# Aptitude Boats and Streams Test Paper 3

16) A man can row, 5km/hr in still water and the velocity of the stream is 1.5 km/hr. He takes an hour when he travels upstream to a place and returns back to the starting point. How far is the place from the starting point?

1. 2.5 km
2. 2.275km
3. 3 km
4. 4.5km

Let the speed of man in still water (Sb) =5km/hr
And the speed of water/stream (Sc) =1.5km/hr

Time taken to upstream and downstream is 1hr.

Apply the formula:

Time = distance/speed
Downstream speed of the man = speed of man in still water+ speed of the stream
Upstream speed of the man= speed of man in still water- speed of the stream

Let the distance = x km

Now, (x/ downstream speed) + (x/ upstream speed) = time
Or, (x/ (Sb + Sc)) + (x/ (Sb - Sc)) = 1hr
Or, (x/ (5+1.5)) + (x/ (5-1.5)) = 1
Or, (x/6.5) + (x/3.5) = 1
Or, LCM of 6.5 and 3.5 = 45.5
Or, (7x+13x)/ 45.5 = 1
Or, 20x= 45.5
Or, x = 2.275 km
The place is 2.275 km away from the starting point.

17) A boatman can row a certain distance down the stream in 2 hours and can row the same distance up the stream in 3 hours. If the velocity of the stream is 4km/hr, what is the speed of the boat in still water?

1. 8km/hr
2. 12km/hr
3. 40km/hr
4. 20km/hr

Let the distance = x km
Time is taken in downstream = 2 hour
So, the speed of downstream is x/2 km/hr
Similarly, the time is taken in upstream = 3 hr
So, the speed of upstream is x/3 km/hr
Speed of stream = 4 km/hr

Now, apply the formula.

Speed of stream = (1/2) [speed of downstream - speed of upstream] Or, 4 = (1/2) [x/2 - x/3]
Take LCM of 2 and 3 = 6
Now, (½) [(3x-2x)/6] = 4
Or, x= 48 km

Now, speed of downstream = 48/2 = 24 km/hr
And the speed of upstream = 48/3 = 16km/hr

Now, apply the formula.

Speed of boat in still water = (½) [24+16] = 20km/hr

18) A man can row 9[1/3] km/hr in still water. He finds that it takes thrice as much time to row upstream as to row downstream (same distance). Find the speed of the current.

1. 3[1/3] km/hr
2. 1[1/4] km/hr
3. 4[2/3] km/hr
4. 3[1/9] km/hr

The speed of man in still water is 9[1/3]
ATQ, time taken while rowing upstream = 3k
Time taken while rowing downstream = k
We know that time is inversely proportional to speed.
Upstream speed (y) = k
Downstream (x) = 3k

Now, apply the formula.

Speed of man in still water = (1/2) [speed of downstream + speed of upstream]

Or, 9[1/3] = (1/2) [3k+ k]
Or, 28/3 = 2k
Or, k = 14/3
So, upstream speed (y) = 14/3
And, downstream speed (x) = (14/3) * 3 = 14

Now, apply the formula.

Speed of current = (1/2) [downstream speed - upstream speed]
= (½) [14 - 14/3]
= 28/6 = 4[2/3]

19) A boat covers 6 km upstream and returns back to the starting point in 2 hours. If the flow of the stream is 4 km/hr, what is the speed of the boat in still water?

1. 5km/hr
2. 6km/hr
3. 7.3 km/hr
4. 8km/hr

ATQ, distance covered in upstream = 6 km, and the same distance is covered in downstream

Now, apply the formula

Time = Distance/ speed

Let the upstream speed = y km/hr, and the downstream speed = x km/hr.
Or, (6/x) + (6/y) = 2
Or, speed in upstream = speed of boat in still water - speed of stream
Or, speed in downstream = speed of boat in still water + speed of stream
Let Sb= speed of boat in still water

6/ (Sb + 4) + 6/ (Sb - 4) = 2
[6* (Sb - 4) + 6* (Sb + 4)]/ [Sb2 - 16] = 2
[6Sb-24 + 6Sb+24]/ [Sb2 - 16] = 2
12Sb = 2Sb2 - 32
2Sb2-12Sb-32=0
Sb2- 6Sb-16=0
Sb2 - 8Sb+2S-16 =0
Sb (Sb-8) +2(Sb - 8)=0
(Sb-8)(Sb+2)=0
Sb-8=0, Sb+2 = 0
Sb= 8, Sb=-2

Since, the speed can't be -ve

Hence, Speed of boat in still water is 8 km/hr.

20) A boat covers 12 km upstream and 18km downstream in 3 hours while it covers 36km upstream and 24 km downstream in 6[1/2] hours, what is the velocity of the stream?

1. 1.5km/hr
2. 2km/hr
3. 3km/hr
4. 2.5km/hr

ATQ, Distance in upstream =12km
Distance in downstream = 18 km
Let the speed in upstream = y km/hr
And the speed in downstream = x km/hr

Now, apply the formula.

Time = Distance/ speed
Or, (18/x) + (12/y) = 3.............. (i)
And (24/x) + (36/y) = 13/2......... (ii)

Now, multiply equation i by 3 to equate both equations.

(54/x) + (36/y) = 9............ (iii)
(24/x) + (36/y) = 13/2........ (iv)

Now subtract equation iii by iv.

30/x = 9-13/2
Or, 30/x = 5/2
Or, 5x=60, i.e., x = 12

Now, put the value of x in equation i

(18/12) + (12/y) = 3
Or, 3/2 + 12/y = 3
Or, 12/y = 3-3/2
Or, 12/y = 3/2
Or, y = 8km/hr

Now, velocity of stream = (x-y)/ 2
= (12-8)/ 2 = 2km/hr.

Aptitude Boats and Streams Test Paper 1
Aptitude Boats and Streams Test Paper 2
Aptitude Boats and Streams Test Paper 3
Boats and Streams Concepts   