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absent on k working days

by sanju09 » Wed Nov 09, 2011 3:00 am
Andrew's office has only 20 working days each month. For receiving his full monthly salary Andrew needs to work for x hours on each working day and in case he is absent on a given working day, he must have to work for y extra hours each day for the next few working days (if available in the same month) until his loss is covered. If Andrew was absent on k working days in the last month and he still managed to receive his full salary, what is x/y?

(1) x + y = 5 k.

(2) Andrew worked for y extra hours each day on 4 k working days the last month.

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by rijul007 » Wed Nov 09, 2011 3:51 am
Option B
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by sanju09 » Wed Nov 09, 2011 4:09 am
rijul007 wrote:Option B
question so long, answer so short

amazing

explanation plz
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by user123321 » Wed Nov 09, 2011 4:18 am
should be B
1) then total hours he missed = k.x
to cover that he should have worked = p.y.k
where p is number of days he worked for y hours daily when he was on leave for one day.
=> kx = pyk => p = x/y
using x+y = 5k it is not possible to determine value of p since three unknows, two equations. hence insufficient.

2) given he worked y extra hours on 4k working days. so by above explnation...
k.x = y.4k
=> x/y = 4. hence sufficient.

[spoiler]is it B?[/spoiler]
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by rijul007 » Wed Nov 09, 2011 4:59 am
sanju09 wrote:
rijul007 wrote:Option B
question so long, answer so short

amazing

explanation plz
sry :D

user123321 has explained the ans...
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by rijul007 » Wed Nov 09, 2011 5:01 am
user123321 wrote:should be B
1) then total hours he missed = k.x
to cover that he should have worked = p.y.k [should have been just p.y]
where p is number of days he worked for y hours daily when he was on leave for one day.
=> kx = pyk => p = x/y [kx = py => p/k = x/y]
using x+y = 5k it is not possible to determine value of p since three unknows, two equations. hence insufficient.

2) given he worked y extra hours on 4k working days. so by above explnation...
k.x = y.4k
=> x/y = 4. hence sufficient.

[spoiler]is it B?[/spoiler]


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by user123321 » Wed Nov 09, 2011 5:09 am
my definition of p is number of days he worked for y hours when he was on leave for one day.
so if he was on leave for k days he might have worked k.p days and y hours each day.
since he worked y hours each day, in hours it will be k.y.p

I am sorry, I am not getting why it should be p.y
please care to explain.

Thanks
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by sanju09 » Wed Nov 09, 2011 5:11 am
B is my answer too
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by rijul007 » Wed Nov 09, 2011 5:44 am
@user123321
man i'm sorry.. i didnt notice "one day"


i thought you said

p is the no of days he worked extra time,

then it should have been
kx = py
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by user123321 » Wed Nov 09, 2011 6:04 am
rijul007 wrote:@user123321
man i'm sorry.. i didnt notice "one day"


i thought you said

p is the no of days he worked extra time,

then it should have been
kx = py
:P I just wanted to understand, if in case I made any error. I am making lot of silly errors in DS that's why :)

Thanks & good day
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by chufus » Wed Nov 09, 2011 9:18 am
sanju09 wrote:Andrew's office has only 20 working days each month. For receiving his full monthly salary Andrew needs to work for x hours on each working day and in case he is absent on a given working day, he must have to work for y extra hours each day for the next few working days (if available in the same month) until his loss is covered. If Andrew was absent on k working days in the last month and he still managed to receive his full salary, what is x/y?

(1) x + y = 5 k.

(2) Andrew worked for y extra hours each day on 4 k working days the last month.

made up
Something seems wrong here. Lets look at the scenario below.

Case 1.

Total Working days = 20

Hours per day required = x

So total no of hours has to be equal for him to receive the full monthly pay.

Total No of hours = kx

Case 2.

Absents = k

EXTRA hours required each day = y
So each day he works for = x + y hours

Since both cases have to be equal, the equation can be setup as follows:

20x = (20-k)x + k(x+y)

So: 20x = 20x - kx + kx + ky

So: 0 = ky

Now how is that possible?????????? I dont know why, but I just cannot seem to put a finger on where I am going wrong. Could somebody help please....
In the above explanations I feel people are missing the point that y are EXTRA hours and assuming that y is the total no of hours he has to work on each day of k absents. Am I wrong?
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by chufus » Wed Nov 09, 2011 9:21 am
user123321 wrote:my definition of p is number of days he worked for y hours when he was on leave for one day.
so if he was on leave for k days he might have worked k.p days and y hours each day.
since he worked y hours each day, in hours it will be k.y.p

I am sorry, I am not getting why it should be p.y
please care to explain.

Thanks
user123321
Doesn't the question state that he works y extra hours? You are assuming he works y hours each day for the remaining days.
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by sanju09 » Thu Nov 10, 2011 2:38 am
chufus wrote:
sanju09 wrote:Andrew's office has only 20 working days each month. For receiving his full monthly salary Andrew needs to work for x hours on each working day and in case he is absent on a given working day, he must have to work for y extra hours each day for the next few working days (if available in the same month) until his loss is covered. If Andrew was absent on k working days in the last month and he still managed to receive his full salary, what is x/y?

(1) x + y = 5 k.

(2) Andrew worked for y extra hours each day on 4 k working days the last month.

made up
Something seems wrong here. Lets look at the scenario below.

Case 1.

Total Working days = 20

Hours per day required = x

So total no of hours has to be equal for him to receive the full monthly pay.

Total No of hours = kx

Case 2.

Absents = k

EXTRA hours required each day = y
So each day he works for = x + y hours

Since both cases have to be equal, the equation can be setup as follows:

20x = (20-k)x + k(x+y)

So: 20x = 20x - kx + kx + ky

So: 0 = ky

Now how is that possible?????????? I dont know why, but I just cannot seem to put a finger on where I am going wrong. Could somebody help please....
In the above explanations I feel people are missing the point that y are EXTRA hours and assuming that y is the total no of hours he has to work on each day of k absents. Am I wrong?

Remember, if Andrew was absent on k number of days, then it doesn't mean that he'll be working y extra hours on k number of days only, in order to compensate his loss. Although, this information is there in the statement (2), which openly tells that the loss incurred by k absents can be compensated by working y extra hours each day on 4 k working days. Those 4 k days are to be taken from the same 20 - k days when Andrew was present, hence those 4 k days are not the EXTRA days of working for x + y hours, rather those 4 k days are the EXTRA days of working for y hours only. In that case the equation would look like

20 x = (20 - k) x + 4 k y

0 = - k x + 4 k y

Or k x = 4 k y

Or x/y = 4.
The mind is everything. What you think you become. -Lord Buddha



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by sanju09 » Thu Feb 16, 2012 3:04 am
Any objections on B, as I have to firm up the answer scheme?
The mind is everything. What you think you become. -Lord Buddha



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