Question

To do a certain work alone A takes 4hours B takes 5hours and c takes 6hrs. How long would A and B together take ro do a certain work which C finishes in 4.5hours​

Answer 1

Let the total work be of 60 units (LCM of 4 , 5 , 6 )

Given :

A takes 4hours B takes 5hours and c takes 6hrs to do total work of 60 units  individually

A can do 60 units of work in 4 hrs  

⇒ A can do 15units of work in 1 hr

B can do 60 units of work in 5 hrs

⇒ B can do 12units of work in 1 hr

C can do 60 units of work in 6 hrs

⇒C can do 10 units of work in 1 hr

also given another C can finish it in 4.5hrs

⇒ total work = 4.5 x 10 = 45 units

A & B if work together they can do a work of  ( 15 + 12 ) = 27 units of work per hr

so to do 45 units of work , A and B together takes ( 45 / 27 ) = 5 / 3 or 1.67hrs

HOPE THIS HELPS YOU !!