 ## Saturday, 12 March 2016

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]