A question of arithmetic regarding erection cost of a structure. > The current erection cost of a structure is Rs. $13,200$. If the labour wages per day increase by $\frac 1 5$ of the current wages and the working hours decrease by $\frac 1 {24}$ of the current period, then the new cost of erection in Rs. is $(A)\ 16,500$. $(B)\ 15,180$. $(C)\ 11,000$. $(D)\ 10,120$. I have got an answer different from the answer which is approximately equal to $16528$. Which is very close to option $(A)$. Is it correct? Please help me in this regard. Thank you very much. Attempt: Labour wages increment is proportional to erection cost and working hours decrement is reverse proportional to the erection cost. So the required erection cost is $13200×\frac{\frac65}{\frac{23}{24}}$ which simplifies to $16528$ (approx.)

Suppose we assuming that the total number of hours needed remain the same, then indeed your solution is correct, that is the answer is

$$13200 \times \frac65 \times \frac{24}{23} \approx 16528$$

which unfortunately not one of the option.

However, suppose for some reason, their efficiency improves and the days needed remains the same, then the answer is $$13200 \times \frac65 \times \frac{23}{24}=15180.$$

This is a badly framed question where the setting is not clear.

Just FYI, $13200 \times \frac65 \times \frac{25}{24}$ gives you the first option but it is not correct.

I am aware of the background of the question which is from GATE, the answer key is $B$, hence they have assumed that the number of days required remain the same.