The current erection cost of a structure is Rs. 13,200. If the labour wages…

Concept: When a project's cost is billed as a wage rate applied over the hours actually worked, the total cost scales directly with both the rate and the hours: new cost = original cost × (rate factor) × (hours factor). This item's numbers describe exactly those two inputs (the wage rate and the working-hours figure), so both factors multiply the original cost in the same step — it is not a ‘fixed output needs proportionally more days’ scheduling problem, since no fixed physical output is specified independent of the wage-and-hours figures given.

Application:

1. A wage increase of 1/5 of the current wage scales the rate factor by 1 + 1/5 = 6/5.

2. A reduction of 1/24 of the working period scales the hours factor by 1 − 1/24 = 23/24.

3. Combined factor = (6/5) × (23/24) = 138/120 = 23/20 = 1.15.

4. New cost = original cost × combined factor = 13,200 × 23/20 = 15,180.

Cross-check: A 20% rate rise against only a ~4.17% hours cut 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. (A tempting alternative treats the hours cut as requiring proportionally more working days for a fixed job, giving a reciprocal 24/23 factor and ≈ Rs. 16,529 — a value that is not among the offered options and does not match this item's direct rate-and-hours cost model or the official GATE 2013 CS answer key, which confirms this exact result: Rs. 15,180.)