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MCQ Practice Test & Solutions: Test: Boat and Stream- 1 (20 Questions)

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Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 20 minutes
  • - Number of Questions: 20

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Test: Boat and Stream- 1 - Question 1

Directions: Study the following questions carefully and choose the right answer.

A boat takes 19 hours for travelling downstream from point A to Point B and coming back to a Point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 12 kmph, what is the distance between A and B?

Detailed Solution: Question 1

Speed downstrem = (12 + 4)km/hr = 16 km/hr;
Speed upstream = (12 - 4) km/hr = 8 km/hr.
Let the distance between A and B be x km, Then,

⇔ 2x/16 = 19 ⇔ x = 152 km.

Test: Boat and Stream- 1 - Question 2

Directions: Study the following questions carefully and choose the right answer.

In stream running at 2 kmph, a motorboat goes 6 km upstream and back again to the starting point in 33 minutes. Find the speed of the motorboat in still water. 

Detailed Solution: Question 2

Let the speed of the motorboat in still water be x kmph. Then,
Speed downstream = (x + 2) kmph; Speed upstream = (x – 2) kmph.

⇒  11x2 – 242x + 2x – 44 = 0  ⇔  (x – 22)(11x + 2) = 0  ⇔  x = 22.
Hence, speed of motorboat in still water = 22 kmph.
Hence, option D is correct.

Test: Boat and Stream- 1 - Question 3

Directions: Study the following questions carefully and choose the right answer.

A man can row 18 kmph in still water. It takes him thrice as long to row up as to row down the river. Find the rate of stream.

Detailed Solution: Question 3

To solve this question, we can apply a short trick approach;

Given,
x = Person speed = 18 kmph
n = the no. of times of hours taken by the boat in the 2nd scenario (upstream) = 3
By the short trick approach, we get

Hence, option C is correct.

Test: Boat and Stream- 1 - Question 4

Directions: Study the following questions carefully and choose the right answer.

Speed of a boat in still water is 8 kmph and speed of stream is 1.5 kmph. A man rows to a place at a distance of 61.75 km and come back to starting point. The total time taken by him is:

Detailed Solution: Question 4

Rate upstream = 8 – 1.5 = 6.5 kmph
Rate downstream = 8 + 1.5 = 9.5 kmph
Time taken to go upstream = 61.75/6.5 = 9.5 hr.
Time taken to go downstream = 61.75/9.5 = 6.5 hr.
Total time = 9.5 + 6.5 = 16 hrs.
Hence, option C is correct.

Test: Boat and Stream- 1 - Question 5

Directions: Study the following questions carefully and choose the right answer.

If a man rows at the rate of 5 kmph in still water and his rate against the current is 3.5 kmph. then the man's rate along the current is:

Detailed Solution: Question 5

Given,

Upstream rate = 3.5 kmph, Speed of a man in still water  = 5 kmph

Let the downstream rate be x kmph, then

By the short trick approach, we get

Speed of the man (boat) in still water = 1/2

[DOWNSTREAM rate + UPSTREAM rate]

⇒ 5 = 1/2 (x + 3.5)  or   x = 6.5 kmph

Hence, option C is correct.

Test: Boat and Stream- 1 - Question 6

A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream.

Detailed Solution: Question 6

Speed downstream
= (13 + 4) km/hr
= 17 km/hr
Time taken to travel 68 km downstream
= 68/17 hours
= 4 hours

Test: Boat and Stream- 1 - Question 7

A boat running upstream takes 8 hours 48 minutes to cover a certain distance, while it takes 4 hours to cover the same distance running downstream. What is the ratio between the speed of the boat and speed of the water current respectively?

Detailed Solution: Question 7

Let the man's rate upstream be x kmph and that downstream be y kmph.
Then, distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.

∴ Required ratio

Test: Boat and Stream- 1 - Question 8

In one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:

Detailed Solution: Question 8

Speed in still water
= 1/2 (11 + 5) kmph
= 8 kmph

Test: Boat and Stream- 1 - Question 9

The speed of a boat in still water in 15 km/hr and the rate of current is 3 km/hr. The distance travelled downstream in 12 minutes is:

Detailed Solution: Question 9

Speed downstream
= (15 + 3) kmph
= 18 kmph
Distance travelled

= 3.6 km

Test: Boat and Stream- 1 - Question 10

A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Detailed Solution: Question 10

Speed downstream = (5 + 1) kmph = 6 kmph
Speed upstream = (5 - 1) kmph = 4 kmph
Let the required distance be x km
Then,

⇒ 2x + 3x = 12
⇒ 5x = 12
⇒ x = 2.4 km

Test: Boat and Stream- 1 - Question 11

If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph then the speed of the boat in still water is:

Detailed Solution: Question 11

Rate upstream = (7/42 × 60) kmph = 10 kmph.
Speed of stream = 3 kmph
Let speed in still water be x km/hr. Then, speed upstream = (x – 3) km/hr.
∴   x – 3 = 10   OR   x = 13 km/hr.

