The rates of working of A and B are in the ratio 3:4.Find the number of days taken by them to finish the work?

Poorly worded.

By "rates of working" , do you mean the amount of work done, or the time taken to do the same job.

To find the number of days taken by A and B to finish the work, we need to know the ratio of their rates of working and the total work to be completed.

Let's assume that the rates at which A and B work are represented by '3x' and '4x' respectively, where 'x' is a common factor.

Since the rates of A and B are in the ratio 3:4, we can say that:

3x / 4x = 3 / 4

Cross-multiplying, we get:

3 * 4x = 4 * 3x
12x = 12x

This means that the rates of A and B are equal, and they work at the same rate.

Now, let's assume that the total work to be completed is represented by 'W'. Since both A and B work at the same rate, the ratio of their work done in a given time will also be 3:4.

So, in a given time, A does 3/7th of the total work, while B does 4/7th of the total work.

Let's assume that A takes 'a' days to finish the work. This means that in 'a' days, A completes 3/7th of the total work. Therefore, we can write:

3/7 * W = a

Similarly, let's assume that B takes 'b' days to finish the work. This means that in 'b' days, B completes 4/7th of the total work. Therefore, we can write:

4/7 * W = b

From the above equations, we can see that the time taken by A and B to finish the work is directly proportional to their respective shares of work.

To find the number of days taken by A and B to finish the work, we need to know either the value of 'a' or 'b', or the value of 'W'.

Please provide additional information or values to proceed further with the calculation.