Question

There are two taps to fill in water tank. If both of them are opened it takes 18 min to get filled. The time take to fill the tank with large tap opened is 15 min lesser than the time taken by smaller one. Find the time taken by small tap to fill the tank

Answer 1

Answer:45 minutes

Step-by-step explanation:

et the smaller tap fill the tank alone in x minutes.

Then, the larger tap will fill the tank in (x - 15) minutes.

In 1 minute, the smaller tap can fill  

x

1

​  

 part of the tank and

The larger tap can fill  

x−15

1

​  

 part of the tank.

The tank is filled up in 18 minutes if both the taps are open.

Thus, in one minute, the taps fill  

18

1

​  

 part of the tank.

x

1

​  

+  

x−15

1

​  

=  

18

1

​  

 

⇒  

x(x−15)

x−15+x

​  

=  

18

1

​  

 

⇒  

x  

2

−15x

2x−15  

⇒36x−270=x  

−15x

−51x+270=0

−45x−6x+270=0

⇒x(x−45)−6(x−45)=0

⇒(x−45)(x−6)=0

⇒x=45 or x=6

Now, x = 6 is inadmissible as x - 15 = 6 - 15 = - 9 is not possible

Thus, the time taken by small tap alone to fill the tank is 45 minutes