The price of a bike is first increased by 21% and later on, it is decreased by 34% due to a reduction in sales. Find the net percentage change in the final price of the bike.
- ADecrease of 13.25%
- BIncrease of 20.14%
- CDecrease of 20.14%
- DIncrease of 13.25%
Solution & Step-by-step Explanation
The net percentage change after successive percentage changes of a% and b% is given by the formula:
Net Percentage Change=a+b+
100
ab
Here, the price is first increased by 21% (a=+21) and then decreased by 34% (b=−34).
Net Change=21−34+
100
21×(−34)
Net Change=−13−
100
714
Net Change=−13−7.14=−20.14%
The negative sign signifies a percentage decrease. Thus, there is a decrease of 20.14%.
Net Percentage Change=a+b+
100
ab
Here, the price is first increased by 21% (a=+21) and then decreased by 34% (b=−34).
Net Change=21−34+
100
21×(−34)
Net Change=−13−
100
714
Net Change=−13−7.14=−20.14%
The negative sign signifies a percentage decrease. Thus, there is a decrease of 20.14%.