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The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is

1. 16,500
2. 15,180
3. 11,000
4. 10,120

Since wages per day increase by $\dfrac{1}{5}$ of current wages, new wages per day becomes $\dfrac{6}{5}$
of current wages.

Similarly, new working hours are $\dfrac{23}{24}$ of current working hours.

So new erection cost becomes $13200\times \dfrac{6}{5} \times \dfrac{23}{24} = 15180.$

So option (B) is correct.

edited
+11

"working hours decrease by 1/24 of the current period" Does this mean workers efficiency improved and they worked faster or the total hours of work per day got reduced which in turn would increase the no. of days for construction? My logic says it should be the latter which would give (A) as answer. Otherwise the question should have mentioned "Total days of construction remained the same". But GATE answer key shows (B)

+1

It says "working hours decrease by 1/24 of the current period", which means total working hours decreased by 1/24 of current total working hours. So it means workers' efficiency improved.

+4
yes. But workers efficiency getting improved is not a usual happening. It should have been explicit in the question.
+3
Arjun sir!! I too thought the same and my answer is (A) if nothing more is given in equation, and I think IITs too can make an error in providing an answer , but it is just so simple to observe that both of these parameters, i.e Increase in wages and decrease in working hours adversely affect erection cost of a structure. Alas !! I am too disappointed by the answer given on internet all over. Are we human race so copy cats that we will justify a wrong answer because it has been given by an authority...
+4
When GATE gives a key what can others say? Suppose I run a coaching institute and I say GATE key is wrong. Students will join some other institute :)

And I have a feeling most aptitude questions in GATE are just copied from somewhere. No where as standard as the technical questions. Even for technical questions I have seen some questions being copied (but very less in number). But in most other exams questions come from some question bank, so GATE is much much better :)
+1
Lets hope this will change from this year, when we will be able to challenge answer ! I was getting Answer A !
0
@arjun sir  how u got A
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Working hours per day increased. So, no. of working days should increase assuming workers work at same efficiency.

New no. of working days * new no. of hours per day = Old no. of working days * old no. of hours per day

New no. of working days * 23/24 old no. of hours per day = Old no. of working days * old no. of hours per day

New no. of working days = 24/23 * Old no. of working days

New cost = New working days * New wage

= 24/23 * Old working days * old wage * 6/5

= Old working days * old wage *144/115

= Old cost * 144/115

= 13,200 * 144/115

= 16,528.69

This is assuming workers work with same efficiency and hence requiring more days to complete the work. But as per GATE official key answer is 15,180 which means with an increase in wage workers got motivated and hence finished the task in same no. of days.
edited by
+1

Suppose earlier days were x and working hours were k. Working hours decreased by 1/24.

x * k = x" * (k- 1/24*k) where x" are new no. of days.

So shouldn't the new no. of days be 24/23 of original no of days instead of 25/24?

0
yes, thats correct. Thanks.
0
I beat my head up with this question. now I see :(
CurrentCost = 13200

Let, CurrentNumberOfDays to complete work = y

Therefore CurrentWagePerDay = CurrentCost/CurrentNumberOfDays = 13200/y

NewWagePerDay = 6*CurrentWagePerDay/5 = (6 * 13200)/(5*y)

NewNumberOfDays to complete work = 23y/24

NewCost = NewWagePerDay *  NewNumberOfDays = (6 * 13200 * 23)y / (5 * 24)y = 15180

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