Concept Of Boat And Stream [नाव और धारा]–03

Question: The ratio of the speed of the boat upstream to the speed of the boat downstream is 2: 3. What is the speed of the boat in still water if it covers 42 km downstream in 2 hours 20 minutes? (in km/h). [एक नाव की धारा के विरुद्ध तथा धारा की दिशा में चालों का अनुपात 2: 3 है. यदि वह नाव धारा की दिशा में 2 घंटे 20 मिनट में 42 कि मी की दूरी तय करती है, तो बताएं कि शांत जल में नाव की चाल क्या है? कि मी/घंटे में]      [Ans. (b) 15]   [IBPS PO PT – 04/10/2015]                                      

(a) 13.5  (b) 15 (c) 18   (d) 20   (e) 16

Solution: 

Detailed explanation: Concept: Let “X” and “Y” are the speeds of boat along downstream and upstream respectively.

Speed of a man boat downstream, X = u + v

Speed of a boat upstream, Y = u - v

Speed of a boat in still water, u = (X + Y)/2

Speed of current in still water, u = (X - Y)/2

First Method: Speed of the boat downstream, X = (42 km)/(2 hours and 20 minutes) = 18 km/h

= X =  = 18 km/h          

u =   =  = 2.5          

3 ≡ 18 km/r

2.5 ≡ ? = 15 km/r

Second Method: The boat covers a distance of 42 km in downstream in 2 hours and 20 minutes, so it will cover (42 × 3) km downstream in 7 hours, that is, 18 km in one hour. So, the speed of speed of the boat downstream = 18 km/h

Speed of boat downstream, X = 3 ≡ 18 km/h

So, speed of boat upstream, Y = 2 ≡ ? = 12 km/h

Speed of boat in still water, u = (X + Y)/2 = (18 + 12)/2 km/h = 15 km/h Ans.