A tank is filled by three pipes with uniform flow. The

Solution

Let time taken by third pipe to fill the tank = x hrs so time taken by 2nd pipe to fill the tank = x + 4 hrs & time taken by 1st pipe to fill the tank = x + 4 + 45 = x + 49 hrs; Hence 1/(x+4) +1/(x+49) = 1/x (x + 4 + x + 49)/ {(x + 4)(x + 49)} = 1/x (2x + 53)/(x² + 53x + 196) = 1/x 2x² + 53x = x² + 53x + 196 x² = 196 x = 14 hrs So time taken by 1st pipe to fill the tank = x + 49 = 14 + 49 = 63 hrs Alternate Method :- Let time taken by third pipe to fill the tank = x hrs so time taken by 2nd pipe to fill the tank = x + 4 hrs & time taken by 1st pipe to fill the tank = x + 4 + 45 = x + 49 hrs; Then x = root of (4 × 49) = root of 196 = 14 hrs So time taken by 1st pipe to fill the tank = x + 49 = 14 + 49 = 63 hrs.