**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 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.

2. 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

3. 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 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.

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. 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

7. 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

8. A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?

**Answer:** Option
C

**Explanation:**

US = 25
DS = 35
M = (35 + 25)/2 = 30

9. 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.

10. 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.

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. 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

13. 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

14. 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

15. 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