Question: 16 -

A man went downstream for 28 km in a motor boat and immediately returned. It took the man twice as long to make the return trip. If the speed of the river flow were twice as high, the trip downstream and back would take 672 minutes. Find the speed of the boat in still water and the speed of the river flow.

9 km/hr, 6 km/hr 

8 km/hr, 2 km/hr 

9 km/hr, 3 km/hr 

2 km/hr, 3 km/hr 

Answer:

9 km/hr, 3 km/hr 

Solution:

Let the speed of the boat = p kmph

Let the speed of the river flow = q kmph

From the given data,

2 x 28p + q = 28p − q

=> 56p - 56q -28p - 28q = 0

=> 28p = 84q

=> p = 3q.

Now, given that if

283q + 2q + 283q − 2q = 67260=> 285q + 28q = 67260=> q = 3 kmph=> x  =3q = 9 kmph

Hence, the speed of the boat = p kmph = 9 kmph and the speed of the river flow = q kmph = 3 kmph.

Question: 17 -

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will he take to go 5km in stationery water? 

40 Minutes

1 Hour

1 hr 15 Min

1 Hr 30 Min

Answer:

1 hr 15 Min

Solution:

Speed upstream = 2km/hr.

Speed downstream = 6 km/hr 

Speed in stationary water = ½ (6 + 2) km/hr = 4 km/hr 

Time is taken to cover 5 km in stationary water 

= (1/4 x 5) 1 hr 15 min

Question: 18 -

A boat takes half time in moving a certain distance downstream than upstream. What is the ratio between the rate in still water and rate of current? 

3 : 1

1 : 2

2 : 1

1 : 3

Answer:

3 : 1

Solution:

Let the speed of the boat in still water be 4 km/hr and speed of the current be u km/hr. 

Rate downstream = (u + v) km/hr. 

Rate upstream = (u- v)km/hr 

Let the distance covered in each case be x km. 

Then 2x/(u + v) = x / (u - v) 

=> 2 (u - v) = ( u + v)

=> u =3v 

=> u/v =3/1

Question: 19 -

A boat travels upstream from B to A and downstream from A to B in 3 hours. If the speed of the boat in still water is 9km/hr and the speed of the current is 3km/hr, the distance A and B is: 

6 km

4km

8 km

12 km

Answer:

12 km

Solution:

Speed downstream = (9+3) km/hr = 12km/hr 

Speed upstream = (9-3) km/hr = 6 km/hr 

Distance AB = x km 

 x/6 + x/12 = 3 

=> 2x + x = 36 

=> x= 12 

Question: 20 -

A boat goes 6 km in an hour in still water. It takes thrice as much time in covering the same distance against the current. Speed of the current is? 

2 km/hr

3km/hr

4km/hr

5 km/hr

Answer:

4km/hr

Solution:

Speed in still water = 6 km/hr 

Speed against the current = 6/3 km/hr = 2 km/hr 

Let the speed of the current be x km/hr 

6-x = 2 => x =4 km/hr