Question
"A boat takes 60 seconds to travel ______ metres
downstream and 40 seconds to travel ______ metres upstream in the same river. The speed of the stream is ______ m/s. Which of the following options will correctly fill the blanks in the same order to make the statement true?" I. 1440, 720, and 3 II. 1500, 600, and 5 III. 1200, 560, and 4Solution
ATQ, Let speed of boat in still water and speed of stream be, 'b' m/s and 's' m/s, respectively. For statement-I: Downstream speed of boat = b + s = (1440/60) So, b + s = 24 .... (i) Upstream speed of boat = b - s = (720/40) So, b - s = 18 .... (ii) Subtract equation (ii) from equation (i) , we get, b + s - b + s = 24 - 18 Or, 2s = 6 So, s = (6/2) = 3 Speed of stream = s = 3 m/s So, data given in statement-I is true. For statement-II: Downstream speed of boat = b + s = (1500/60) So, b + s = 25 .... (i) Upstream speed of boat = b - s = (600/40) So, b - s = 15 .... (ii) Subtract equation (ii) from equation (i), we get, b + s - b + s = 25 - 15 Or, 2s = 10 So, s = (10/2) = 5 Speed of stream = s = 5 m/s So, data given in statement-II is true. For statement-III: Downstream speed of boat = b + s = (1200/60) So, b + s = 20 .... (i) Upstream speed of boat = b - s = (560/40) So, b - s = 14 .... (ii) Subtract equation (ii) from equation (i) , we get, b + s - b + s = 20 - 14 Or, 2s = 6 So, s = (6/2) = 3 Speed of stream = s = 3 m/s ≠ 4 m/s So, data given in statement-III is false. Therefore, data given in both statement-I and statement-II is false
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