Quantitative Aptitude — Boats and Streams

Formula: Speed downstream = Speed of boat in still water + Speed of stream Given: Speed of boat in still water (B) = 12 km/h Speed of stream (S) = 3 km/h Speed downstream (D) = B + S = 12 + 3 = 15 km/h

Formula: Speed upstream = Speed of boat in still water - Speed of stream Given: Speed of boat in still water (B) = 10 km/h Speed of stream (S) = 2 km/h Speed upstream (U) = B - S = 10 - 2 = 8 km/h

Formula: Time = Distance / Speed First, calculate the speed upstream: Speed upstream (U) = Speed of boat in still water (B) - Speed of stream (S) Given: B = 15 km/h S = 5 km/h U = 15 - 5 = 10 km/h Distance = 80 km Time = Distance / U = 80 / 10 = 8 hours

Formula for speed in still water (B) = (Speed downstream (D) + Speed upstream (U)) / 2 Formula for speed of stream (S) = (Speed downstream (D) - Speed upstream (U)) / 2 Given: Speed downstream (D) = 20 km/h Speed upstream (U) = 12 km/h Speed in still water (B) = (20 + 12) / 2 = 32 / 2 = 16 km/h Speed of stream (S) = (20 - 12) / 2 = 8 / 2 = 4 km/h

Let the speed of the boat in still water be B and the speed of the stream be S. Speed downstream (D) = B + S Speed upstream (U) = B - S Distance = Speed x Time Since the distance is the same for both downstream and upstream travel: (B + S) * 6 = (B - S) * 9 6B + 6S = 9B - 9S Rearrange the terms to find the ratio B:S: 9S + 6S = 9B - 6B 15S = 3B B/S = 15/3 B/S = 5/1 So, the ratio of the speed of the boat in still water to the speed of the stream is 5:1.

Formula: Speed = Distance / Time First, calculate the speed upstream (U) and speed downstream (D): Speed upstream (U) = 50 km / 5 hours = 10 km/h Speed downstream (D) = 60 km / 4 hours = 15 km/h Now, calculate the speed of the boat in still water (B): Formula: B = (D + U) / 2 B = (15 + 10) / 2 = 25 / 2 = 12.5 km/h

Let the speed of the man in still water (B) = 8 km/h Let the speed of the stream (S) = 2 km/h Speed upstream (U) = B - S = 8 - 2 = 6 km/h Speed downstream (D) = B + S = 8 + 2 = 10 km/h Let the distance be X km. Time taken to go upstream = X / U = X / 6 hours Time taken to return downstream = X / D = X / 10 hours According to the problem, it takes 2 hours more to go upstream than downstream: X/6 - X/10 = 2 To solve for X, find a common denominator for 6 and 10, which is 30: (5X - 3X) / 30 = 2 2X / 30 = 2 X / 15 = 2 X = 2 * 15 X = 30 km

Let the speed of the boat in still water (B) = 15 km/h Let the speed of the stream be S km/h. Speed downstream (D) = B + S = (15 + S) km/h Speed upstream (U) = B - S = (15 - S) km/h Distance = Speed x Time Given that the distance is the same: Distance downstream = (15 + S) * 4 Distance upstream = (15 - S) * 6 Equating the distances: (15 + S) * 4 = (15 - S) * 6 60 + 4S = 90 - 6S Combine S terms and constant terms: 4S + 6S = 90 - 60 10S = 30 S = 30 / 10 S = 3 km/h Now, calculate the distance using either the downstream or upstream values: Distance = (15 + S) * 4 = (15 + 3) * 4 = 18 * 4 = 72 km (Alternatively, Distance = (15 - S) * 6 = (15 - 3) * 6 = 12 * 6 = 72 km)

Let the speed of the man in still water be B km/h and the speed of the stream be S km/h. Speed downstream (D) = B + S Speed upstream (U) = B - S From the second condition: He can row 4 km with the stream in the same time as 3 km against the stream. Time = Distance / Speed 4 / (B + S) = 3 / (B - S) 4(B - S) = 3(B + S) 4B - 4S = 3B + 3S 4B - 3B = 3S + 4S B = 7S (Equation 1: Relationship between B and S) From the first condition: He rows 48 km distant and back in 14 hours. Total time = Time downstream + Time upstream 14 = 48 / (B + S) + 48 / (B - S) Substitute B = 7S from Equation 1 into this equation: 14 = 48 / (7S + S) + 48 / (7S - S) 14 = 48 / (8S) + 48 / (6S) 14 = 6/S + 8/S 14 = (6 + 8) / S 14 = 14 / S S = 14 / 14 S = 1 km/h So, the speed of the stream is 1 km/h.

Let the speed upstream be U km/h and the speed downstream be D km/h. Time = Distance / Speed From the first condition: 30/U + 44/D = 10 (Equation 1) From the second condition: 40/U + 55/D = 13 (Equation 2) Let 1/U = x and 1/D = y. The equations become: 30x + 44y = 10 (Equation 1') 40x + 55y = 13 (Equation 2') Multiply Equation 1' by 4 and Equation 2' by 3 to eliminate x: (30x + 44y) * 4 = 10 * 4 => 120x + 176y = 40 (40x + 55y) * 3 = 13 * 3 => 120x + 165y = 39 Subtract the second modified equation from the first: (120x + 176y) - (120x + 165y) = 40 - 39 11y = 1 y = 1/11 Since y = 1/D, we have 1/D = 1/11, so D = 11 km/h. Substitute y = 1/11 into Equation 1': 30x + 44(1/11) = 10 30x + 4 = 10 30x = 10 - 4 30x = 6 x = 6/30 = 1/5 Since x = 1/U, we have 1/U = 1/5, so U = 5 km/h. Now, calculate the speed of the boat in still water (B) and the speed of the stream (S): Formula: B = (D + U) / 2 B = (11 + 5) / 2 = 16 / 2 = 8 km/h Formula: S = (D - U) / 2 S = (11 - 5) / 2 = 6 / 2 = 3 km/h So, the speed of the boat in still water is 8 km/h and the speed of the stream is 3 km/h.