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Doubts of Time and work sheet (Pages: 1 2 )

In this forum, please discuss the questions appearing in the QA class sheets :especially the practice and the DS questions at the end of the sheet.

Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Thu Feb 28, 2013 1:21 pm

11. If 75 men can dig a trench 300 m long, 9 m wide and 3 m
deep in 6 days working 5 hours a day, in how many days
will 50 men dig another trench 540 m long, 6 m wide and
4.5 m deep working 4 hours a day ?

Solution: Such questions are best solved by work equivalence method

Work done has two facets - the input side and the output side -
On the input side is the effort of the group of men and on the output side is the output - which in this case is the trench measured in terms of its volume.
Thus we have the first equation

75 x 6 x 5 = k. 300 x 9 x 3 (Note: we multiplied the RHS by K to ensure equality of units on both sides - which is the role of any constant of proportionality)

The second equation => 50 x z days x 4 =k. 540 x 6 x 4.5 ------2

On dividing equation 1 by 2 , k, the constant of proportionality will be eliminated and we will get the value of z = 20.25

On the first glance this method looks time consuming. But this method is the most efficient way of solving this question- this is even more efficient than the chain rule method - for a simple reason that this method is mechanical. With some practice you can instinctively reach the last step in no time.
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby tpsriram » Thu Feb 28, 2013 1:23 pm

thankyou sir!!!
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby gaurav1399 » Thu Feb 28, 2013 1:23 pm

sir my doubts in time and work are as follows:
15,28,
practice questions:1,2,6,15,24,25,26,27
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Thu Feb 28, 2013 1:24 pm

15. If the wages of 45 women amount to Rs. 15525 in 48
days, how many men must work for 16 days to receive
Rs. 5750, the daily wages of a man being double that of
a woman?

solution

This is as good as saying that 45 women, in 48 days perform work whose value is Rs 15525

There fore the equation - 45 x 48 = k x 15525 ....1 ( k IS THE constant of proportionality)

1 man = 2 women ( given that the daily wage of one man is twice the daily wage of a woman)

if the number of men is "x" then the equivalent number of women =2x

2x X 1 6 = k x 5750 ........2

On dividing 1 by 2 you should be able to get the value of "x" = 25

Answer
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Thu Feb 28, 2013 1:25 pm

28. Two pipes A and B can separately fill a cistern in 10
minutes and 15 minutes respectively. A person opens
both the pipes together. When the cistern should have
been full, he finds the waste pipe open. He then closes
the waste pipe and in another 4 minutes, the cistern was
full. In what time can the waste pipe empty the cistern
when full ?

solution

For this question it is important to note that if a person opens two pipes which can fill the cistern in 10 and 15 minutes respectively, he should come back in 6 minutes ( the time taken by these two pipes to fill the cistern if they are in operation at the same time)

But because of a waste pipe being open along with the above two pipes, the cistern is not full when this man comes back.

In fact once the waste pipe is closed by the man after coming back - the cistern is full in 4 more minutes -

The volume of cistern filled in the last four minutes = 4/6 ( if 6 minutes are required by the two pipes to fill the cistern, then the two pipes will fill 1/6 * 4 fraction of the cistern in the last four minutes)

This implies that during the first six minutes only 2/6th of the cistern got full because the waste pipe was operational.

Thus we have the equation

(1/6 -1/w)* 6 =2/6

On solving the above equation w = 9 minutes
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Fri Mar 01, 2013 5:36 am

Practice -1

1. If A takes half as long to do a piece of work as B takes,
and if C does it in the same time as A and B together,
and if all three working together would take 7 days, how
long would each take separately ?
(a) 21 days, 21 days, 14 days
(b) 21 days, 42 days, 14 days
© 21 days, 21 days, 21 days
(d) 7 days, 21 days, 28 days

Solution

A, B, C are days required by A, B and C respectively to do the required work

If A takes half the time as B to do some work , then the rate of A must be two times that of B
1/A = 2/B ..........1

If C takes the same time as A and B working together, the combined rate of A and B must be equal to the rate of C

1/A + 1/B = 1/C OR 2/B + 1/B = 1/C => 3/B =1/C

We have been given the additional information that A,B and C together can do the work in 7 days - therefore we have


1/A + 1/B + 1/C =1/7


2/B + 1/B +3/B =1/7 => B=42 ,A= 21 C =14
option b


A better approach to solving this question is to work it backward from the options.

(a) 21 days, 21 days, 14 days - can not be the answer because it does not satisfy the relations between the rates of filling of
(b) 21 days, 42 days, 14 days
© 21 days, 21 days, 21 days
(d) 7 days, 21 days, 28 days
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Fri Mar 01, 2013 5:38 am

Practice Questions -2
2. Paul finishes 3/10 of a work in 6 days and then finishes
the remaining with the assistance of Peter in 6 days. In
what time can Peter alone finish the same work ?
(a) 6 days (b) 15 days © 20 days (d) 11 days
Solution

If Paul finishes 3/10th of the work in 6 days then he will take 20 days to complete the work. If peter takes "P" days to complete the work - then

Further because 3/10th the work has already been done by Paul working alone, the balance of the work that is 7/10 th of the work shall be done by Both in the last six days - hence we have
(1/20 +1/p)* 6 =7/10

p =15 days
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Fri Mar 01, 2013 5:40 am

6. A cistern has a leak which would empty it in 8 hrs. A tap
is turned on which admits 6 litres a minute into the cistern,
and it is now emptied in 12 hours. How many litres does
the cistern hold ?
(a) 8460 litres (b) 8640 litres
© 8660 litres (d) 84440 litres

Solution
Let the volume of the cistern be "V" L
The rate of the leak = V/8
The combined rate of the inlet and the leak =V/12

V/8 -V/12 = 6 X 60

On solving the above equation we get the value of V =8640 L[/align]
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Fri Mar 01, 2013 5:41 am

24. A and B together can do a job in 20 and 30 days
respectively. With the help of C, they finished the job in 8
days and are paid Rs. 3750 for the whole job done. Find
the daily wages of C.
(a) Rs. 187.50 (b) Rs. 150.00
© Rs. 150.25 (d) Rs. 156.25

Solution

The money is shared in the ratio of the rates of work of A,B, C.
1/A +1/B+ 1/C =1/8

1/20 + 1/30 +1/C =1/8

C =24

Thus the money shalll be shared between A,B and C in the ratio
1/20 :1/30 :1/24 i.e. 6:4:5

The daily wages of C can be found by dividing the share of C by 8.
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Re: Doubts of Time and work sheet (Pages: 1 2 )

Postby sadmin » Fri Mar 01, 2013 5:42 am

Practice Questions
25. If two pipes function simultaneously, the reservoir will be
filled in 12 hours. One pipe filled the reservoir 10 hours
faster than the other. How many hours does the faster
pipe take to fill the reservoir ?
(a) 25 hrs (b) 28 hrs
© 30 hrs (d) 20 hrs.

Solution

If the slower pipe fills the reservoir in "x" hours then the faster one fills it in "x+10" hours

1/x + 1/(x+10) =1/12

On solving the above equation
x =20 hours
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