Two water taps together can fill a tank in 9 (3/8) hours. The tap of larger diameter takes 10 hrs less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Answer:

Let the tap with smaller diameter fills the tank alone in x hours

Let the tap with larger diameter fills the tank alone in (x – 10) hours.

In 1 hour, the tap with a smaller diameter can fill 1/x part of the tank.

In 1 hour, the tap with larger diameter can fill 1/(x – 10) part of the tank.

The tank is filled up in 75/8 hours.

Thus, in 1 hour the taps fill 8/75 part of the tank.

1/x + 1/(x-10) = 8/75

(x-10) + x / x(x-10) = 8/75

2x – 10/x(x-10) = 8/75

75 (2x-10) = 8(x2-10x) by cross multiplication

150x – 750 = 8x2 – 80x

8x2 − 230x + 750 = 0

4x2−115x + 375 = 0

4x2 − 100x −15x + 375 = 0

4x(x−25)−15(x−25) = 0

(4x−15)(x−25) = 0

4x−15 = 0 or x – 25 = 0

x = 15/4 or x = 25

Case 1: When x = 15/4

Then x – 10 = 15/4 – 10

⇒ 15-40/4

⇒ -25/4

Time can never be negative so x = 15/4 is not possible.

Case 2: When x = 25 then

x – 10 = 25 – 10 = 15

∴ The tap of smaller diameter can separately fill the tank in 25 hours, and the time taken by the larger tap to fill the tank = ( 25 – 10 ) = 15 hours.

For further reference, check out the video

Articles to Explore:

  1. A pendulum oscillates 40 times in 4 seconds. Find its time period and frequency

Was this answer helpful?

 
   

4.5 (45)

(115)
(24)

Choose An Option That Best Describes Your Problem

Thank you. Your Feedback will Help us Serve you better.

3 Comments

  1. Sheikh Salman parveiz

    This is good app for learning

  2. I am a student and it helps to learn with too good answers I want to just say that it is too good

  3. This all are too good

Leave a Comment

Your Mobile number and Email id will not be published. Required fields are marked *

*

*

DOWNLOAD

App Now

Ask
Question