It can take 12hours to fill …

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 .