SOLUTION: A motorist reduces his annual distance travel by x% when the price of petrol is increased by y%. Find the increase percent in his petrol bill.

Question 1120734: A motorist reduces his annual distance travel by x% when the price of petrol is increased by y%. Find the increase percent in his petrol bill.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The distance traveled (and therefore presumably the amount of petrol used) is multiplied by a factor of (1-x/100); the price is multiplied by a factor of (1+y/100). The total cost of the petrol is

(1-x/100)(1+y/100) = 1+y/100-x/100-xy/10000

The change in the cost of the petrol is

y/100-x/100-xy/10000

Multiplying by 100 to get the change as a percentage, the percent change in the cost is y-x-xy/100.

Note we don't know whether that is an increase or a decrease in total cost.

Example 1:
Decrease travel by 10% when the price increases by 20% (x=10,y=20)
The distance traveled gets multiplied by (1-.10) = .90; the price gets multiplied by (1+.20) = 1.20
The total cost gets multiplied by (.90)(1.20) = 1.08, an increase of 8%
By the formula, 20-10-200/100 = 10-2 = 8 percent

Example 2:
Decrease travel by 30% when the cost increases by 10% (x=30, y=10)
The distance traveled gets multiplied by (1-.30) = .70; the price gets multiplied by (1+.10) = 1.10
The total cost gets multiplied by (.70)(1.10) = 0.77, an decrease of 23%
By the formula, 10-30-300/100 = -20-3 = -23 percent

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