MAT Exam 2023 Paper

Concept:The river current increases the boat’s speed downstream and decreases its speed upstream.Explanation:Let the rate of flow of the river be $r$ km/h.Speed of the boat in still water is $10$ km/h.Downstream speed is $(10 + r)$ km/h.Upstream speed is $(10 - r)$ km/h.Time is distance divided by speed.Total time for going 91 km downstream and 91 km upstream is 20 hours.So, we write:$$\frac{91}{10+r} + \frac{91}{10-r} = 20$$Taking the common denominator:$$\frac{91(10-r) + 91(10+r)}{(10+r)(10-r)} = 20$$$$\frac{91[(10-r) + (10+r)]}{100 - r^2} = 20$$$$\frac{91 \times 20}{100 - r^2} = 20$$Cancel 20 from both sides:$$\frac{91}{100 - r^2} = 1$$$$100 - r^2 = 91$$$$r^2 = 9$$$$r = 3$$Answer:The rate of flow of the river is $3$ km/h, which is Option A.