The speed of a boat in still water is 15 km/hr. It can go 30 km upstre

1.	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» (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.

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»

(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.