Practice MCQ Questions and Answer on Boats and Streams

41.

A boat can go 5 km upstream and $$7\frac{1}{2}$$ km downstream in 45 minutes. If can also go 5 km downstream and 2.5 km upstream in 25 minutes. How much time (in minutes) will it take to go 6 km upstream?

• (A) 30
• (B) 36
• (C) 24
• (D) 32

Show Answer

 $$\eqalign{ & \frac{5}{{x - y}} + \frac{{15}}{{2\left( {x + y} \right)}} = \frac{3}{4}{\text{hr }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {\text{i}} \right) \cr & \frac{{2.5 \times 2}}{{x - y}} + \frac{{5 \times 2}}{{x + y}} = \frac{{5 \times 2}}{{12}}{\text{hr }}{\text{. }}{\text{. }}{\text{. }}{\text{. }}\left( {{\text{ii}}} \right) \cr & \frac{5}{{2\left( {x + y} \right)}} = \frac{1}{{12}} \cr & x + y = 30 \cr & {\text{Put }}x + y = 30{\text{ in equation }}\left( {\text{i}} \right) \cr & \frac{5}{{x - y}} + \frac{{15}}{{2 \times 30}} = \frac{3}{4} \cr & \frac{5}{{x - y}} = \frac{1}{2} \cr & x - y = 10 \cr & {\text{Now,}} \cr & \,x + y = 30 \cr & \underline {\,x - y = 10\,} \cr & x = 20 \cr & y = 10 \cr & \frac{{6\,{\text{km}}}}{{x - y}} = \frac{6}{{10}} \times 60 = 36\min \cr} $$

42.

A man rows to a place 48 km distant and comes back in 14 hours. He finds that he can row 4 km with the stream in the same time as 3 km against the stream. The speed of the stream is:

• (A) 1.5 km/h
• (B) 3.5 km/h
• (C) 1.8 km/h
• (D) 1 km/h

Show Answer

 $$\eqalign{ & {\text{Let, speed of boat}} = x \cr & {\text{Speed of stream}} = y \cr & \Rightarrow \frac{{48}}{{x + y}} + \frac{{48}}{{x - y}} = 14\,.\,.\,.\,.\,.\,\left( {\text{i}} \right) \cr & {\text{and, }}\frac{4}{{x + y}} = \frac{3}{{x - y}} \cr & \frac{{x - y}}{{x + y}} = \frac{3}{4} = \frac{6}{8} \cr & {\text{From equation }}\left( {\text{i}} \right), \cr & \frac{{48}}{8} + \frac{{48}}{6} = 14 \cr & 14 = 14\,\,\,\left( {{\text{Satisfied}}} \right) \cr & {\text{So, }}x - y = 6 \cr & \,\,\,\,\,\,\,\,\,x + y = 8 \cr & \,\,\,\,\,\overline {\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,y = 1\,\,} {\text{km/hr}} \cr} $$

43.

On a river , Q is the mid - point between two points P and R on the same bank of the river. A boat can go from P to Q and back in 12 hours, and from P to R in 16 hours 40 minutes. How long would it take to go from R to P?

• (A) $${\text{3}}\frac{3}{7}$$ hr
• (B) 5 hr
• (C) $${\text{6}}\frac{2}{3}$$ hr
• (D) $${\text{7}}\frac{1}{3}$$ hr

