**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. 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

2. 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. What is the total distance traveled by the man?

**Answer:** Option
C

**Explanation:**

M = 6
S = 1.2
DS = 7.2
US = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
D = 2.88 * 2 = 5.76

4. A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?

**Answer:** Option
B

**Explanation:**

30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8

5. A man rows his boat 85 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?

**Answer:** Option
D

**Explanation:**

Speed downstream = d/t = 85/(2 1/2) = 34 kmph Speed upstream = d/t = 45/(2 1/2) = 18 kmph The speed of the stream = (34 - 18)/2 = 8 kmph

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 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

8. A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?

**Answer:** Option
D

**Explanation:**

Speed downstream = 20 + 6 = 26 kmph. Time required to cover 60 km downstream = d/s = 60/26 = 30/13 hours.

9. A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?

**Answer:** Option
D

**Explanation:**

100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph

10. 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

11. 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.

12. A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?

**Answer:** Option
D

**Explanation:**

Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.

13. The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?

**Answer:** Option
C

**Explanation:**

The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1 Speed of the stream = 42/3 = 14 kmph.

14. 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

15. 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