BANK & INSURANCE (BOAT AND STREAM) PART 3

Total Questions: 30

21. The speed of a boat in still water is 25% more than that of the stream. The boat travelled for 4 hours in downstream and then changed its direction and travelled for 2 hours more. If total distance travelled by the boat is 304 km, then find the speed of the stream.

Correct Answer: (c) 32 km/hr
Solution:Let the speed of the stream be ‘x’ km/hr

Therefore, speed of the boat in still water

= 1.25x km/hr

According to question,

Downstream speed of the boat = x + 1.25x

= 2.25x km/hr

Upstream speed of the boat = 1.25x - x = 0.25x km/hr

According to question,

2.25x × 4 + 0.25x × 2 = 304

9x + 0.5x = 304

x = 304/9.5 = 32

Therefore, speed of the stream = x = 32 km/hr

Hence, option c.

22. The speed of two boats M and N in the still water is in the ratio of 3: 4 and the speed of the current is 2km/hr. M starts from point P, 30 minutes earlier than N in the downstream direction. If N catches boat M in 2 hours, then, find the time taken by boat N to cover 22 km distance each downstream and upstream.

Correct Answer: (d) 5.9 hours 
Solution:Let the speed of boat M is 3x and speed of boat N is 4x.

Now we can say,

[3x + 2] × 2.5 = [4x + 2] × 2

0.5x = 1

x = 1/0.5 = 2

Speed of boat N = 4 × 2 = 8 km/hr

So, time taken = 22/10 + 22/6 = 5.9 hours

23. A boat goes 120 km upstream and returns to its starting place in 36 hours. The same boat goes 80 km upstream and returns to its starting place in 24 hours. Find the time taken to go 60 km downstream and come back 2/3rd of the distance in downstream.

Correct Answer: (d) 13 km/h 
Solution:The speed of the boat is x km/hour and the speed of the stream is y km/hr.

So, we can say,

120/(x + y) + 120/(x - y) = 36

80/(x + y) + 80/(x - y) = 24

By solving the above, we get x = 12 km/hour and y = 8 km/hr.

Required time = 60/20 + [2 × 60/(3 × 4)]

= 3 + 10 = 13 km/hr

24. A boatman travels from A to B (with the flow of the river) and comes back to point A, if the speed of the boat in still water increases by 100%, then his total travelling time gets reduced by 60%. Find the ratio of the speed of the boat in still water (original) to the speed of the current?

Correct Answer: (d) 2:1 
Solution:Total distance travelled in both cases is the same.

Ratio of time taken = 100 : 40 = 5 : 2

So ratio of their speed = 2 : 5

Let the speed of the boat in still water and speed of current be a km/h and b km/h.

Average speed in first case

= [2 × (a + b) × (a - b)] / [(a + b + a - b)] = (a + b)(a - b)/a

Average speed in second case

= [2 × (2a + b) × (2a - b)] / [(2a + b + 2a - b)] = (2a + b) x (2a - b)/2a

Now, [(a + b) (a - b)/a] / [(2a + b)(2a - b)/2a] = 2/5

5a² - 5b² = 4a² - b²

a² = 4b²

So, a/b = 2/1

Hence, the answer is option d

25. If the difference between the speed of boat A in still water and the speed of stream is 15 kmph and the speed of the boat C is 40% less than the speed of boat B in still water. The time taken by boat B covers x km along with stream in 6 hours and boat A covers the same distance along with stream in 7.2 hours and boat C covers 160 km along stream in 8 hours. If the time taken by boat A covers (x + y) km against with stream is 7.6 hours more than the time taken by boat B covers x km along with stream. Find the values of y?

Correct Answer: (b) 24 km 
Solution:Speed of boat B = 5b

Speed of boat C = 5b × 60/100 = 3b

Speed of boat A = a

Speed of the stream = c

a - c = 15 kmph

c = a - 15

x/(5b + a - 15) = 6 ..........(1)

x/(a + a - 15) = 7.2

x/(2a - 15) = 7.2 ..........(2)

160/(3b + a - 15) = 8

3b + a = 35 ..........(3)

From (1) and (2),

6 × (5b + a - 15) = 7.2 × (2a - 15)

30b + 6a - 90 = 14.4a - 108

8.4a - 30b - 18 = 0 ..........(4)

From (3) and (4)

18.4a = 368

a = 20, b = 5

c = 20 - 15 = 5 kmph

Speed of boat A = 20 kmph

Speed of boat B = 5 × 5 = 25 kmph

Speed of boat C = 5 × 3 = 15 kmph

x/(20 + 5) = 7.2

x = 7.2 × 25

x = 180 km

If the time taken by boat A covers (x + y) km against with stream is 7.6 hours more than the time taken by boat B covers x km along with stream. Find the values of y.

180/(25 + 5) + 7.6 = (180 + y)/(20 - 5)

13.6 = (180 + y)/15

y = 24 km

26. A boat that travels a total distance of 630 km downstream in three equal parts with the speed of the boat is 5x km/hr, 6x km/hr and 8x km/hr respectively. If the speed of the stream is x km/hr and the boat takes a total 88 1/3 hours, then find the time taken by the boat to travel the total distance upstream in three equal parts with their speeds.