Show Answer

 $$\eqalign{ & {\text{P - - - - - - - - - - }}\mathop {\text{ - }}\limits_{\text{Q}} {\text{ - - - - - - - - - - R}} \cr & {\text{ - - - - - - - 16}}{\text{.40 - - - - - - - > }} \cr & \because {\text{Time required travelling from P to R}} \cr & {\text{ = 16H 40M}} \cr & \because {\text{PQ = QR}}\left( {\because {\text{Q is mid point}}} \right){\text{ }} \cr & {\text{Required time to travel PQ}} \cr & {\text{ = }}\frac{1}{2}\left( {{\text{16H 40M}}} \right) = \,\,{\text{8H 20M}} \cr & {\text{total required time from}} \cr & {\text{P to Q + Q to P = 12H}} \cr & {\text{ = 8H 20M + Q to P = 12H}} \cr & {\text{Time Q to P}} \cr & {\text{ = 12H - 8H 20M}} \cr & {\text{ = 3H 40M}} \cr & \because \overrightarrow {{\text{QP}}} {\text{ = }}\frac{1}{2}\overrightarrow {{\text{RP}}} {\text{ }}\,\,\left( {{\text{Distance}}} \right) \cr & \therefore {\text{Required time to }}\overrightarrow {{\text{RP}}} {\text{ }} \cr & {\text{ = 2}} \times \left[ {\overrightarrow {{\text{QP}}} } \right] \cr & {\text{ = 2}}\left[ {3{\text{H 40M}}} \right]{\text{ }} \cr & {\text{ = 7 H 20M}} \cr & {\text{ = 7}}\frac{1}{3}{\text{hr}}{\text{ }} \cr} $$

44.

A boat running downstream covers a distance of 16 km in 2 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?

• (A) 4 kmph
• (B) 6 kmph
• (C) 8 kmph
• (D) Data inadequate

Show Answer

 Rate downstream = $$\frac{{16}}{2}$$ kmph = 8 kmph Rate upstream = $$\frac{{16}}{4}$$ kmph = 4 kmph ∴ Speed in still water = $$\frac{1}{2}$$(8 + 4) kmph = 6 kmph

45.

A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

• (A) 4 km/hr
• (B) 5 km/hr
• (C) 6 km/hr
• (D) 10 km/hr

Show Answer

 Let the speed of the stream be x km/hr Then, Speed downstream = (15 + x) km/hr Speed upstream = (15 - x) km/hr $$\eqalign{ & \therefore \frac{{30}}{{ {15 + x} }} + \frac{{30}}{{ {15 - x} }} = 4\frac{1}{2} \cr & \Rightarrow \frac{{900}}{{225 - {x^2}}} = \frac{9}{2} \cr & \Rightarrow 9{x^2} = 225 \cr & \Rightarrow {x^2} = 25 \cr & \Rightarrow x = 5\,km/hr \cr} $$

46.

The speed of a boat in still water is 18 km/h and the speed of the current is 6 km/h. In how much time (in hours) will the boat travel a distance of 90 km upstream and the same distance downstream?

• (A) $$9\frac{1}{2}$$
• (B) $$11\frac{1}{4}$$
• (C) 12
• (D) 10

Show Answer

 $$\eqalign{ & \frac{{90}}{{{\text{Boat}} - {\text{Stream}}}} + \frac{{90}}{{{\text{Boat}} + {\text{Stream}}}} = {\text{Time}} \cr & \frac{{90}}{{12}} + \frac{{90}}{{24}} = {\text{Time}} \cr & {\text{Time}} = \frac{{270}}{{24}} = \frac{{45}}{4} = 11\frac{1}{4} \cr} $$

47.

A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:

• (A) 0.4
• (B) 0.2
• (C) 1
• (D) 0.6

Show Answer

Answer & Solution Answer: Option D No explanation is given for this question Let's Discuss on Board

48.

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

• (A) 2 hours
• (B) 3 hours
• (C) 4 hours
• (D) 5 hours

Show Answer

 Speed downstream = (13 + 4) km/hr = 17 km/hr Time taken to travel 68 km downstream = $$\frac{{68}}{{17}}$$ hours = 4 hours

49.

A boat moves 25 km upstream and 39 km downstream in 8 hours. It travels 35 km upstream and 52 km downstream in 11 hours. What is the speed of the stream if it travels at a uniform speed?

• (A) 4 km/h
• (B) 5 km/h
• (C) 6 km/h
• (D) 3 km/h

Show Answer

 Let speed of boat is x and stream is y km/hr According to the question $$\eqalign{ & \frac{{25}}{{x - y}} + \frac{{39}}{{x + y}} = 8 \cr & \frac{{35}}{{x - y}} + \frac{{52}}{{x + y}} = 11 \cr} $$ By hit and trail method x = 9, y = 4 it satisfy the both equations Speed of stream = 4 km/hr