Question

PLEASE ANSWER

One pump can fill a tank of water in 2 hours. A second tank can fill the same tank in 3 hours. If both pumps are used together, how long will it take to fill the tank? 5/6 hours 6/5 hours 3/2 hours 2/3 hours

Answer 1

6/5 hours

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)

⇒
`(1)/(2) + (1)/(3)`

`=> (5)/(6)` 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.