Question

A and b working together, can do a piece of work in 4 1/2h.B and c working together can do it in 3h.C and a working together can do it in 2 1/4h. Find how much time they will take to finish the piece of work.

Answer 1

Hii dear...

Solution :-

Given that

A & B take time to complete a task = 4(1/2) H = 9/2 H

And

B & C take time to complete the same task = 3 H

and

A & C take time to complete the same task = 2(1/4) H = 9/4 H

here,

Total work =

LCM of 9/2 , 3 and 9/4 = 9

now ,

Efficiency of A & B to do this work = 9 / (9/2) = 2 units

and

Efficiency of B & C to do the same = 9 / 3 = 3 units

and

Efficiency of A & C to do that work = 9 / (9/4) = 4 units

Now,

If A , B and C work together there Efficiency of doing that work = { 2 + 3 + 4 } / 2 = 4.5 units

[ => Hint. if we add efficiencies {( A + B) + ( B + C ) + ( A + C ) } give 2 times of there real Efficiency ]

Now,

time taken by the three to complete the work = 9 / 4.5 = 2 H Answer

Hope it helps :-)