General Mathematics

Question: A,B and C together can complete a piece of work in 10 days.All the three started working at it together and after 4 days, A left.Then,B and C together complete the work in 10 more days.A alone could complete the work in complete the work in 10 more days. A alone could complete the work in
A
15 days

B
16 days

C
25 days

D
50 days

Note: (A + B + C)'s 4 days work` = (1/10 xx 4)` `= 2/5` Remaining work` = (1 - 2/5) = 3/5` `3/5` work is done by (B + C) in days whole work can be done by (B + C) in `((10 xx 5)/3)`days :. (B + C)'s 1 days work `= 3/50` A's 1 days work` = (1/10 - 3/50)` `= 1/25` :. A alone can finish the work in 25 days
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Question: 20 men can finish a piece of work in 30 days.After how many days should 5 men leave the work so that it may be finished in 35 days ?
A
10

B
12

C
15

D
20

Note: Suppose they leave after x days Work done in x days` = x/30` Remaining work` = (1 - x/30)` `= ((30 - x)/30)` Remaining days` = (35 - x)` 15 men's 1 days work` = (1/(20 xx 30) xx 15)` `= 1/40` `:. 1/40 (35 - x) = (30 - x)/(30) => 1050 - 30x` `= 1200 - 40x => x = 15`
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Question: A man, a woman or a boy can do a piece of work in 3, 4 and 12 days respectively. How many boys must one man and one woman to do the work in one day ?
A
6

B
8

C
9

D
5

Note: 1 man's 1 day's work` = 1/3,` 1 woman's 1 days work` = 1/4,` 1 boy's 1 day's work` = 1/12` Let x boys must be there. Then `1/3 + 1/4 + x/12` `= 1 => x = 5.`
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Question: If 2 men and 3 boys can do a piece of work in 8 days. while 3 men and 2 boys can do it in 7 days, how long will 5 men and boys take to do it ?
A
3 days

B
4 days

C
5 days

D
6 days

Note: Let 1 man's 1 day work = x and 1 boys 1 days work = y. Then, 2x + 3y `= 1/8, 3x + 2y = 1/7` Solving we get `: x = 1/28` and` y = 1/56` `:. 5x + 4y = 5/28 + 4/56` `= 14/56 = 1/4.` So, 5 men and 4 boys can finish the work in 4 days.
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Question: A and B can do a work in 8 days, B and C can do the same work in 12 days.A,B and C together can finish it in 6 days.A and C together will do it in :
A
4 days

B
6 days

C
8 days

D
12 days

Note: (A + B)'s 1 days work` 1/8`. (B + C)'s 1 day's work` = 1/12` (A + C)'s 1 day's work` = 1/x` :.2 (A + B + C)'s 1 days work` = (1/8 + 1/12 + 1/x)` `:. 1/2 (5/24 + 1/x)` `= 1/6 => 5/24 + 1/x` `= 1/3 or 1/x` `= 1/3 - 5/24` `= 1/8 => x = 8`
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Question: If I would have been twice as efficient as today,then I would have finished a work in 12 days.If my efficiency is reduced to one-third of what it is at present,then in how many days,I would be able to finish the work ?
A
8

B
18

C
52

D
72

Note: Suppose, I finish a work now in x days. With double efficiency, time taken` = x/2` days `:. x/2 = 12 => x = 24` With one third efficiency time taken = 3 x days `= 3 xx 24` days = 72 days
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Question: The ratio between the rates of walking of A and B is 2 : 3. If the time taken by B to cover that much distance is :
A
24

B
38

C
48

D
54

Note: Ratio of rates of working = inverse ratio of time taken `:. 2/3 = 36/x => 2x = 108 => x = 54` min.
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Question: I have to be at a certain place at a certain time and find that I shall be 20 minutes too late if I walk at 3 km/hr and 10 minutes too soon if I walk at 4 km/hr. How far I have to walk ?
A
6 km

B
10 km

C
`12 1/2` km

D
`16 2/3` km

Note: Let the distance be x km `x/3 - x/4 = 30/60 => x/12` `= 1/2 => x = 6 km`
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Question: Sound travels at 330 metres a second.How many kilometres away is a thunder cloud when its sound follows the flash after 10 seconds ?
A
3.3

B
33

C
0.33

D
3.33

Note: Distance `= (time xx speed)` `= (330 xx 10) m` `= (330 xx 10)/(1000) km` = 3.3
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Question: Walking `6/7 th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :
A
1 hour

B
1 hour 12 min

C
1 hour 15 min

D
1 hour 20 min

Note: New speed` = 6/7` of the usual speed. New time taken` = 7/6` of the usual time `(7/6 of usual time)` - (usual time) = 12 min. `:. 1/6` of usual time = 12 min. or usual time = 72 min.
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Question: A,B and C together can complete a piece of work in 10 days.All the three started working at it together and after 4 days, A left.Then,B and C together complete the work in 10 more days.A alone could complete the work in complete the work in 10 more days. A alone could complete the work in

Question: 20 men can finish a piece of work in 30 days.After how many days should 5 men leave the work so that it may be finished in 35 days ?

Question: A man, a woman or a boy can do a piece of work in 3, 4 and 12 days respectively. How many boys must one man and one woman to do the work in one day ?

Question: If 2 men and 3 boys can do a piece of work in 8 days. while 3 men and 2 boys can do it in 7 days, how long will 5 men and boys take to do it ?

Question: A and B can do a work in 8 days, B and C can do the same work in 12 days.A,B and C together can finish it in 6 days.A and C together will do it in :

Question: If I would have been twice as efficient as today,then I would have finished a work in 12 days.If my efficiency is reduced to one-third of what it is at present,then in how many days,I would be able to finish the work ?

Question: The ratio between the rates of walking of A and B is 2 : 3. If the time taken by B to cover that much distance is :

Question: I have to be at a certain place at a certain time and find that I shall be 20 minutes too late if I walk at 3 km/hr and 10 minutes too soon if I walk at 4 km/hr. How far I have to walk ?

Question: Sound travels at 330 metres a second.How many kilometres away is a thunder cloud when its sound follows the flash after 10 seconds ?

Question: Walking `6/7 th of his usual speed, a man is 12 minutes too late. The usual time taken by him to cover that distance is :