FORMULAS:Still water: If the speed of water of the river is zero, then water is said to be still.Stream: If the water of the river is moving at a certain speed, then it is said to be a stream. Speed of the boat: It means speed of the boat in still water. Downstream: If the boat is moving in the direction of the stream. Upstream: If the boat is moving against the direction of the stream. If the speed of the boat in still water and stream be b and s km/hr Downstream speed = (b + s) km/hr Upstream speed = (b – s) km/hr s = (Downstream speed + Upstream speed)/2 b = (Downstream speed – Upstream speed)/2 Q1) A boatman rows 1 km in 5 min along the stream and 6 km in 1 hour against the stream. The speed of the stream is? 1) 3 km/hr 2) 6 km/hr 3) 10 km/hr 4) 12 km/hr Solution: Let the speed of the boat in still water and stream be b and s km/hr Speed of the boat along the stream be (b + s) km/hr = b + s = 12 km/hr Speed of the boat against the stream be (b – s) km/hr = b – s = 6 km/hr On solving, b = 9 km/hr, s = 3 km/hr Hence, option 1. Q2) A motorboat can travel at 10 km/hr in still water. It travelled 91 Km downstream in a river and then returned to the same place, taking altogether 20 hours. The rate of flow of the river is 1) 3 km/hr 2) 4 km/hr 3) 2 km/hr 4) 5 km/hr Solution: Speed of the boat = 10 km/hr Let the speed of the stream be s km/hr Upstream speed of the boat = (10 – s) km/hr Downstream speed of the boat = (10 + s) km/hr 91/(10 - s) + 91/(10 + s) = 20 For the above equation to be true, 91 must be divisible by 10 – s and 10 + s. So, 10 – s = 7; 10 + s = 13 s = 3 km/hr Hence, option 1. Q3) A boat goes 48 Km downstream in 20 hours. It takes 4 hours more to cover the same distance against the stream. What is the speed of the boat in still water? 1) 2.2 km/hr 2) 2 km/hr 3) 4 km/hr 4) 4.2 km/hr Solution: Let the speed of the boat in still water and stream be b and s km/hr Upstream speed of the boat = b – s = 48/24 = 2 km/hr Downstream speed of the boat = b + s = 48/20 = 2.4 km/hr b = 2.2 km/hr Hence, option 1. Download: Practice Questions on Boats and StreamsQ4) A sailor sails a distance of 48 Km along the flow of the river in 8 hours. If it takes 12 hours to return the same distance, then the speed of the flow of the river is 1) 0.5 km/hr 2) 1 km/hr 3) 1.5 km/hr 4) 2 km/hr Solution: Let the speed of the boat in still water and stream be b and s km/hr Upstream speed of the boat = b – s = 48/12 = 4 km/hr Downstream speed of the boat = b + s = 48/8 = 6 km/hr s = 1 km/hr Hence, option 2. Q5) A boat takes 9 hours to travel a distance upstream and 3 hours to travel the same distance downstream. If the speed of the boat in still water is 4 km/hr, then the speed of the stream is 1) 2 km/hr 2) 3 km/hr 3) 4 km/hr 4) 6 km/hr Solution: Let the speed of the stream be s km/hr Upstream speed of the boat = (4 – s) km/hr Downstream speed of the boat = (4 + s) km/hr According to the question, 3(4 + s) = 9(4 – s) s = 2 km/hr Hence, option 1. Q6) A man can row at 10 km/hr in still water. It he takes total 5 hours to go to a place 24 km away and return, then the speed of the water current is 1) 2 km/hr 2) 3 km/hr 3) 0.5 km/hr 4) 1 km/hr Solution: Let the speed of the current/stream be s km/hr Upstream speed = (10 – s) km/hr Downstream speed = (10 + s) km/hr 24/(10 - s) + 24/(10 + s) = 5 For the above equation to be true, 24 must be divisible by 10 – s and 10 + s. So, 10 – s = 8; 10 + s = 12 Hence, s = 2 km/hr Hence, option 1. Q7) A steamer goes downstream from one port to another in 4 hours. It covers the same distance upstream in 5 hours. If the speed of the stream is 2 km/hr, then find the distance between the two ports. 1) 50 km 2) 60 km 3) 70 km 4) 80 km Solution: Let the distance between the two ports be x km. Upstream speed = x/5 km/hr Downstream speed = x/4 km/hr Speed of the stream = (x/4 – x/5)/2 = 2 On solving, x = 80 km Hence, option 4. Q8) A motorboat travelling at some speed, can cover 25 km upstream and 39 km downstream in 8 hours. At the same speed, it can travel 35 km upstream and 52 km downstream in 11 hours. The speed of the stream is. 1) 2 km/hr 2) 3 km/hr 3) 4 km/hr 4) 5 km/hr Solution: Let the speed of the boat in still water and stream be b and s km/hr Upstream speed = (b – s) km/hr Downstream speed = (b + s) km/hr 25/(b - s) + 39/(b + s) = 8 35/(b - s) + 52/(b + s) = 11 For the above equations to be true, 25 and 35 must be divisible by b – s; 39 and 52 must be divisible by b + s. So, b – s = HCF(25, 35) = 5; b + s = HCF(39, 52) = 13 s = 4 km/hr. Hence, option 3. |