The expenditure of a household on food, clothing, and entertainment is in the ratio 2 : 4 : 4. In the coming year, the cost of fo…

Question

The expenditure of a household on food, clothing, and entertainment is in the ratio 2 : 4 : 4. In the coming year, the cost of food is expected to fall by 10%, clothing to rise by 5%, and entertainment to fall by 15%. What is the percent change (increase or decrease) in the total household expenditure?

1. A. 5% decrease
2. B. 6% increase
3. C. 6% decrease (Correct answer)
4. D. 5% increase

Correct Answer

Option C — 6% decrease

Detailed Solution & Explanation

The correct answer is 6% decrease.

Key Points

• Treat the ratio 2 : 4 : 4 as actual amounts totalling 10 units.
• Apply each change to its own component:
  • Food: 2 × 0.90 = 1.8 (down 10%)
  • Clothing: 4 × 1.05 = 4.2 (up 5%)
  • Entertainment: 4 × 0.85 = 3.4 (down 15%)
• New total = 1.8 + 4.2 + 3.4 = 9.4 against an original 10.
• Change = (9.4 − 10) / 10 × 100 = 6% decrease.
• The percentages must be weighted by the ratio; averaging −10, +5 and −15 gives −6.67% and is the mistake the distractors are built on.

Additional Information

• Percentage changes applied to parts of a whole must always be weighted by the size of each part; averaging the percentages is valid only when the parts are equal.
• Treating a ratio as actual units (here 2, 4 and 4 out of 10) is the quickest route, since the answer is a percentage and therefore independent of the true rupee amounts.
• Multiply by 0.9 for a 10% fall and 1.05 for a 5% rise rather than computing the change separately and subtracting — fewer steps, fewer sign errors.

प्रश्न (हिन्दी में)

एक परिवार का भोजन, कपड़े और मनोरंजन पर व्यय 2 : 4 : 4 के अनुपात में है। आने वाले वर्ष में, भोजन की लागत में 10% की गिरावट, कपड़ों की लागत में 5% की वृद्धि और मनोरंजन की लागत में 15% की गिरावट आने की उम्मीद है। कुल घरेलू व्यय में प्रतिशत परिवर्तन (वृद्धि या कमी) क्या है?

1. A. 5% कमी
2. B. 6% वृद्धि
3. C. 6% कमी
4. D. 5% वृद्धि