Question

. A pipe can fill an empty tank in 12 h. After it is
kept open for 3 h, another pipe which can fill the
tank in 8 h is opened. In how many more hours
will the tank be filled?
(a) 571
18
(b) - h
5
20
16
(c)
h
(d)
h
5​

Answer 1

Answer:

( b ) 18/5 hours

Step-by-step explanation:

A pipe can fill the tank in 12 hours

So, Portion of work done by a pipe in one hour = 1 / 12

Another pipe can fill the tank in 8 hours

So, Portion of work done by another pipe in one hour = 1 / 8

After a pipe is open for 3 hours, another pipe is opened

Let the time taken by another pipe be ' x ' hours

Portion of work done by another pipe in ' x ' hours = x( 1 / 8 ) = x / 8

Time taken by a pipe to fill the tank = ( x + 3 ) hours

Portion of work done by a pipe in ( x + 3 ) hours = ( x + 3 )( 1 / 12 ) = ( x + 3 ) / 12

We know that

Total work = 1

$\sf\Rightarrow\dfrac{x}{8} +\dfrac{x+ 3}{12} =1\\\\\\\sf\Rightarrow\dfrac{3x+2(x+3)}{24} =1\\\\\\\sf\Rightarrow\dfrac{3x+2x+6}{24} =1\\\\\\\sf\Rightarrow\dfrac{5x+6}{24} =1$

⇒ 5x + 6 = 24

⇒ 5x = 24 - 6

⇒ 5x = 18

⇒ x = 18/5

' x ' is nothing but the extra time take by both pipes to fill the tank

Hence the tank will be filled in [ Option b ] 18/5 hours more.