**(Q1) A man rows down a river 15 km in 3 hrs with the stream and returns in 15/2 hrs. The rate at which he rows in still water is:**

(a) 2.5 kmph (b) 1.5 kmph

(c) 3.5 kmph (d) 4.5 kmph

Read Solution**Solution: **

Downstream speed=x

Upstream Speed=y

Upstream Time=15/2 hrs

Downstream Time=3 hrs

Distance=15 km

x = Distance/downstream time = 15/3 = 5 km/hr

y = Distance/upstream time =15 / (15/2) = 2 km/hr

Speed of person = (x + y)/2 = (5 + 2)/2 = 3.5 km/hr**Option (c) is the right answer**

**(Q2) A boat takes half time in moving a certain distance downstream than upstream. The ratio of the speed of the boat in still water and that of the current is**

(a) 3:1 (b) 4:3

(c) 1:2 (d) 2:1

Read Solution

Let the speed of boat in still water=x kmph

Speed of current=y kmph

Downstream Rate= (x+y) kmph

Upstream Rate=(x-y) kmph

Distance=Speed × Time

=> (x – y) × 2t = (x + y) ×t

=> (x – y) × 2 =(x + y)

=> (x – y) × 2=(x + y)

=> 2x – 2y= x + y

=>2x – x= y + 2y

=> x = 3y

x : y = 3 : 1**option (a) is the right answer**

**(Q3). A man rows 12 km in 5 hours against the stream and the speed of current being 4 kmph. What time will be taken by him to row 15 km with the stream?**

(a) 1 hr 27 min

(b) 1 hr 24 min

(c) 1 hr 25 min

(d) 1\ hour\ 26\frac{7}{13} \ minutes \\\ \\ Read Solution

Let x is speed of boat in still water

Speed of current=4 kmph

Distance=12 km

Upstream Speed=(x-4) kmph

Upstream Speed= Distance / Time

=> x – 4= 12/5

=> 5 (x-4) =12

=> 5x-20=12

=> x= 32/5**x=6.4 kmph**

Downstream Speed=(x+y)

Downstream Speed=6.4 + 4

Downstream Speed=10.4 kmph

Time= Distance/Speed

Time= 15/10.4

Time= 1\ hour\ 26\frac{7}{13} \ minutes

**Option (d) is the right answer**

**(Q4) A man rows to a place 60 km distance and back in 13 hours 30 minutes. He finds that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the Rate of the stream?**

(a) 8 kmph (b) 0.5 kmph

(c) 10 kmph (d) 1 kmph

Read Solution

Let the speed of man is x kmph

Speed of stream=y kmph

Upstream Speed=(x-y) kmph

Downstream Speed=(x+y) kmph

Distance=60 km

Time= 27/2 hours

Distance/Downstream + Distance/Upstream Speed = Time

\frac{60}{x+y} \ +\ \frac{60}{x-y} \ =\ \frac{27}{2} \ \ \ \ \ \ \ \ \ \ ----eq( a)

Given that,

Downstream Distance= 5 km

Upstream Distance= 4 km

ATQ

\frac{Downstream\ Distance}{Downstream\ Speed} =\ \frac{Upstream\ Distance}{Upstream\ Speed} \ \ \ \ \ (as \ time\ is\ same) \\\ \\ \frac{5}{x+y} =\ \frac{4}{x-y}

==> 5 (x – y) = 4 ( x + y)

==> 5x – 5y = 4x + 4y

==> x = 9y

Put the value of x in equation ‘a’

\frac{60}{9y+y} +\frac{60}{9y-y} =\ \frac{27}{2}

On solving the above equation we get **y=1 kmph**

**Option (d) is the right answer**

**(Q5). A boat running upstream takes 5 hours and 40 minutes to cover a certain distance, while it takes 3 hours to cover the same distance downstream. What is the ratio between the speed of the boat and speed of water current respectively?**

(a) 13:4 (b) 20:1

(c) 19:2 (d) 1:19

Read SolutionSol:

Let the speed of boat be x kmph

Speed of current = y kmph

Upstream rate = (x-y) kmph

Upstream Time= 5 hrs 40 min

Downstream rate = (x+y) kmph

Downstream time= 3 hrs

Distance=Time × Speed

According to question

(5+40/60) × (x-y) = 3 (x+y)

On solving we get

4x = 13y

x : y =13 : 4

**Option (a) is the right answer**

**(Q6) .The speed of boat downstream is 15 km/hr and speed of current is 3 km/hr. Find the total time taken by the boat to cover 15 km upstream and 15 km downstream**.

