Bramley Farm harvested 640 tonnes of wheat last season. This season the harvest rose 25 per cent. Next season it is expected to fall 12 per cent. Find this ...
Question 1 Report
Bramley Farm harvested 640 tonnes of wheat last season. This season the harvest rose 25 per cent. Next season it is expected to fall 12 per cent.
- Find this season's harvest. (2)
- Find the expected harvest for next season. (2)
Answer Details
Percentage changes are handled with multipliers, and each change is applied to the amount immediately before it, not to the original figure.
(a) A rise of \(25\) per cent means this season is \(125\) per cent of last season, a multiplier of \(1.25\):
\[640 \times 1.25\][1]
\[= 800 \text{ tonnes}\][1]
(b) A fall of \(12\) per cent leaves \(100 - 12 = 88\) per cent, a multiplier of \(0.88\). The question says the fall applies to next season relative to this season, so it acts on the \(800\) tonnes:
\[800 \times 0.88\][1]
\[= 704 \text{ tonnes}\][1]
Applying the \(12\) per cent fall to the original \(640\) tonnes is the error to avoid; a percentage change always refers to the figure it is measured from.
The two changes do not cancel out even though \(25\) and \(12\) might look close to balancing. The combined multiplier is \(1.25 \times 0.88 = 1.1\), so the expected harvest is \(10\) per cent above the \(640\) tonnes of last season, because the \(12\) per cent fall is taken from the larger figure of \(800\).
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