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Quant toughest question of Time & Work

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Quant toughest question of Time & Work [#permalink] New post 05 Aug 2009, 23:41
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A
B
C
D
E

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Please give the solution

1) A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. the number of days taken by B to finish the work is:
a) 12
b) 15
c) 20
d) 30

2) A does half as much work as B in 3/4 of the time. If together they take 18 days to complete the work, how many days will B take to do it?
a) 30
b) 35
c) 40
d) 45


3) A works twice as fast as B. If B can complete a piece of work independently in 12 days, then the number of days taken by A and B together to finish the work is:
a) 4
b) 6
c) 8
d) 18

4) A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?
a) 10 1/2
b) 10 1/4
c) 10 2/3
d) 10 1/3

5) 8 men can dig a pit in 20 days. if a man works half as much again as a boy, then 4 men and 9 boys can dig it in:
a) 10 days
b) 12 days
c) 15 days
d) 16 days

6) A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 liters a minute into the cistern and it is now empited in 12 hours. how many litres does the cistern hold.
a) 7580
b) 7960
c) 8290
d) 8640

7) two pipes M and N can fill a cistern in 24 min and 32 min , repectively. If both the pipes are opened together, then after hoe many minutes N should be closed so that the tank is full in 18 minutes ?
a) 6
b) 8
c) 10
d) 21
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Re: Quant toughest question of Time & Work [#permalink] New post 06 Aug 2009, 04:35
3) A works twice as fast as B. If B can complete a piece of work independently in 12 days, then the number of days taken by A and B together to finish the work is:
a) 4
b) 6
c) 8
d) 18

Speed of B --- 1/12
Speed of A -- 1/6

So A+B combined speed = 1/12 + 1/6 = 1/4

So total days they can finish the work ====>4
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Re: Quant toughest question of Time & Work [#permalink] New post 06 Aug 2009, 05:49
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sanjali wrote:
Please give the solution

1) A is thrice as good a workman as B and takes 10 days less to do a piece of work than B takes. the number of days taken by B to finish the work is:
a) 12
b) 15
c) 20
d) 30

R*3 *(D-10) = R * D
3RD - 30R = RD
2RD = 30R
D = 15.
R is the rate and D is the days. B


2) A does half as much work as B in 3/4 of the time. If together they take 18 days to complete the work, how many days will B take to do it?
a) 30
b) 35
c) 40
d) 45
D?
A = 3/2*R since it says it takes to do HALF unit of work in 3/4 rate of B. since we need to keep the rate to 1unit of work we multiply by 2 to get 3/2R for A. Now we find R by doing: (3/2R +R) *18 = 1 since they combined to get 1 work done in 18 days. we find R ~= .0222 and plug into R*D = 1 we get ~=45



3) A works twice as fast as B. If B can complete a piece of work independently in 12 days, then the number of days taken by A and B together to finish the work is:
a) 4
b) 6
c) 8
d) 18
A. I first looked at it and used POE to find the answer. If B takes 12 days, A takes 6 days so we KNOW combining it has to be lower than 6 so A.
Here is analytical:
A=.1/6 B = 1/12 (1/6+1/12)D=1 D=4
remember the rate of work is 1 work/time. since they gave that it takes 12 days to do 1 work it is just 1/12 rate.


4) A and B working separately can do a piece of work in 9 and 12 days respectively.If they work for a day alternately, A beginning, in how many days, the work will be completed?
a) 10 1/2
b) 10 1/4
c) 10 2/3
d) 10 1/3

B
A = 1/9 B=1/12
i gonna "cheat" here and go straight to final day (since answer choice give us that advantage). so we know each worked 5 days so total work done so far is:
5/9+5/12 =.97222 We know last day is A's turn so we have 1/9 * D = (1-.97222) D = .25 so B



5) 8 men can dig a pit in 20 days. if a man works half as much again as a boy, then 4 men and 9 boys can dig it in:
a) 10 days
b) 12 days
c) 15 days
d) 16 days

C?
8*R *20 = 1 R=.00625 for ONE Man
(2*R+9*R)D = 1 11R*D =1 D = 14.5 = 15.


6) A cistern has a leak which would empty it in 8 hours. A tap is turned on which admits 6 liters a minute into the cistern and it is now empited in 12 hours. how many litres does the cistern hold.
a) 7580
b) 7960
c) 8290
d) 8640

D.???
C = X/8H T = 6L/M = 360L/H

Since tap is turned on for 12 hours we have 360*12 = 4320L for 12 hours

X/8 *12 = 4320+X .5X = 4320 X=8640???? The rate is still X liters / 8 hours but multiplied by 12 now. It is STILL ONE UNIT OF WORK on the right BUT we know how much that work is - 4320 (max water from tap) + X(unknown amount in cistern).



7) two pipes M and N can fill a cistern in 24 min and 32 min , repectively. If both the pipes are opened together, then after hoe many minutes N should be closed so that the tank is full in 18 minutes ?
a) 6
b) 8
c) 10
d) 21

B.
M = 1/24 N = 1/32
1/24*18 + 1/32*(18-M)=1
18-M = 8 M=10 so 18-10 =8 B



If anyone has a faster way to do any of these or shortcuts please share. I also understand some of the calculations i did it right off a calculator and you should know how to do it with fractions!!!
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Last edited by shaselai on 06 Aug 2009, 06:33, edited 2 times in total.
Re: Quant toughest question of Time & Work   [#permalink] 06 Aug 2009, 05:49
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