A haulage company that delivers building materials across the region sees its monthly fuel costs rise to £1242, an increase of 15% compared with last year, ...
Question 1 Report
A haulage company that delivers building materials across the region sees its monthly fuel costs rise to £1242, an increase of 15% compared with last year, because of rising diesel prices at the pump.
- Work out last year's monthly fuel cost. (3)
- Work out the increase in the monthly fuel cost, in pounds. (1)
Answer Details
When a cost after a percentage increase is known, the cost before the increase is found by dividing by the increase multiplier, and the increase itself is then found by subtraction.
(a) Let \(x\) be last year's monthly fuel cost. A 15% rise means \(1.15x = 1242\):
\[1.15x = 1242\] [1 mark]
\[x = 1242 \div 1.15\] [1 mark]
\[x = \pounds 1080\] [1 mark]
(b) The increase in pounds is the difference between the two monthly costs:
\[1242 - 1080 = \pounds 162\] [1 mark]
Note that £162 is not simply 15% of £1242; 15% of the original £1080 gives £162 exactly, confirming the reverse-percentage answer in part (a) is consistent with the stated 15% rise.
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