There are three taps of diameter 1 cm, 4/3 cm and 2 cm, respectively. The ratio of the water flowing through them is equal to the ratio of the square of their diameters. The biggest tap can fill the tank alone in 61 min. If all the taps are opened simultaneously, how long will the tank take to be filled?

Time taken to fill the tank by the tap having 2 cm diameter = 61 min
∴ Time taken to fill the tank by the tap having 1 cm diameter
= 61 x (2/1)² = 244 min
Similarly, time taken to fill the tank by the tap having 4/3 cm diameter
= 61 x [(2 x 3)/4]² = 61 x 9/4 = 549/4 min.
∴ Part of the tank filled by all the three pipes in 1 min
= 1/61 + 1/244 + 1/(549/4)
= (36 + 9 + 16)/2196 = 61/2196 = 1/36
Hence, required time taken = 36 min