A number is increased by 20%, then decreased by 27%, and then further increased by 10%. What is the net increase/decrease percentage in the number (correct to the nearest integer)?
- A5% increase
- B4% decrease
- C7% increase
- D6% increase
Solution & Step-by-step Explanation
Let the initial number be 100.
First Change: Increased by 20%
New Number=100×(1+
100
20
)=100×1.2=120
Second Change: Decreased by 27%
New Number=120×(1−
100
27
)=120×0.73=87.6
Third Change: Increased by 10%
Final Number=87.6×(1+
100
10
)=87.6×1.1=96.36
Net Percentage Change:
Net Change=Final Number−Initial Number
Net Change=96.36−100=−3.64%
The negative sign indicates a decrease.
Rounding −3.64% to the nearest integer gives a 4% decrease.
First Change: Increased by 20%
New Number=100×(1+
100
20
)=100×1.2=120
Second Change: Decreased by 27%
New Number=120×(1−
100
27
)=120×0.73=87.6
Third Change: Increased by 10%
Final Number=87.6×(1+
100
10
)=87.6×1.1=96.36
Net Percentage Change:
Net Change=Final Number−Initial Number
Net Change=96.36−100=−3.64%
The negative sign indicates a decrease.
Rounding −3.64% to the nearest integer gives a 4% decrease.