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Official PYQ · 2013Q65MCQ1 mark

GATE CS 2013 Q65 — General Aptitude

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The current erection cost of a structure is Rs. 13,200.13,200. If the labour wages per day increase by 1/51/5 of the current wages and the working hours decrease by 1/241/24 of the current period, then the new cost of erection in Rs. is

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Answer: B

The erection cost of a structure is directly proportional to both the daily labour wages and the total working period (duration).

Let WW be the initial daily wage and TT be the initial working period. The initial cost is given by:

C=k×W×T=13,200C = k \times W \times T = 13,200

According to the problem:

  • The new daily wage increases by 15\frac{1}{5}: W′=W(1+15)=65WW' = W \left(1 + \frac{1}{5}\right) = \frac{6}{5}W
  • The working period decreases by 124\frac{1}{24}: T′=T(1−124)=2324TT' = T \left(1 - \frac{1}{24}\right) = \frac{23}{24}T

The new cost of erection C′C' is:

C′=k×W′×T′=k×(65W)×(2324T)C' = k \times W' \times T' = k \times \left(\frac{6}{5}W\right) \times \left(\frac{23}{24}T\right) C′=C×65×2324=13,200×2320C' = C \times \frac{6}{5} \times \frac{23}{24} = 13,200 \times \frac{23}{20} C′=660×23=15,180C' = 660 \times 23 = 15,180

Thus, the new cost of erection is Rs. 15,180.

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