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18 votes
18 votes

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. $10,120$
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6 Answers

31 votes
31 votes

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 by
18 votes
18 votes
Working hours per day decreased. 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 votes
1 votes

Old Scenario:

$\text{Total Cost} = \text{₹}13200$

$\text{Working Hours(per day)} = t_d$

$\text{Total Days of Work} = d$

$\text{Total Working Hours} = \text{Working Hours(per day)} \times \text{Total Days of Work} = t_d \times d$

$\text{Labour Wages(per day)} = w_d$

$\text{Total Cost} = \text{Total Days of Work} \times \text{Labour Wages(per day)} = \text{₹}13200$

$\therefore d \times w_d = \text{₹}13200$

 

New Scenario:

$\text{Labour Wages(per day)} = w_d \times (1 + 1/5) = \frac{6}{5} w_d$

$\text{Working Hours(per day)} = t_d \times (1 - 1/24) =\frac{23}{24} t_d$

 

Assuming, NO change in worker efficiency, the $\underline{\text{Total Working Hours}}$ will remain constant.

$\therefore$ Since the working hours per day have decreased, The number of working days will increase.

$\therefore \text{Total Days of Work} = \frac{\text{Total Working Hours}}{\text{Working Hours(per day)}} = (t_d \times d)/(\frac{23}{24}\times t_d) = \frac{24}{23} d$

 

$\therefore \text{Total Cost} = \text{Total Days of Work} \times \text{Labour Wages(per day)} =  (\frac{24}{23} d) \times (\frac{6}{5} w_d)$

$= \frac{6 \times 24}{5 \times 23}(d \times w_d) = \frac{6 \times 24}{5 \times 23} \times 13200 = 16528.69$

0 votes
0 votes
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
Answer:

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