Test: Boat and Stream- 1 - Question 12

A man can row upstream at 7 kmph and downstream at 10 kmph. Find man's rate still water and the rate of current.

Detailed Solution: Question 12

Rate in still water = 1/2 (10 + 7) km/hr = 8.5 km/hr
Rate of current = 1/2 (10 – 7) km/hr = 1.5 km/hr.

Test: Boat and Stream- 1 - Question 13

A boat covers 24 km upstream and 36 km downstream in 6 hours while it covers 36 km upstream and 24 km downstream 
in 61/hours. The velocity of the current is:

Detailed Solution: Question 13

Let the upstream = x kmph and rate downstream = y kmph.
Then,

Adding (i) and (ii) we get:

Subtracting (i) and (ii), we get:

Adding (iii) and (iv), we get 2/x = 6/24 or  x = 8.
So,

∴  Speed upstream = 8 kmph, Speed downstream = 12 kmph.
Hence, rate of current 1/2(12 – 8) kmph = 2 kmph.
Hence, option C is correct.

Test: Boat and Stream- 1 - Question 14

A man can row 15/2 kmph in still water, if the river is running at 1.5 km an hour. It takes him 50 mins to row to a place and back, how far off is the place?

Detailed Solution: Question 14

Speed downstream
= (15/2 + 1.5) kmph
= (7.5 + 1.5) kmph
= 9 kmph;
Speed upstream
= (15/2  – 1.5) kmph
= (7.5 – 1.5) kmph
= 6 kmph.
Let the required distance be x km. Then,


⇔  5x = 15  ⇔  x = 3
Hence, the required distance is 3 km.

Test: Boat and Stream- 1 - Question 15

A man can row 40 km upstream and 55 km downstream in 13 hours, also he can row 30 km upstream and 44 km downstream in 10 hours. Find the speed of the man in still water and the speed of the current.

Detailed Solution: Question 15

Let rate upstream = x km/hr and rate downstream = y km/hr.
Then, 40/x + 55/y = 13 ... (i)    and
30/x + 44/y = 10    .... (ii)
Multiplying (ii) by 4 and (i) by 3 and subtracting,
we get: 11/y = 1 or y = 11.
Substituting y = 11 in (i), we get: x = 5.
∴ Rate in still water = 1/2 (11 + 5) kmph = 8 kmph.
Rate in current = 1/2(11 – 5) kmph = 3 kmph.
Hence, option B is correct.  

Test: Boat and Stream- 1 - Question 16

A boatman goes 2 km against the current of the stream in 1 hour and goes 1 km along the current in 10 minutes. How long will it take to go 5 km in stationary water?

Detailed Solution: Question 16

Rate downstream

Rate upstream = 2km/hr
Speed in still water
= 1/2 (6 + 2)km/hr = 4km/hr
∴Required time
= 5/4 hrs
= 11/4 hrs
= 1hr 15min.

Test: Boat and Stream- 1 - Question 17

Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:

Detailed Solution: Question 17

Speed upstream = 7.5 kmph
Speed downstream = 10.5 kmph
∴ Total time taken

= 24 hours

Test: Boat and Stream- 1 - Question 18

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:

Detailed Solution: Question 18

Suppose he move 4 km downstream in x hours
Then,
Speed downstream = 4/x km/hr
Speed upstream = 3/x km/hr

So, Speed downstream = 8 km/hr
Speed upstream = 6 km/hr
∴ Rate of the stream
= 1/2 (8 - 6) km/hr
= 1 km/hr

Test: Boat and Stream- 1 - Question 19

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?

Detailed Solution: Question 19

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

M = 32
∴ Distance = 32 km

Test: Boat and Stream- 1 - Question 20

The speed of a boat along the stream is 12 km/hr and against the stream is 8 km/hr. The time taken by the boat to sail 24 km in still water is?

Detailed Solution: Question 20

Speed of downstream
D = 12 km/h
Speed of upstream
U = 8 km/h
Speed of boat in still water
= D + U/2
= 20/2
= 10 km/h
Time taken by the boat in still water

= 2.4 hours

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