Answer:
12 hours
Step-by-step explanation:
Let the larger pipe can drain the tank in x hours
Than, time taken by smaller tank to drain the tank= (x+6) hours
If working togather, both pipe can drain the tank= 4 hours
A.T.Q
[tex]\frac{1}{x}[/tex] + [tex]\frac{1}{x+6}[/tex]= [tex]\frac{1}{4}[/tex]
[tex]\frac{x+x+6}{x(x+6)}[/tex]= [tex]\frac{1}{4}[/tex]
[tex]\frac{2x+6}{x^{2}+6x }[/tex]= [tex]\frac{1}{4}[/tex]
8 x +24= [tex]x^{2}[/tex] + 6 x
[tex]x^{2}[/tex] - 2 x- 24= 0
[tex]x^{2}[/tex] -6 x+ 4 x -24=0
x(x-6) + 4(x-6)= 0
(x-6)(x+4)=0
X= 6, X=-4 is rejected
Hence, time taken by larger tank to fill the drain= 6 hours
Hence, time taken by smaller tank to drain the tank = 6+6= 12 hours
Hence, the correct answer is 12 hours
