) = 1 / (4/60) = 60 /4 = 15 days.

Since B and C together do the work in 10 days, C alone can do the work in

1 / ((1/10 - (1/15)) = 1 / (5/150) = 150/5 = 30 days.

So, we have A, B and C doing the work individually in 10, 15 and 30 days respectively.

So, together they would do the work in

1 / ((1/10)+(1/15)+(1/30)) = 1 / (6/30) = 30/6 = 5 days.

As I said in the beginning, unique answer is not possible as there are fewer equations than the variables. And one of the answers is 5 days, considering they do the work individually in 10, 15 and 30 days.

By assuming different values for A, more answers could be found out.

Thus, one of the answers is, A, B and C together can do the work in 5 days.