Correct Answer: (a) 124.5 hours 
Solution:Speed of the boat = x km/hr

Three equal part of journey = 630/3 ⇒ each 210 km

Then, according to the question,

210/(5x + x) + 210/(6x + x) + 210/(8x + x) = 265/3

210/6x + 210/7x + 210/9x = 265/3

(4410 + 3780 + 2940)/126x = 265/3

(11,130 × 3)/(126 × 265) = x

x = 1 Km/hr

So, the speed of the boat = 1 km/hr

Thus, the time taken upstream is = 210/(5x - x) + 210/(6x - x) + 210/(8x - x)

= 210/4x + 210/5x + 210/7x

= 210/4 + 210/5 + 210/7

= 52.5 + 42 + 30

= 124.5 hours

Hence, the required answer = 124.5 hours.

27. A boat can cover 7 km upstream and 40 km downstream together in 6 hours. The speed of the boat in still water is 2 km/h more than the speed of the stream. Find the time taken by the boat to cover 30 km upstream and 48 km downstream together

Correct Answer: (b) 18 hours 
Solution:Let the speed of the stream = x km/h

So, the speed of the boat in still water = x + 2 km/h

According to question: 7/(x + 2 - x) + 40/(x + 2 + x) = 6

7/2 + 20/(x + 1) = 6

20/(x + 1) = 6 - 7/2

20/(x + 1) = 5/2

5x + 5 = 40

x = 7

So, the upstream and downstream speeds of the boat are 2 km/h and 16 km/h, respectively.

So, the time taken to cover 30 km upstream and 48 km downstream

= 30/2 + 48/16 = 15 + 3 = 18 hours

Hence, option b.

28. The distance between Y to Z is ‘m’ km. And the distance between X to Y is ‘m+56’ km. Boat A travels downstream from point X to Y and Boat B travels upstream from Y to Z. The speed of boat A in still water is 20% of ‘m’ and its equal to the upstream speed of boat B. Boat A travels downstream and it takes 20 minutes more time than the boat B travels in Upstream. What is the distance between Y and Z, if the speed of the current is the same in both cases that is 8 km/hr?

Correct Answer: (c) 200 km
Solution:The speed of boat A in still water = 20/100 of m => 0.2 m km/hr

Speed of the current = 8 km/hr

Downstream speed of boat A = (0.2m + 8) km/hr

Boat A in still water = upstream speed of boat B=> 0.2m

So, upstream speed of boat B = 0.2m km/hr

m + 56/0.2m + 8 = m/0.2m = 1/3

m + 56/0.2m + 8 = 16/3

3m + 168 = 3.2m + 128

0.2m = 40

m = 200

So, Distance between Y and Z = 200 km

29. Speed of Boat P, in still water is 80% of the downstream speed of boat Q and the upstream speed of Boat P is 18 km/hr. Boat Q can travel 192 km upstream in 12 hours 48 minutes. Find which of the following statements can be determined?

I. % by which upstream speed of boat P is more/less than that of boat Q
II. Upstream speed of boat R, if the speed of the boat in still water of boat R is 40 km/h, Speed of the stream of boat R is the same as that of boat Q.
III. Units digit of (K) 197, where K is speed of stream.

Correct Answer: (e) All statements can be determined
Solution:Let speed of stream = a km/h

Speed of boat P, in still water = (18 + a)

Downstream speed of boat Q = 125% of (18 + a)

Upstream speed of Boat Q = 125% of (18 + a) - 2a

Now,

125% of (18 + a) - 2a = 192/12.8

90 + 5a - 8a = 60

So, value of a = 10

I. % by which upstream speed of boat Q is more/less than that of boat P

Upstream speed of Boat Q = 125% of (18 + 10) - 20 = 15 km/h

Required % change = (18 - 15)/15 × 100 = 20%

This statement can be determined

II. Upstream speed of boat R = 40 - 10 = 30 km/h

This statement can be determined

III. Unit digit of (K) 197 = (10) 197 = 0

This statement can be determined

30. A boat covers 120 km downstream in 8 hours and the same distance covers by upstream in 40 hours. If the speed of boat in still water and speed of stream is increased by 6 kmph and 4 kmph respectively, then what is the total time taken by the boat to covers 200 km in upstream and downstream?

Correct Answer: (d) 48 hours 
Solution:Speed of downstream = 120/8 = 15 kmph

Speed of upstream = 120/40 = 3 kmph

Speed of the boat in still water = (15 + 3)/2 = 9 kmph

Speed of the stream = (15 - 3)/2 = 6 kmph

After increased the speed by boat = 9 + 6 = 15 kmph

Stream speed = 6 + 4 = 10 kmph

Downstream speed = 15 + 10 = 25 kmph

Upstream speed = 15 - 10 = 5 kmph

Required time = 200/25 + 200/5 = 8 + 40 = 48 hours