Mathmetics

ISBT Mathmetics for all banking PO,Clerk,IBPS PO,Railway,SSC,IAS,OAS Exams

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Q1.
A river is flowing at 2 kmph. It takes a man twice as long to row up as, to row down the river. What is the rate (in km/hr) of the man in still water ?
1) 2 2) 4
3) 6 4) 8
5)None of these
Answer : 6
Explanation :
Let,speed of boat man be x kmph.
So, speed in down stream =(x+2) kmph. and speed in up-stream = (x-2) kmph.
Since, distance is constant for both case ,
the equation = 2(x-2) = (x+2)
or 2x-4 = x+2
or x= 6 kmph

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Q2.
A motorboat went down the river for 14 km and then up the river for 9 km. It took a total of 5 hours for the entire journey. What is the speed of the river flow if the speed of the boat in still water is 5 km/hr ?
1) 1 km/hr. 2) 1.5 km/hr.
3) 2 km/hr. 4) 3 km/hr.
5)None of these
Answer : 1.5 km/hr.
Explanation :
Let, the speed of the stream be x km/hr.
Then, upward speed =(5- x)km/hr.
downward speed = (5 + x) km/hr.
So, (15/5+x) + (9/5-x) = 5
or x = 2 km/hr
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Q3.
A motorboat whose speed in still water is 10 km/h went 91 km downstream and then returned to its starting point. What is the speed of the river flow if the round trip took a total of 20 hours ?
1) 3 km/hr. 2) 4 km/hr.
3) 6 km/hr. 4) 8 km/hr
5)None of these
Answer : 3 km/hr.
Explanation :
Let, the speed of the stream be x km/hr.
Then, (91/10-x) + (91/10+x) = 20
or x = 3 km./hr
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Q4.
A man can row 30 km upstream and 44 km downstream in 10 hour. It is also known that he can row 40 km upstream and 55 km downstream in 13 hours. Find the speed of the man in still water ?
1) 4 km/hr 2) 6 km/hr
3) 8 km/hr 4) 12 km/hr.
5)None of these
Answer : 8 km/hr
Explanation :
Let, the speed of the man in still water be x km/hr and speed of the stream be y km/hr, then
(30/x-y) + (44/x+y) = 10   ......... (i)
(40/x-y) + (55/x+y) = 13 ........ (ii)
Solving equation. (I) and (II), we get  x = 8 km/hr y = 3 km/hr

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Q5.
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is:
1) 2:1 2) 3:2
3) 2:3 4) 3:1
5)None of these
Answer : 3:1
Explanation :

Let man's rate upstream be x kmph.

Then, his rate downstream = 2x kmph.

 (Speed in still water) : (Speed of stream) = (2x+2) /2 : (2x-x)/2

   =3x/2: x/2 = 3 : 1.

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Q6.
A boat covers a certain distance downstream in 1 hour, while it comes back in 1 hours. If the speed of the stream be 3 kmph, what is the speed of the boat in still water ?
1) 10kmph 2) 12kmph
3) 15kmph 4) 18kmph
5)None of these
Answer : 15kmph
Explanation :

Let the speed of the boat in still water be x kmph.  Then,

Speed downstream = (x + 3) kmph,

Speed upstream = (x - 3) kmph.

 (x + 3) x 1 = (x - 3)/2 x3

Or 2x + 6 = 3x - 9

Or  x = 15 kmph.

 

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Q7.
A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place ?
1) 2.4 km 2) 2.5km
3) 3km 4) 3.6km
Answer : 2.4 km
Explanation :

Speed downstream = (5 + 1) kmph = 6 kmph.

Speed upstream = (5 - 1) kmph = 4 kmph.

Let the required distance be x km.

Then,x/6 +x/4 = 1

 Or  2x + 3x = 12

Or  5x = 12

Or  x = 2.4 km.

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Q8.
A motorboat, whose speed in 15 km/hr in still water goes 30 km downstream and comes back in a total of 4 hours 30 minutes. The speed of the stream (in km/hr) is:

1) 4 2) 5
3) 6 4) 10
5)None of these
Answer : 5
Explanation :



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Q9.
A man's speed with the current is 15 km/hr and the speed of the current is 2.5 km/hr. The man's speed against the current is:
1) 7.5 km/hr 2) 8.5 km/hr
3) 10 km/hr 4) 12.5 km/hr
5)None of these
Answer : 10 km/hr
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Q10.
n one hour, a boat goes 11 km/hr along the stream and 5 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
1) 3 km/hr 2) 5 km/hr
3) 8 km/hr 4) 9 km/hr
5)None of these
Answer : 8 km/hr
Explanation : Speed in still water = ½(11 + 5) kmph = 8 kmph.
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