There are three pipes attached with a tank whose diameters are 1cm, 1\(\frac{1}{3}\) cm and 2 cm. If the largest pipe alone fill it in 61 minutes and the amount of water flowing by each pipe being proportional to the square of its diameter, then working together in what time would a cistern be filled by three pipes?

36 min

Given, amount of water = k (diameter)²

Ratio of water flowing by each pipe = (1)² : (\(\frac{4}{3}\))² : (2)²

                                                         = 9  :  16  : 36 = 61

Efficiency of Largest pipe = 36

Tank Capacity =Efficiency × Time = 36 × 61

Time taken by all three pipes together = \(\frac{36\;×\;61}{61}\) = 36 min