In the question, two Quantities I and II are given. You have to solve both the Quantity to establish the correct relation between Quantity-I and Quantity-II and choose the correct option. The speed of boat 'B' in still water is 8 km/h more than that of boat 'A'. The ratio of downstream speed of boat 'A' to upstream speed of boat 'B' is 9:8. The ratio of upstream speed of boat 'A' to downstream speed of boat 'B' is 6:11. (Both the boats are travelling in the same stream) Quantity-I: Find the sum of distance travelled by boat 'A' in downstream in 125 minutes and distance travelled by boat 'B' in upstream in 75 minutes. Quantity-II: Speed of Boat 'C' in still water is 50 km/h. Find the sum of distance travelled by boats 'A', 'B' and 'C' together while travelling in upstream for 1 hour. Boat 'C' is also travelling in the same stream.

Explanation

1 Detailed solution: Let the speed of boat 'A' in still water = 'x' km/h Then, speed of boat 'B' in still water = (x + 8) km/h Let the speed of the stream = 'y' km/h Upstream speed of boat 'A' = (x - y) km/h Downstream speed of boat 'A' = (x + y) km/h Upstream speed of boat 'B' = (x + 8 - y) km/h Downstream speed of boat 'B' = (x + 8 + y) km/h According to the statement, (x + y) : (x + 8 - y) = 9:8 Or, 8x + 8y = 9x - 9y + 72 Or, 17y = x + 72 - [equation I] Also, according to the statement, (x - y) : (x + 8 + y) = 6:11 Or, 11x - 11y = 6x + 48 + 6y Or, 5x = 17y + 48 Or, 17y = 5x - 48 - [equation II] Equating equations (I) and (II) So, x + 72 = 5x – 48 Or, 120 = 4x So, x = (120/4) = 30 Therefore, speed of boat 'A' and boat 'B' in still water is 30 km/h and 38 km/h, respectively So, y = (5 X 30 - 48) ÷ 17 = 102 ÷ 17 = 6 So, upstream and downstream speed of boat 'A' is 24 km/h and 36 km/h respectively Upstream and downstream speed of boat 'B' is 32 km/h and 44 km/h. Quantity I: Distance travelled by boat 'A' in downstream in 125 minutes = 36 X (125/60) = 75 km Distance travelled by boat 'B' in upstream in 75 minutes = 32 X (75/60) = 40 km So, Quantity I = 75 + 40 = 115 km Quantity II: Upstream speed of boat 'C' = 50 - 6 = 44 km/h Distance travelled by boat 'A' and boat 'B' in upstream in 1 hour is 24 km and 32 km, respectively. Speed of boat 'C' in upstream = 50 - 6 = 44 km/h Distance travelled by boat 'C' in upstream in 1 hour = 44 km So, Quantity II = 24 + 32 + 44 = 100 km Therefore, quantity I > quantity II