Answer:
6/5 hours
Step-by-step explanation:
GIVEN :-
Lets say ,
- Pump A takes 2 hours to fill the tank alone
- Pump B takes 3 hours to fill the tank alone
TO FIND :-
- Time taken by both pumps to fill the tank when used together
PROCEDURE :-
In 2 hours , Pump A fills the whole tank.
⇒ In 1 hour , Pump A will fill 1/2 part of tank. (By using Unitary method)
In 3 hours , Pump B fills the whole tank.
⇒ In 1 hour , Pump B will fill 1/3 part of tank. (By using Unitary method)
In 1 hour , when both pumps will be used together , they will fill =
(Part of tank filled by A in 1hr) + (Part of tank filled by B in 1hr)
⇒ [tex]\frac{1}{2} + \frac{1}{3}[/tex]
[tex]=> \frac{5}{6}[/tex] part of tank
5/6 part of tank will be filled by both the pumps in = 1 hour.
Using unitary method, multiplying both the sides with 6/5 -
⇒ 5/6 × 6/5 part of tank will be filled by both the pumps in = 1 × 6/5 hours
⇒ Total tank (or 1 whole tank) will be filled by both the pumps in = 6/5 hours
∴ Both the pumps will take 6/5 hour to fill the tank , when used together.
