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

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Solution

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Official answer: B) 15,180

Quantitative Aptitude

Let the original daily wage rate be $W$ and the total working period (in days/hours) be $T$ .

The initial cost of erection is:

C = W \times T = 13{,}200

According to the problem:

New labour wages per day, $W^{\prime} = W + \frac{1}{5}W = \frac{6}{5}W$
New working hours/period, $T^{\prime} = T - \frac{1}{24}T = \frac{23}{24}T$

Therefore, the new cost of erection is:

C^{\prime} = W^{\prime} \times T^{\prime} = \left(\frac{6}{5}W\right) \times \left(\frac{23}{24}T\right) = \left(\frac{6}{5} \times \frac{23}{24}\right) \times (W \times T)

C^{\prime} = \frac{23}{20} \times 13{,}200 = 23 \times 660 = 15{,}180

Thus, the new cost of erection is Rs. 15,180, which corresponds to option (B).

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This Quantitative Aptitude previous year question is Q65 of the GATE CSE 2013 paper. Find more GATE CSE PYQs on Quantitative Aptitude in General Aptitude, or browse all GATE CSE PYQs.

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