A boat makes a journey from point P to point Q and

Solution

Let the speed of boat in upstream = x km/hr Speed of boat in downstream = y km/hr Condition I: 48/x + 48/y = 20/3 ………..(1) Condition II: 48/(x – 2) + 48/(y + 2) = 36/5 ………..(2) Solving these equations: 48x + 48y = 20xy/3 …………(1) 48x + 48y = 36(x – 2)(y + 2)/3 …………(2) 100xy = 108(x – 2)(y + 2) ………(3) Product of speed boat in downstream and upstream = 216 xy = 216 ……(4) 100 x 216 = 108 (x – 2)(y + 2) 200 = 216 + 2x – 2y + 4 x – y = 6 …….(5) From eq (4) and (5), we got 216/y – y = 6 216 – y² = 6y y² + 6y – 216 = 0 (y + 18)(y – 12) = 0 Hence, y = 12 and x = 12 + 6 = 18 Speed of boat in still water = 1/2 (18 + 12) = 15 km/hr