Discussion
The price of tea increased by 40% and then decreased by 20%. If a person now reduces his consumption of tea by \(6\frac{1}{4}\)%, then what is the percentage change in his expenditure?
Answer: C
The expenditure increases by 5%. Take the original price as 100. After a 40% rise it is 140, and after a 20% fall it is \(140\times 0.8 = 112\), so the price factor is 1.12. A reduction of \(6\frac{1}{4}\%\) in consumption leaves \(1 - \frac{1}{16} = \frac{15}{16}\) of it. \[ 1.12\times\frac{15}{16} = 1.05 \] The expenditure is 105% of the original, an increase of 5%. A decrease of 5% or 15% would need a factor below 1, and an increase of 15% would need the factor 1.15, neither of which results.
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