Answer:
The correct option is E.
Step-by-step explanation:
It is given that pumps A and B, operating simultaneously, can fill a certain tank in 6/5 hours.
One hour work of A and B = 5/6
Pumps A and C, operating simultaneously, can fill the tank in 3/2 hours.
One hour work of A and C = 2/3
Pumps B and C, operating simultaneously, can fill the tank in 2 hours.
One hour work of B and C = 1/2
We need to find the how many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
Add one hour work
A and B + A and C + B and C = [tex]\frac{5}{6}+\frac{2}{3}+\frac{1}{2}[/tex]
[tex]2A+2B+2C=\frac{5+4+3}{6}[/tex]
[tex]2(A+B+C)=\frac{12}{6}[/tex]
[tex]2(A+B+C)=2[/tex]
Divide both sides by 2.
[tex](A+B+C)=1[/tex]
Reciprocal of 1 is 1. It means ABC can fill the tank in 1 hour simultaneously. Therefore the correct option is E.
