Practice MCQ Questions and Answer on Boats and Streams

1.

A man takes 2.2 times as long to row a distance upstream as to row the same distance downstream. If he can row 55 km downstream in 2 hour 30 minutes, what is the speed of the boat in the still water?

• (A) 40 km/h
• (B) 8 km/h
• (C) 16 km/h
• (D) 24 km/h

Show Answer

 $$\eqalign{ & {\text{Speed of the boat in downstream }} \cr & {\text{ = }}\frac{{55}}{{2.5}} = \frac{{55 \times 10}}{{25}} = 22\,km/hr \cr & {\text{Then, speed of the boat in upstream}} \cr & {\text{ = }}\frac{{22}}{{2.2}} = \frac{{22 \times 10}}{{22}} = 10\,km/hr \cr & \therefore {\text{Speed of the boat in still water}} \cr & {\text{ = }}\frac{{22 + 10}}{2} = 16\,km/hr \cr} $$

2.

A boat covers 24 km upstream and 36 km downstream in 6 hours, while it covers 36 km upstream and 24 km downstream in $$6\frac{1}{2}$$ hours. The speed of the current is?

• (A) 1 km/hr
• (B) 2 km/hr
• (C) 1.5 km/hr
• (D) 2.5 km/hr

Show Answer

 let speed of boat in still water = x km/h Speed of stream current = y km/h According to question, $$\eqalign{ & \frac{{24}}{{x - y}} + \frac{{36}}{{x + y}} = 6h\,......\,(i) \cr & \frac{{36}}{{x - y}} + \frac{{24}}{{x + y}} = \frac{{13}}{2}h\,......\,(ii) \cr} $$ In these type of questions, make factor of 24 and 36 and choose the common values which satisfy the above equations. $$\eqalign{ & {\text{24 = 2,3,4,6,8,}}\boxed{12} \cr & 36 = 3,4,9,\boxed{12} \cr} $$ Choose the common factor i.e. Put this value in equation (i) $$\eqalign{ & \frac{{24}}{{x - y}} + \frac{{36}}{{12}} = 6 \cr & \frac{{24}}{{x - y}} + 3 = 6 \cr & x - y = 8 \cr & \therefore x + y = 12 \cr & \therefore x = 10\,\,\,,\,\,\,\,y = 2 \cr & {\text{Speed of the current,}} \cr & y = 2{\text{ km/h}} \cr} $$

3.

A man rows to a place 48 km distant and come 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 rate of the stream is:

• (A) 1 km/hr
• (B) 1.5 km/hr
• (C) 2 km/hr
• (D) 2.5 km/hr

Show Answer

 Suppose he move 4 km downstream in x hours Then, Speed downstream = $$\frac{4}{x}$$ km/hr Speed upstream = $$\frac{3}{x}$$ km/hr $$\eqalign{ & \therefore \frac{{48}}{{\left( {4/x} \right)}} + \frac{{48}}{{\left( {3/x} \right)}} = 14\,or\,x = \frac{1}{2} \cr} $$ So, Speed downstream = 8 km/hr Speed upstream = 6 km/hr ∴ Rate of the stream = $$\frac{1}{2}$$(8 - 6) km/hr = 1 km/hr

4.

A man can row upstream at 12km/hr and downstream at 18 km/hr. The man rowing speed in still water is?

• (A) 15 km/hr
• (B) 5 km/hr
• (C) 3 km/hr
• (D) 10 km/hr

Show Answer

 Speed of boat in still water = $$\frac{{x + y}}{2}$$ Where (x = downstream speed) and (y = upstream speed) ∴ Boat's speed $$\eqalign{ & {\text{ = }}\frac{{18 + 12}}{2} \cr & = \frac{{30}}{2} \cr & = 15\,km/hr \cr} $$

5.

The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream at the same time, the speed of the stream is-

• (A) 2 km/hr
• (B) 2.5 km/hr
• (C) 3 km/hr
• (D) 4 km/hr

Show Answer

 Let the speed of the stream be x km/hr Then speed downstream = (10 + x) km/hr Speed upstream $$\eqalign{ & {\text{ = }}\left( {10 - x} \right)km/hr \cr & \therefore \frac{{26}}{{\left( {10 + x} \right)}} = \frac{{14}}{{\left( {10 - x} \right)}} \cr & \Rightarrow 260 - 26x = 140 + 14x \cr & \Rightarrow 40x = 120 \cr & \Rightarrow x = 3\,km/hr \cr} $$

6.

A man rows a boat a certain distance downstream in 9 hours, while it takes 18 hours to row the same distance upstream. How many hours will it take him to row $$\frac{3}{5}$$ of the same distance in still water?

• (A) 9.5
• (B) 7.2
• (C) 10
• (D) 12

Show Answer

 $$\eqalign{ & {\text{Speed of boat}} = x \cr & {\text{Speed of stream}} = y \cr & {\text{Distance}} = 9\left( {x + y} \right) = 18\left( {x - y} \right) \cr & x + y = 2x - 2y \cr & x = 3y \cr & {\text{Distance}} = 9\left( {x + y} \right) \cr & = 9\left( {3y + y} \right) \cr & = 36y \cr & 36y \times \frac{3}{5} = t \times x \cr & 36y \times \frac{3}{5} = t \times 3y \cr & t = \frac{{36}}{5} = 7.2 \cr} $$

7.

The speed of a boat in still water is 15 km/h, and the speed of the current is 5 km/h. In how much time (in hours) will the boat travel a distance of 60 km upstream and the same distance downstream?

• (A) 10 hr
• (B) 9 hr
• (C) 20 hr
• (D) 12 hr

Show Answer

 Speed of boat in still water = 15 km/hr Speed of stream = 5 km/hr Total time of upstream and downstream $$\eqalign{ & = \frac{{60}}{{15 - 5}} + \frac{{60}}{{15 + 5}} \cr & = 6 + 3 \cr & = 9{\text{ hr}} \cr} $$

8.

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

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

9.

A motorboat goes 24 km in 2 hour along the stream and 10 km in 1 hour against the stream. The speed of the motorboat in kilometres per hour, is:

• (A) 14
• (B) 10
• (C) 11
• (D) 12

Show Answer

 $$\eqalign{ & {\text{B}} + {\text{W}} = 12{\text{ km/h}} \cr & {\text{B}} - {\text{W}} = 10{\text{ km/h}} \cr & \overline {\,{\text{B}} = \frac{{22}}{2} = 11{\text{ km/h}}\,} \cr} $$

10.

A man can row 6 km/hr in still water. If the speed of the current is 2 km/hr he takes 4 hours more in upstream than the downstream. The distance is?

• (A) 30 km
• (B) 24 km
• (C) 20 km
• (D) 32 km

Show Answer

 Speed of man in still water, x = 6 km/h Speed of current, y = 2 km/h Let distance = M According to question Upstream time = Downstream time + 4 $$\eqalign{ & \frac{M}{4} = \frac{M}{8} + 4 \cr & \frac{M}{4} = \frac{{M + 32}}{8} \cr & M = 32 \cr & \therefore {\text{Distance = 32 }}km \cr} $$