Given below are three quantities named 1, 2 and 3. Based on the given information, you have to determine the relation between the three quantities. You should use the given data and knowledge of Mathematics to choose between the possible answer. Quantity 1: Manish can row at a speed of 4.5 km/h in still water and rows to a certain upstream point and back to the starting point in a river which flows at 1.5 km/hr. Find his average speed for total journey. Quantity 2: A man can row 6 km/h in still water. It takes him twice as long to row up as to row down the river. Find the rate of stream. Quantity 3: The rate of flow of river water is 4 km/h. A boat goes up 6 km and back to the starting point in 2 hour. Find the speed of the boat in still water. Correct Answer If Quantity 3 is maximum Quantity 1: Downstream speed = u + v = 4.5 + 1.5 = 6 km/h Upstream speed = u – v = 4.5 – 1.5 = 3 km/h Average speed for two equal distance = (2ab)/(a + b) ⇒ (2 x 6 x 3)/(6 + 3) = 4 km/h Quantity 2: It takes him twice as long to row up as to row down the river. It means upstream time is twice of downstream time or we can say that downstream speed is two times upstream speed. Downstream speed = 2 × upstream speed ⇒ u + v = 2(u – v) ⇒ 6 + v = 2(6 – v) ⇒ v = 2 km/h Quantity 3: Let boat speed in still water = u Downstream speed = u + 4 Upstream speed = u – 4 Total time = t1 + t2 = 2 × h ⇒ 6/(u + 4) + 6/(u – 4) = 2 -----eq 1 ⇒ 6(u + 4) + (u – 4) / (u2 – 16) = 2 ⇒ 6u = u2 – 16 ⇒ u2 – 8u + 2u – 16 = 0 ⇒ (u + 2)(u – 8) = 0 u = -2 is not possible ∴ u = 8 km/h Comparing all three quantities ∴ Quantity 3 > Quantity 1 > Quantity 2