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The budget of a factory is distributed among raw materials, wages, and maintenance in the ratio 4:3:3. During a year, the cost of raw materials rises by 12%, wages by 8%, and maintenance falls by 10%. What is the overall percentage change in the total budget?

1. 0.4% decrease
2. 4.2% increase
3. 3.2% increase
4. 2.0% decrease

Correct answer: 4.2% increase

Solution

Let the original budget be 10 units, split as 4, 3, and 3. After changes, the new cost becomes 4×1.12 + 3×1.08 + 3×0.90 = 10.42 units, so the increase is 0.42 units out of 10, i.e. 4.2%.

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