(a) 2 hours 40 minutes

(b) 2 hours 42 minutes

(c) 3 hours 10 minutes

(d) 2 hours 30 minutes

Read Solution

Distance = 15 km

Downstream Speed= 15 kmph

Speed of Current = 3kmph

Speed of boat in still water= Downstream Speed-Speed of current

Speed of boat in still water=15 – 2=12 kmph

Upstream Speed= Speed of boat in still water- Speed of Current

Upstream Speed=12 – 3 = 9 kmph

Upstream Time=Distance/Speed= 15/9 = 1 h 40 min

Downstream Time= Distance Speed =15/(12+3) =1 hour

Total Time = 2hr 40 min**Option (a) is the right answer**

**(Q7). A man rows to a place 35 km in distance and back in 10 hours 30 minutes. He found that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the rate of flow of the stream.**

(a) 1 km/hrs (b) 0.75 km/hrs

(c) 1.33 km/hrs (d) 1.5 km/hrs

Read Solution

Let the speed of man is x kmph

Speed of stream=y kmph

Upstream Speed=(x-y) kmph

Downstream Speed=(x+y) kmph

Distance=35 km

Time=10 hour 30 mins = 21/2 hours

(Distance/Downstream Speed) + (Distance/Upstream Speed) =Time

\frac{35}{x+y} +\frac{35}{x-y} =\ \frac{21}{2} \ \ \ \ \ \ \ \ \ \ .\ .\ .\ .\ eq( a)

Given that,

Downstream Distance= 5 km

Upstream Distance= 4 km

ATQ

\frac{Downstream\ Distance}{Downstream\ Speed} =\frac{Upstream\ Distance}{Upstream\ Speed} \ \ \ \ \ \ \ \ \ \ \ {Given\ that\ time\ is\ same} \\\ \\ \frac{5}{x+y} =\ \frac{4}{x-y} \ \ \ \ \ \ \ \ \

=> 5 (x – y) = 4 (x + y)

=> x = 9y

Put the value of x in equation ‘a’

\frac{35}{9y+y} +\frac{35}{9y-y} =\ \frac{21}{2} \ \ \ \ \ \ \

On solving the equation we get;

y=0.75 km/hr

**Option (b) is the right answer**

**(08) The water in a river is flowing at the rate of 4 km/hr. If the width and depth of the river is 8m and 4m respectively, then how much water will enter the sea in 15 minutes.**

(a) 60000 cu meter (b) 18000 cu meter

(c) 28800 cu meter (d) 32000 cu meter

If water Flows at 4kmph

So in 15 minutes it travels= 1 km=1000 m

Volume of water entering the sea in 15 minutes= Width×Depth×Distance

Volume of water entering the sea in 15 minutes=8×4×1000

Volume of water entering the sea in 15 minutes=32000 cu meter

**option (d) is the right answer**

**(09) A boat goes 75 km upstream in 3 hours and 60 km downstream in 1.5 hours. Then the speed of the boat in still water is:**

(a) 32.5 kmph (b) 30 kmph

(c) 65 kmph (d) 60 kmph

Read SolutionUpstream Distance= 75 km

Upstream Time= 3 hours

Downstream Distance= 60 km

Downstream Time=1.5 hours

Upstream Speed=Distance/Time= 75 / 3 =25 kmph

Downstream Speed= Distance/Time = 60/1.5 =40 kmph

Speed of boat in still water = (Upstream Speed + Downstream Speed) / 2

Speed of boat in still water= (25 + 40) /2=32.5 kmph**Option (a) is the right answer**