Question

A, B and C working together completed a work in 4 days. If A worked with 25% more efficiency, B worked with 25% less efficiency and C worked with 30% more efficiency than their respective actual efficiency, then the same work is completed in 3.75 days. However, if A worked with 50% efficiency, B worked with three fourth of its efficiency and C worked with 20% more efficiency than their respective actual efficiency, then the whole work is completed in 4.8 days. Find the time taken by A and B together to complete the whole work.​

Answer 1

Answer:

Let’s use x to represent the amount of work needed to complete the job.

’a’ is the amount of work done by worker A in one day.

’b’ is the amount of work done by worker B in one day.

By the wording of the question, we know that:

5a + 5b = x

(3a) 2 + (3b)/3 = x

Since both equations are equal to the same value (x), we can set them equal to each other, and solve for b in terms of a.

5a + 5b = (3a)2 + (3b)/3

5a + 5b = 6a + b (simplify the right side)

4b = a (subtract 5a and b from each side)

b = a/4

We now know that A works 4 times faster than B.

By inserting our value for b (in terms of a) into the very first equation, we get:

5a + 5b = x

5a + 5(a/4) = x

(5 + 5/4)a = x

6.25a = x

So worker A can do the same job alone in 6.25 days.