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 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone , A would require

Answer 1

Let A complete x part of a work in 1 day.
And B completes y part of work in 1 day.

A/Q,
 ∵ A and B together complete a work in 5 days.
i.e,
     5x + 5 y = 1
or, x + y = 1/5 ----------------(i)

Now,
If A worked twice as efficient as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days.i.e,
 rate of A = 2x ,
 rate of B = y/3
 ∵ A and B together complete a work in 3 days .
i.e,
     3(2x) + 3(y/3) = 1
or, 6x + y =1   --------------(ii)
By subtracting the Eqn(i) from Eqn(ii)
or, 5x = 1 - 1/5 = 4/5
or, x = 4/25
and, y = 1/5 - 4/25 
        y = 1/25
Therefore Rate of A = 4/25 work per day.
and rate Of B = 1/25 work per day.
∵ A complete 14/25 part of work in 1 day .
∴ A complete a whole work in 25/4 days = 6.25 days ≈ 6 days.