Hi Bhavey.So, we are given that one X-type canal can fill a lake in 20 hours, and one Y-type canal can empty the same lake in 30 hours.So, we can consider the lake's total volume to be 60 Litres.This makes the inflow rate from one X-type canal 3 Litres/hour, and the outflow rate from one Y-type canal 2 Litres/hour.Now, let us consider that out of P canals, n are of type X.Now, since we want to fill the lake in 5 hours, we can say that the total rate of inflow has to be 12 Litres/hour.Now the total inflow of the given system can be given as:12 = 3n - 2(P - n)12 = 5n - 2P-> 5n = 12 + 2P-> n = (12 + 2P) / 5Now, for n to be an integer, we have to take 2P = 10k - 2 -> P = 5k - 1 (k is an integer)So, the possible values of P are:-> 29 (5 * 6 - 1)-> 54 (5 * 11 - 1)Thus, the answer is 2.

Please help me solve this question step by step image.png 27.67 KB

Please help me solve this question step by step image.png 27.67 KB