Discussion
In the summer, water consumption is known to decrease overall by 25%. A Water Board official states that in the summer household consumption decreases by 20%, while other consumption increases by 70%.
Which of the following statements is correct?
Answer: D
The correct statement is that there are errors in the official's statement.
Let household consumption be h and other consumption o before summer. The official's figures, together with the known overall fall of 25%, require
\[ \begin{aligned} 0.8h + 1.7o &= 0.75(h + o) \\ 0.05h + 0.95o &= 0 \end{aligned} \]
Both h and o are positive, so the left side is positive and can never be zero. No positive amounts of household and other consumption can fit: a 20% fall in one part and a 70% rise in the other can never add up to an overall fall of 25%, since even the fall in the first part is only 20%.
The three ratio options therefore describe a situation that cannot exist; none of them makes the equation hold.
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