General Mathematics

Question: A man can row `9 1/3` kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance of in the river. The speed of the current is :
A
`3 1/3 km∕hr`

B
`3 1/9 km∕hr`

C
`4 2/3 km∕hr`

D
`14 km∕hr`

Note: Let speed upstream be x kmph Then, speed downstream`= 3x kmph` :. Speed in still water `= 1/2 (3x + x) kmph` `= 2x kmph` `:. 2x = 28/3 ⇒ x = 14/3` :. speed upstream`= 14/3 km/hr,` Speed downstream`= 14 km∕hr` :. Speed of the current`= 1/2 (14 - 14/3) km/hr` `= 14/3 km∕hr` `= 4 2/3 km∕hr`
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Question: A man can row a boat at `10` kmph in still water. If the speed of the stream is `6` kmph , the time taken to row a distance of `80` km down the stream is :
A
`8 hours`

B
`5 hours`

C
`10 hours`

D
`20 hours`

Note: Speed downstream `= (10 + 6) km/hr` `= 16 km/hr` Time taken to cover `80` km downstream `= (80/16) hrs` `= 5 hrs`
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Question: A boat takes `4` hours for travelling downstream from point A to point B and coming back to point A upstream. If the velocity of the stream is `2` kmph and the speed of the speed of the boat in still water is `4` kmph, what is the distance between A and B ?
A
`4 kms`

B
`6 km`

C
`8 km`

D
`9 km`

Note: Let the distance between A and B x hm. Speed downstream`= 6` kmph, speed upstream`= 2 kmph` `:.x/6 + x/2 = 4 ⇔ 4x = 24 ⇔ x = 6` :. Distance AB`= 6 km.`
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Question: If a man rows at `6` kmph in still water and `4.5`kmph against the current then his rate along the current is :
A
`9.5 km/hr`

B
`7.5 km/hr`

C
`7 km/hr`

D
`5.25 km/hr`

Note: Let the rate of the stream be x kmph Then, rate against the current `= (6 - x) kmph` `:. 6 - x = 4.5` `or x = 1.5` :. Rate of current `= 1.5 kmph` Rate along the current `= (6 + 1.5) kmph = 7.5 kmph`
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Question: If a man,s rate with the current is `11` kmph and the rate of the current is `1.5` kmph, then the man,s rate against the current is :
A
`8 km/hr`

B
`9.5 km/hr`

C
`9 km/hr`

D
`6.25 km/hr`

Note: Man,s rate in still water `= (11 - 1.5) kmph` `= 9.5 kmph` Man,s rate against the current `= (9.5 - 1.5) kmph` `= 8 kmph`
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Question: Speed of a boat in standing water is `9` kmph and the speed of the stream is `1.5` kmph. A man rows to a place at a distance of `10.5` km and comes back to the starting point. The total time taken by him is :
A
`16 hours`

B
`18 hours`

C
`20 hours`

D
`24 hours`

Note: Speed upstream `= 7.5 kmph,` speed downstream `= 10.5 kmph` :. Total time taken `= (105/7.5 + 105/10.5) hrs` `= 24 hours.`
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Question: A boat moves upstream at the rate of `1` km in `10` minutes and downstream at the rate of `1` km in `6` minutes. The speed of the current is :
A
`1 km∕hr`

B
`1.5 km∕hr`

C
`2 km∕hr`

D
`2.5 km∕hr`

Note: Rate upstream `= (1/10 xx 60) km∕hr` `= 6 km∕hr` Rate downstream `= (1/6 xx 60) km∕hr` `= 10 km∕hr` Rate of the current `= 1/2 (10 - 6) km∕hr` `= 2 km∕hr`
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Question: A man rows to a place `48` km distance and back in `14` hours. He finds that he can row `4` km with the stream in the same time as `3` km against the stream. The rate of the stream is :
A
`1 km∕hr`

B
`1.8 km∕hr`

C
`3.5 km∕hr`

D
`1.5 km∕hr`

Note: Suppose he moves `4` km downstream in xj hours, Then, speed downstream `= (4/x) km∕hr,` speed downstream `= 6 km∕hr.` Rate of the stream `= 1/2 (8 - 6) km∕hr` `= 1 km∕hr.`
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Question: The current of stream runs at kmph. A motor boat goes `35` km upstream and back again to the starting point in `12` hours. The speed of the motor boat in still water is :
A
`6 km∕hr`

B
`7 km∕hr`

C
`8 km∕hr`

D
`8.5 km∕hr`

Note: Let the speed in still water be x kmph Then, speed upstream `= (x - 1) kmph, speed downstream `= (x + 1) kmph` `:. 35/(x - 1) + 35/(x + 1) = 12` `⇔ 6x^2 - 35x - 6 = 0` `:. (x - 6) (6x + 1) = 0` `or x = 6.` Hence, the speed in still water `= 6 kmph.`
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Question: A boat covers `24` km upstream and `36` km downstream in `6`hours while it covers `36` km upstream and `24` km downstream in `6 1/2` hours, The velocity of the current is :
A
`1 km∕hr`

B
`1.5 km∕hr`

C
`2 km∕hr`

D
`2.5 km∕hr`

Note: Let rate upstream = x kmph and rate downstream = y kmph Then`24/x + 36/y = 6 .....(i)` and`36/x + 24/y = 13/2 ....(ii)` Adding (i) and (ii), `60 (1/x + 1/y) = 25/2` `or 1/x + 1/y = 5/24 ... (iii)` Subtracting (i) and from (ii) `12 (1/x - 1/y) = 1/2` `or 1/x - 1/y = 1/24 .....(iv)` Adding (iii) and (iv), we get `2/x = 6/24 or x = 8.` `1/8 + 1/y = 5/24 ⇔ 1/y` `= (5/24 - 1/8) = 1/12` `⇔ y = 12. :. Speed upstream = 8 kmph, speed downstream = 12 kmph :. Rate of the current`= 1/2 (12 - 8) kmph` `= 2 kmph`
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Question: A man can row `9 1/3` kmph in still water and finds that it takes him thrice as much time to row up than as to row down the same distance of in the river. The speed of the current is :

Question: A man can row a boat at `10` kmph in still water. If the speed of the stream is `6` kmph , the time taken to row a distance of `80` km down the stream is :

Question: A boat takes `4` hours for travelling downstream from point A to point B and coming back to point A upstream. If the velocity of the stream is `2` kmph and the speed of the speed of the boat in still water is `4` kmph, what is the distance between A and B ?

Question: If a man rows at `6` kmph in still water and `4.5`kmph against the current then his rate along the current is :

Question: If a man,s rate with the current is `11` kmph and the rate of the current is `1.5` kmph, then the man,s rate against the current is :

Question: Speed of a boat in standing water is `9` kmph and the speed of the stream is `1.5` kmph. A man rows to a place at a distance of `10.5` km and comes back to the starting point. The total time taken by him is :

Question: A boat moves upstream at the rate of `1` km in `10` minutes and downstream at the rate of `1` km in `6` minutes. The speed of the current is :

Question: A man rows to a place `48` km distance and back in `14` hours. He finds that he can row `4` km with the stream in the same time as `3` km against the stream. The rate of the stream is :

Question: The current of stream runs at kmph. A motor boat goes `35` km upstream and back again to the starting point in `12` hours. The speed of the motor boat in still water is :

Question: A boat covers `24` km upstream and `36` km downstream in `6`hours while it covers `36` km upstream and `24` km downstream in `6 1/2` hours, The velocity of the current is :