(a) A machine was purchased for ₹4,50,000 on 1st January 2001 and erection and installation work costed ₹80,000. The same machine…

(a) Depreciation of the machine

Total cost C = 4,50,000 + 80,000 = ₹5,30,000. Life n = 20 years (1.1.2001 to 31.12.2020). Scrap value S = ₹1,50,000. No interest rate is given, so the straight-line method is used.

Annual depreciation D = (C − S)/n = (5,30,000 − 1,50,000)/20 = ₹19,000 per year, which is 19,000/5,30,000 = 3.585% of the cost per annum.

(i) On 15 June 2010, the elapsed time is 3452 days = 9.45 years. The depreciation fund accumulated = 19,000 × 9.45 = ₹1,79,600 (about ₹1.8 lakh), at the rate of ₹19,000 a year (3.585%).

(ii) After 12 years the book value = 5,30,000 − 12 × 19,000 = ₹3,02,000. Adding the replacement cost of ₹1,50,000 gives a new value of ₹4,52,000. Assuming the scrap value stays ₹1,50,000 and the machine is still replaced at the end of the original 20 years, the remaining life is 8 years.

New depreciation = (4,52,000 − 1,50,000)/8 = ₹37,750 per year, which is 37,750/4,52,000 = 8.35% per annum of the revised value.

(b) Dampness in buildings

Dampness is the presence of unwanted moisture in walls, floors, roofs or other parts of a building. It causes decay of plaster, efflorescence, peeling paint, mould, rotting of timber, corrosion of reinforcement and an unhealthy interior.

Main causes: rising damp by capillary action from the ground where the damp-proof course (DPC) is missing or defective, or the water table is high; rain penetrating porous walls, cracks, parapets, sills and defective roofs, gutters and downpipes; condensation of indoor vapour on cold surfaces in poorly ventilated rooms; leakage from plumbing, tanks and drains; and poor site drainage, bad materials and faulty construction joints.

Remedies: provide a continuous DPC of bitumen, polythene sheet, cement concrete or lead at plinth, parapet and sill levels; use cavity walls and damp-proof membranes; apply water-repellent coatings and cement plaster with waterproofing compounds; give roofs proper slope, flashing and waterproofing; provide surface and subsoil drains and slope the ground away from the building; ventilate rooms; and repair plumbing promptly. For existing buildings, use chemical DPC by injection, electro-osmosis or pressure grouting, and replaster with waterproof mortar.

(c) New design life of the pavement

Original design: construction ends 31.3.2020, two years after the count. Traffic at completion = 750 × 1.1² = 907.5 per direction, or 1815 both ways. With F = [(1.1)¹⁰ − 1]/0.1 = 15.937, design traffic on the two-lane road,

N = 365 × A × F × VDF × LDF = 365 × 1815 × 15.937 × 2.0 × 0.75 = 1.584 × 10⁷ standard axles (15.84 msa).

Revised scheme: work starts 1.4.2023. Assuming the same two-year construction period, it finishes on 31.3.2025, seven years after the count. Traffic in each direction = 750 × 1.1⁷ = 1461.5 CV/day. For the four-lane divided road, LDF = 0.75 per direction.

The pavement section stays as designed for 15.84 msa, so equate:

365 × 1461.5 × 2.0 × 0.75 × [(1.1)ⁿ − 1]/0.1 = 1.584 × 10⁷

800 192 × [(1.1)ⁿ − 1]/0.1 = 1.584 × 10⁷, so [(1.1)ⁿ − 1]/0.1 = 19.79.

(1.1)ⁿ = 2.979, so n = ln 2.979/ln 1.1 = 11.45 years, about 11.5 years. The design life rises from 10 years because the traffic per carriageway is now lower.