Alright, lets gets started.
If water enters through a pipe alone, swimming pool can be filled in 12 hr.
Or say, in 12 hrs, swimming pool can be filled with help of pipe.
It means in 1 hr, the part of swimming pool filled =
(For pipe only)
Similarly, with hose only, , in 1 hr, the part of swimming pool filled = ![\frac{1}{30}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B30%7D%20%20)
So, water is coming from both, pipe and hose , then in 1 hr, the part of pool filled will be = ![\frac{1}{12} + \frac{1}{30}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B12%7D%20%20%2B%20%5Cfrac%7B1%7D%7B30%7D%20%20)
Suppose in x hrs, with both supplies, pipe and hose, pool is filled.
Means
![\frac{1}{12} + \frac{1}{30} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B12%7D%20%20%2B%20%5Cfrac%7B1%7D%7B30%7D%20%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20%20)
making common denominator
![\frac{30}{360} + \frac{12}{360} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%7D%7B360%7D%20%20%20%2B%20%5Cfrac%7B12%7D%7B360%7D%20%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20%20)
![\frac{30 + 12}{360} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B30%20%2B%2012%7D%7B360%7D%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20%20%20)
![\frac{42}{360} = \frac{1}{x}](https://tex.z-dn.net/?f=%20%5Cfrac%7B42%7D%7B360%7D%20%20%3D%20%5Cfrac%7B1%7D%7Bx%7D%20%20)
Flipping
![\frac{360}{42} = x](https://tex.z-dn.net/?f=%20%5Cfrac%7B360%7D%7B42%7D%20%20%3D%20x%20)
![x = \frac{60}{7}](https://tex.z-dn.net/?f=%20x%20%3D%20%5Cfrac%7B60%7D%7B7%7D%20%20)
Means 8.57 hrs : Answer
Hope it will help :)