1. If the speed for a swimmer in still water is 9 km/h. Find the downstream speed of the swimmer,

when the river is flowing with the speed of 6km/h.

1) 15 km/h 2) 18 km/h 3) 3 km/h 4) 12 km/h 5) None of these

Solution: (1).

Given,

Swimmer’s speed in still water = x = 9 km/h

Rate of stream = y = 6 km/h

Therefore speed downstream = x + y

= 9 + 6 = 15 km/h

2. A boatman rows 1 km in 5 min along the stream and 6 km in 1 h against the stream. The speed of

the stream is

1) 3 km/h 2) 6 km/h 3) 10km/h 4) 12km/h 5) None of these

Solution: (1).

Let the speed of boat and stream be x and y km/h.

Therefore speed of boat along stream = ( x + y)km/h

and speed of boat against stream = ( x – y ) km/h

According to the question,

x+y = 1 / (5/60) = 60/5

= x + y = 12

And x – y = 6

On adding Eqs.(i) and (ii), we get 2x = 18

x = 18/2 = 9

On putting the value of x in Eq. (i), we get

9 + y = 12

y = 12 – 9 = 3

Hence, speed of boat = 9 km/h and speed of stream = 3 km/h

3. A motorboat can travel at 10 km/h in still water. It travelled 91km downstream in a river and then

returned to the same place, taking altogether 20h. the rate of flow of river is

1) 3 km/h 2) 4 km/h 3) 2km/h 4) 5 km/h 5) None of these

Solution: (1).

Given , speed of boat = 10 km/h

Let speed of flow of river = x km/h

Therefore Upstream speed of boat = (10 – x )km/h and downstream speed of boat

According to question,

= (10 + x) km/h

91 / (10 - x) + 91 / (10 + x) = 20

= 91(10 + x + 10 –x ) / ( 10 – x) ( 10 + x) = 20

= 91 (20) / 100 – x2 = 20

= 91 = 100 – x2

= x2 = 9

Therefore x = 3

4. A man can row against the current three-fourth of a kilo meter in 15 min and returns same distance

in 10 min, then ratio of his speed to that of current is

1) 3 : 5 2) 5 : 3 3) 1 : 5 4) 5 : 1 5) None of these

Solution: (4).

Let the speed of man and current be x and y km/h, respectively.

Speed upstream = (x – y) km/h

Speed down stream = ( x + y) km/h

According to the question,

3 x 60 / 4 x 15 = x – y

= x – y = 3 and ¾ x 60/10 = x + y

= x + y = 9/2

On adding Eqs. (i) and (ii), we get 2x = 3 + 9/2

2x = 3 + 9/2

2x = 6 + 9/2

x=15/4

On putting the value of x in Eq.(ii), we get

15/4 + y = 9/2

y = 9/2 – 15/4 = 18 – 15/4

y=¾

Hence, speed of man x = 15/4 and speed of current y = ¾

Hence, required ratio = 15/4 : ¾ = 5 : 1

5. The speed of the current is 5 km/h . A motorboat goes 10 km upstream and back again to the

starting point in 50 min. The speed, (in km/h) of the motorboat in still water is

1) 20 km/h 2) 26 km/h 3) 25 km/h 4) 28 km/h 5) None of these

Solution: (3)

Let speed of boat be x km/h.

Given speed of current = 5km/h

Therefore Upstream speed of boat = ( x – 5) km/h

Downstream speed of boat = ( x+5) km/h

According to the question,

(10 / x – 5) + (10/ x + 5) = 50/60

10 ( x + 5 + x – 5/ x2 – 25) = 5/6

= 12 X 2x = x2 – 25

= x2 – 24x – 25 = 0

x2 – 25x + x – 25 = 0

= ( x – 25) (x+1) = 0

Therefore x = 25 [ since x ≠- 1]

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