**Important formulae and tricks and shortcuts of Boats And Sreams :**

We are providing you Important Concepts and Tricks on **Boats And Sreams **which are usually asked in almost all competitive exams like IBPS, Govt. Exams and CAT and in quantitative aptitude of MNCs. Use these below given tricks to solve questions within minimum time. These tricks will be very helpful for your upcoming Competitive Exam.

**Terms Related To Boats And Sreams:**

**Speed of the boat:**It refers to the velocity of the boat in standing water ,let it be X.

**Speed of the Stream: **It refers to the velocity at which the water flows,let it be Y.

**Upstream Speed (U): **It is expressed as the (Speed of the Boat – Speed of the Stream) =X-Y.

They row the boat in the opposite direction to the flow of the stream.

**Downstream Speed (D): **It is expressed as the (Speed of the Boat + Speed of the Stream) =X+Y.

They Row along the flow of Stream.

**Speed of the boat in still water when upstream and downstream speed is given=1/2(D+U)**

**Lets understand in detail:**

**Upstream: **When the boat moves against the current of the river (i.e. in opposite direction), then the relative speed of the boat is the difference of the speed of the boat and stream. It is known as upstream speed.

Remember it with UP as going up the hill means against the direction of the force (speed) of the river.

If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

**Speed of boat upstream = (x − y) km/h**

**Downstream:** When the boat moves with the current of the river (i.e. in same direction), then the relative speed of the boat is the sum of the speed of the boat and stream. It is known as downstream speed.

emember it with DOWN as going down the hill means towards the direction of the force (speed) of the river.

If speed of boat or swimmer is x km/h and the speed of stream is y km/h then,

**Speed of boat downstream = (x + y) km/h**

**Important Points**

When speed of boat is given then it means speed in the still water, unless it is stated otherwise.

Some Basic Formulas

**Speed of boat in still water is
= ½ (Downstream Speed + Upstream Speed)**

**Speed of stream is
= ½ (Downstream Speed – Upstream Speed)**

**For solved problems on above formulas please visit below sections:**

1. The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?

**Answer:** Option
C

**Explanation:**

S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8

2. A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?

**Answer:** Option
B

**Explanation:**

M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4

4. A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?

**Answer:** Option
A

**Explanation:**

M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3

5. A man can swim in still water at 4.5 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?

**Answer:** Option
D

**Explanation:**

M = 4.5
S = x
DS = 4.5 + x
US = 4.5 + x
4.5 + x = (4.5 - x)2
4.5 + x = 9 -2x
3x = 4.5
x = 1.5

6. The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is?

**Answer:** Option
A

**Explanation:**

S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6

7. A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?

**Answer:** Option
B

**Explanation:**

72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5

8. The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?

**Answer:** Option
D

**Explanation:**

Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.

9. A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?

**Answer:** Option
D

**Explanation:**

Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.

10. The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?

**Answer:** Option
B

**Explanation:**

Speed downstream = 60 + 20 = 80 kmph Speed upstream = 60 - 20 = 40 kmph

11. A man can row downstream at 18 kmph and upstream at 10 kmph. Find the speed of the man in still water and the speed of stream respectively?

**Answer:** Option
D

**Explanation:**

Let the speed of the man in still water and speed of stream be x kmph and y kmph respectively.
Given x + y = 18 --- (1)
and x - y = 10 --- (2)
From (1) & (2) 2x = 28 => x = 14, y = 4.

12. A man can row his boat with the stream at 6 km/h and against the stream in 4 km/h. The man's rate is?

**Answer:** Option
A

**Explanation:**

DS = 6
US = 4
S = ?
S = (6 - 4)/2 = 1 kmph

13. A boat can move upstream at 25 kmph and downstream at 35 kmph, then the speed of the current is?

**Answer:** Option
A

**Explanation:**

US = 25
DS = 35
M = (35 - 25)/2 = 5

14. The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?

**Answer:** Option

**Explanation:**

Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2 = 10 kmph.

15. A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?

**Answer:** Option
B

**Explanation:**

M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88