The budget for a construction project is allocated to land acquisition, building materials, and labor in the ratio 5 : 3 : 2. Dur…

Question

The budget for a construction project is allocated to land acquisition, building materials, and labor in the ratio 5 : 3 : 2. During the project, the cost of land acquisition rose by 5%, building materials rose by 10%, and labor fell by 20%. What is the percent change (increase or decrease) in the total project cost?

1. A. 1.0% increase
2. B. 1.5% decrease
3. C. 1.5% increase (Correct answer)
4. D. 2.0% decrease

Correct Answer

Option C — 1.5% increase

Detailed Solution & Explanation

The correct answer is 1.5% increase.

Key Points

• Treat the ratio 5 : 3 : 2 as actual units totalling 10.
• Apply each change to its own component:
  • Land: 5 × 1.05 = 5.25 (up 5%)
  • Materials: 3 × 1.10 = 3.30 (up 10%)
  • Labour: 2 × 0.80 = 1.60 (down 20%)
• New total = 5.25 + 3.30 + 1.60 = 10.15 against an original 10.
• Change = 0.15/10 × 100 = 1.5% increase.

Additional Information

• Percentage changes on parts of a whole must be weighted by each part's size; a plain average of +5, +10 and −20 gives −1.67% and is exactly the trap the "decrease" options exploit.
• Multiplying by 1.05, 1.10 and 0.80 is safer than computing each change separately and adding, since it removes a sign-error step.
• The direction is a useful check: the two components that rose carry 8 of the 10 units between them, so the total was always likely to rise despite the larger percentage fall in labour.

प्रश्न (हिन्दी में)

एक निर्माण परियोजना के लिए बजट भूमि अधिग्रहण, निर्माण सामग्री और श्रम के लिए 5 : 3 : 2 के अनुपात में आवंटित किया जाता है। परियोजना के दौरान, भूमि अधिग्रहण की लागत 5% बढ़ गई, निर्माण सामग्री में 10% की वृद्धि हुई और श्रम में 20% की गिरावट आई। कुल परियोजना लागत में प्रतिशत परिवर्तन (वृद्धि या कमी) क्या है?

1. A. 1.0% वृद्धि
2. B. 1.5% कमी
3. C. 1.5% वृद्धि
4. D. 2.0% कमी