(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) Total cost C = ₹4,50,000 + ₹80,000 = ₹5,30,000. Life n = 1 January 2001 to 31 December 2020 = 20 years. Scrap value S = ₹1,50,000. Using straight-line depreciation: Annual depreciation D = (C − S)/n = (5,30,000 − 1,50,000)/20 = ₹19,000 per year. Rate of depreciation = (D/C) × 100 = (19,000/5,30,000) × 100 = 3·5849% ≈ 3·585% per annum.

(i) On 15 June 2010, elapsed period from 1 January 2001 = 9 years + 5 months 15 days = 9·4583 years. Depreciation fund accumulated = D × elapsed time = 19,000 × 9·4583 = ₹1,79,708·33 ≈ ₹1,79,708. Thus the annual rate is 3·585% per annum, and the depreciation fund accumulated on 15 June 2010 is ₹1,79,708 approx.

(ii) After 12 years, book value = C − 12D = 5,30,000 − 12 × 19,000 = ₹3,02,000. Replacement cost added = ₹1,50,000. New capital cost = 3,02,000 + 1,50,000 = ₹4,52,000. Remaining life = 20 − 12 = 8 years. New annual depreciation = (4,52,000 − 1,50,000)/8 = ₹37,750. New rate of depreciation = (37,750/4,52,000) × 100 = 8·3518% ≈ 8·35% per annum.

(b) Dampness in a building is the undesirable presence of moisture in walls, floors, roofs or other components. It causes plaster decay, efflorescence, mould, timber rot, corrosion of reinforcement and unhealthy indoor conditions.

Main causes:

• Rising damp by capillary action from ground due to absent or defective DPC, porous materials or high water table.
• Penetrating damp by rain through porous walls, cracks, defective flashing, sills, roof leakage, faulty gutters and downpipes.
• Condensation due to warm moist indoor air meeting cold surfaces, poor ventilation, cooking, bathing and temperature difference.
• Leakage from plumbing, sanitary fittings, water tanks and drains.
• Construction defects such as inadequate DPC, unfilled joints, poor mortar, bad quality materials and faulty roof slopes.
• Hygroscopic salts in bricks and mortar attracting moisture.
• Defective site drainage and wet adjoining ground.

Remedies:

• Provide continuous DPC at plinth, roof, parapet and sills using bitumen, polythene, cement concrete or lead.
• Use cavity walls, damp-proof membranes and water-repellent external coatings such as silicone, cement paint or bituminous treatment.
• Ensure proper roof slope, flashing, waterproofing and repair of cracks, gutters and downpipes.
• Provide surface drains, French drains, subsoil drains and slope ground away from the building.
• Improve ventilation and use exhaust fans or dehumidifiers to prevent condensation.
• Remove affected plaster, replaster with waterproof mortar and treat soluble salts.
• For existing dampness, use chemical DPC by silicone injection, electro-osmotic damp proofing or pressure grouting.
• Maintain plumbing and drainage regularly to stop leaks.

(c) Given: r = 10% = 0·10, VDF = 2·0, LDF for 2-lane single carriageway = 0·75, design life n₀ = 10 years. Traffic count on 31·03·2018 = 750 CV/day in each direction.

For the original two-lane single carriageway, two-way traffic at completion on 31·03·2020: A₂₀₂₀ = 2 × 750 × (1·10)² = 1815 CV/day. Using IRC cumulative standard axle formula: N = 365 × A × VDF × LDF × [((1+r)ⁿ − 1)/r] N₀ = 365 × 1815 × 2·0 × 0·75 × [((1·10)¹⁰ − 1)/0·10] = 365 × 1815 × 1·5 × 15·9374246 = 15,837,218 standard axles ≈ 15·837 MSA.

Assume the construction period remains 2 years, as indicated by the original completion date. New work starts on 01·04·2023, so new completion is 31·03·2025. Traffic in each direction at new completion: A₂₀₂₅ = 750 × (1·10)⁷ = 1461·538 CV/day. For four-lane dual carriageway, LDF = 0·75 in each direction. Let new design life be n years. Equate new per-carriageway design traffic to the originally planned design traffic: 365 × 1461·538 × 2·0 × 0·75 × [((1·10)ⁿ − 1)/0·10] = 15,837,218 800,191·96 × [((1·10)ⁿ − 1)/0·10] = 15,837,218 ((1·10)ⁿ − 1)/0·10 = 19·7918 (1·10)ⁿ = 2·97918 n = ln(2·97918)/ln(1·10) = 1·09165/0·09531 = 11·45 years.

Thus the new design life is 11·45 years ≈ 11 years 5·5 months. In practice, it may be adopted as 11·5 years or 12 years depending on rounding policy.