There are two taps P and Q. Milk flows out from tap P, whereas water flows out from tap Q. P alone can fill the tank in 20 hours and Q alone can fill the tank in 60 hours. When the tank is empty, tap P is opened. After how much time should tap Q be opened so that the ratio of milk and water in the tank is 5 : 1, when the tank is full?

Let P be open for T hours and Q be open for (T-x) hours. P fills 1/20 per hour, Q fills 1/60 per hour. Total volume = T/20 + (T-x)/60 = 1. Ratio of milk to water = (T/20) / ((T-x)/60) = 5/1. 3T / (T-x) = 5 => 3T = 5T - 5x => 2T = 5x => x = 0.4T. Substituting into T/20 + (T-0.4T)/60 = 1 => 3T + 0.6T = 60 => 3.6T = 60 => T = 16.66. x = 0.4 * 16.66 = 6.66.