BANK & INSURANCE (BOAT AND STREAM) PART 2

Total Questions: 40

1. A boat can travel a distance of 220 km in upstream and 252 km in downstream in 10 hours. Find the time taken by the boat to cover a distance of 156 km in still water if ratio of speed of boat in still water to speed of stream is 6:1 respectively.

Correct Answer: (b) 3 hour 15 minutes
Solution:Let us assume that

Speed of Stream = x

∴ Speed of Boat = 6x

ATQ,

220/(6x − x) + 252/(6x + x) = 10

220/5x + 252/7x = 10

44/x + 36/x = 10

80/x = 10

x = 8

Time taken = 156/6x = 156/6×8 = 13/4

= 3 hr 1/4 hr = 3 hr 15 min.

2. The speed of a boat in still water is 40% more than the speed of the stream. If the speed of the stream would have been 4 km/hr more, the boat would have taken 8.5 hours to cover 442 km downstream. Find the time taken by the boat to cover 100 km in upstream with original speed of the stream.

Correct Answer: (c) 12.5 hours
Solution:Let us assume that

Speed of Stream = 5x

∴ Speed of Boat = 7x

ATQ,

442/(7x+5x+4) = 8.5

442 = 102x + 34

x = 10

Time taken = 100/(7x−5x) = 100/2x = 12.5 hrs

3. The speed of boat ‘B’ in still water is equal to the upstream speed of boat ‘A’. If the time taken by the boat ‘B’ to travel 180 km downstream is 7.5 hours, then find 25% of the speed of boat ‘A’ in still water.

Correct Answer: (c) 6 km/hr
Solution:Let us assume that

Speed of Boat B = x,

Speed of Boat A = y and

Speed of Stream = z

x = z − y ⇔ x + y = z

ATQ,

180/(x+y) = 7.5

180/z = 7.5

z = 180/7.5 = 24 km/hr

∴ 25% of z = 25 × 24/100 = 6 km/hr

4. Speed of a boat in downstream is 25% more than speed of boat in still water. If the boat can travel a distance of 216km in upstream and 180km in downstream in 12 hours, then find the time taken by boat to cover 135 km in upstream as well as downstream

Correct Answer: (c) 8 hours
Solution:25% = 1/4

∴ Speed of Boat = 4x and Speed of Stream = x

ATQ,

216/(4x−x) + 180/(4x+x) = 12

72/x + 36/x = 12

108/x = 12

x = 9

Time taken = 135/(4x+x) + 135/(4x−x) = 135/5x9 + 135/3x9

= 3 + 5 = 8 hrs

5. A boat can travel 300 km downstream in 7.5 hours and 72 km upstream in 4.5 hours. If the speed of the boat in still water had been 2 km/hr more while the speed of stream had been 4 km/hr less, then find the time taken by the boat to travel 176 km upstream.

Correct Answer: (c) 8 hours
Solution:Let us assume that

Speed of Stream = y & Speed of Boat = x

ATQ,

300/(x+y) = 7.5 & 72/(x−y) = 4.5

x + y = 40 & x − y = 16

On solving both eqn.

x = 28 & y = 16

Time taken = 176/(x+2−y+4) = 176/22 = 8 hrs

6. The speed of a boat in still water is 6 km/hr more than that of the current. The time taken by the boat to cover 625 km downstream is 12.5 hours. Find the total time taken by boat to travel 525 km downstream and 45 km upstream.

Correct Answer: (a) 18 hours 
Solution:Let us assume that

Speed of Stream = x

∴ Speed of Boat = x + 6

ATQ,

625/(x+x+6) = 12.5

625/(2x+6) = 12.5

2x = 44

x = 22

Time taken = 525/[22+(22+6)] + 45/[-22+(22+6)]

= 525/50 + 45/6 = 10.5 + 7.5 = 18 hrs

7. Boats ‘A’ and ‘B’ are rowing a river. Boat ‘A’ can travel 160 km downstream and 135 km upstream in 6 hours 15 minutes and ratio of speed of boat ‘A’ in upstream and downstream is 9:16. If speed of boat ‘B’ in still water is 36% less than that of boat A, then time taken by boat ‘B’ to cover 36 km in upstream is:

Correct Answer: (c) 2 hours

8. At its usual rowing rate, a boat can travel 32 km upstream in 2 hours more than it takes to cover the same distance in downstream. If speed of boat in still water is reduced to half of its initial speed then it takes 8 hours more to cover a distance of 20 km in upstream than in downstream. What is the reduced speed of boat in still water?

Correct Answer: (d) 6 km/hr 
Solution:Let us assume that

Speed of Boat = x & Speed of Stream = y

ATQ,

32/(x−y) + 32/(x+y) = 2

x² − y² = 32y ……(i)

20/[(x/2)−y] + 20/[(x/2)+y] = 8

x² − 4y² = 20y ……(ii)

On solving eqn. (i) & (ii)

y = 4 km/hr, x = 12 km/hr

Reduced speed = 12/2 = 6 km/hr

9. The river flows towards the city Q from city P. The distance between City P and City Q is 360 km. Two boats A and B run daily from city P and Q respectively at the same time and come back. If the speed of A is 20 km/hr in still water, speed of B in still water is 16 km/hr and speed of stream is 4 km/hr, then find the time when they meet together for the first and second time from start?

Correct Answer: (e) 10 hours and 33 hours 20 mins
Solution:Speed of boat A in still water = 20 km/hr

Speed of boat B in still water = 16 km/hr

Speed of stream = 4 km/hr

The distance between P and Q is 360 km.

Meeting time of two bodies

= Distance between them / Relative speed

20 km/hr      16 km/hr

A ←────────────→ B

4 km/hr

P ───────────────────────── Q

360 km

The boat A starts from P and move towards Q with the speed of (20 + 4) = 24 km/hr

And boat B starts from Q and move towards P with the speed of (16 − 4) = 12 km/hr

∴ They will meet first time after

= 360/(24 + 12) = 10 hours

Distance traveled by boat A in 10 hrs = 240 Km,

therefore boat B has to travel 240 Km, whereas boat A now has to travel only 120 Km, to reach point P and Q respectively.

Time taken by boat A to travel 120 Km till point Q = 5 hrs

whereas in 5 hr boat B could only travel 60 Km (It has to travel 180 Km more to reach point P)

Time taken by boat B to reach point P will be = 180/12 = 15 hrs

Whereas boat A leaves point Q and starts moving towards point P upstream,

Distance travelled by boat A towards P in 15 hrs upstream, will be (20 - 4) × 15 = 240 Kms.

During this time boat B is in point P, while boat A is 240 kms away from point Q.

Time at which downstream boat B and upstream boat A will meet:

= 360 - 240 / 20 + 16 = 10/3 hrs

Therefore,

First meeting of boat A and boat B will be after 10 hrs.

Second meeting of boat A and boat B will be after 33hrs 20mins from the start.

10. Time taken by a boat to cover 54 km in upstream is 45 minutes more than time taken by it to cover 45 km in downstream. Find the time taken by boat to cover 144 km in still water if difference between speed of boat in upstream and downstream is 24 km/h.

Correct Answer: (b) 3 hours 
Solution:Let us assume that

Speed of Stream = y & Speed of Boat = x

∴ (x+y) - (x-y) = 24 ⇒ y = 12

ATQ,

54/(x-y) - 45/(x+y) = 45/60

x² - 12x - 1728 = 0

x = 48

Time taken = 144/48 = 3 hrs