Question

Two workers A and B working together completed a job in 5 days. If A worked twice as
efficiently as he actually did and B worked '/3 as efficiently as he actually did, the work
would have completed in 3 days. Find the time for A to complete the job alone.​
​

Answer 1

• 6.25 days.

• 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.