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.