Answer:

HAPPY LEARNING !

Step-by-step explanation:

Let there are two pipes A and B and DIAMETER of A is larger than B.

Now suppose that  

Pipe A take X HOURS and Pipe B takes y hours to fill the pool separately .

In 1 hour pipe A can fill the pool =  

x

1

​  

In 1 hour pipe B can fill the pool=  

y

1

​  

If both pipe are together then they take 12 hour to fill the pool.

If the are togther then in 1 hour they fill the pool.

x

1

​  

+  

y

1

​  

=  

12

1

​  

−−−−(1)

Now  

In 4 hour pipe A can fill the pool is=  

x

4

​  

In 9 hour pipe B can fill the pool is=  

y

9

​  

than they fill half of the pool,so

x

4

​  

+  

y

9

​  

 =  

2

1

​  

−−−−−(2)  

Now Let  

x

1

​  

=P &  

y

1

​  

=Q  and puuting in equation 1 &2, than

P+Q=  

12

1

​  

⇒12P+12Q=1−−−−(3)

And  

4P+9Q =  

2

1

​  

⇒8P+18Q=1−−−−−(4)

Now solving equation 3 & 4

Equation (3) multiplying by 2 and (4) multiplying by 3 and substract.

⇒−30Q=−1

⇒Q=  

30

1

​  

now put value of Q in equation 3

We get P=  

20

1

​  

So we found

P=  

20

1

​  

   & Q=  

30

1

​  

So x=20 and y=30

Hence the A pipe would take 20 hours and the pipe B would take 30 hours separately  .