Question

The efficiency ratio of A, B and C is 3:4:5. Working together they can complete the work in 8.5 days. They work for 6 days. 80% of the remaining work will be completed by B alone
in:​

Answer 1

Given : -

The efficiency ratio of A , B , C = 3 : 4 : 5 .

All together can complete the work in 8.5 days.

Concept : -

Efficiency is inversely proportional to the no. of days required to complete the work.

Solution : -

(efficiency) x (days) = work done

Let us take the total work to be of 60 units. (L.C.M of 3 , 4 , 5)

and efficiencies of A , B , C be 3k , 4k , 5k

⇒ 8.5 x ( 3k + 4k + 5k ) = 60

⇒ k = 60 / (8.5 x 12) = 10/17

Now given that all have worked for 6 days , so amount of work completed in these days is given by,

⇒ 6 x ( 3k + 4k + 5k )

⇒ 6 x 12k

⇒ 6 x 12 x 10/17 = 720 / 17

Amount of work remaining  = 60 - (720 / 17) = 300 / 17

Now 80% of this remaining work completed by B alone is given by,

⇒ D x 4k = 0.8 x (300/17)

⇒ D x 4 x (10/17) = 0.8 x (300 / 17)

⇒ D = 6 days

∴ 80% of the remaining work will be completed by B alone in 6 days.