Question

The speed of a boat in still water is 15 km/hr. It can go 30 km upstream and return downstream to the original point in 4 hrs 30 min. The speed of the stream is : 

(a) 5 km /hr 

(b) 8 km/ hr 

(c) 10 km/hr 

(d) 15 km/hr

Answer 1

(a) 5 km/hr

Let the speed of the stream be x km/hr. 

Speed downstream = (15 + x) km/hr 

Speed upstream = (15 – x) km/hr

∴ \(\frac{30}{(15+x)}\) + \(\frac{30}{(15-x)}\) = \(4\frac{30}{60}\)

⇒ \(\frac{30(15-x)+30(15+x)}{(15+x)(15-x)}\) = \(\frac92\) 

⇒ 900 x 2 = 9 (225 - x²) 

⇒ x² - 225 = 200 ⇒ x² = 25 ⇒ x = 5.