The current erection cost of a structure is Rs. 13,200. If the labour wages…
20132013
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
- A.
16,500
- B.
15,180
- C.
11,000
- D.
10,120
Attempted by 39 students.
Show answer & explanation
Correct answer: B
Concept: When an activity's cost depends on a daily rate applied over a number of working units (days/hours), the total cost is directly proportional to the product of the rate and the working period. So a new total cost equals the original cost multiplied by the rate-change factor and the period-change factor combined.
Application:
A wage increase of 1/5 of the current wage scales the rate by 1 + 1/5 = 6/5.
A reduction of 1/24 of the working period scales the period by 1 - 1/24 = 23/24.
Combined factor = (6/5) × (23/24) = 138/120 = 23/20 = 1.15.
New cost = original cost × combined factor = 13,200 × 23/20 = 15,180.
Cross-check: A 20% rate rise against only a ~4.17% period drop must give a net rise, and 13,200 × 1.15 = 15,180 is indeed above 13,200, confirming the result. Equivalently, 13,200 ÷ 20 = 660 and 660 × 23 = 15,180.