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RV-09-001 · Successive percentages and a reverse comparison

A membership total increases by 20% in one year and decreases by 40% the next year. The final total is 44352.

(a) Work out the original membership total.

(b) Work out the overall percentage change, stating whether it is an increase or a decrease.

Part (a) Reverse Successive Percentages & Overall Percentage Change Booklet p. 51, p. 52 & p. 53
Method
1) Multiply annual multipliers: m = ((100 + p)/
1
0
0) × ((100 − r)/
1
0
0)
2) Reverse percentage: divide final total by m
3) Overall change = (m −
1) × 100%
Worked Example (RV-09-001 · Part (a))
Work out the original membership total.
Booklet p. 53 (Reverse %): Call Original x  ⇒  x×(100±%100)=New Amount\mathbf{x} \;\Rightarrow\; \mathbf{x \times \left(\frac{100 \pm \%}{100}\right) = \text{New Amount}} (Divide both sides by multiplier!)
1) 65×35=1825\frac{6}{5}\times \frac{3}{5}=\frac{18}{25}
2) Divide the final total by the combined multiplier.
3) 61600
61600
Part (b) Reverse Successive Percentages & Overall Percentage Change Booklet p. 51–52
Method
1) Multiply the two percentage multipliers
2) Subtract 1 and multiply by 100
3) State increase or decrease
Worked Example (RV-09-001 · Part (b))
Work out the overall percentage change, stating whether it is an increase or a decrease.
1)
Combine the multipliers: (1+20/100)(1−40/100)=0.72(1+20/100)(1-40/100)=0.72.
2)
Percentage change: (0.72−1)×100=−28%(0.72-1)\times100=-28\%. The sign shows a decrease.
Ans = 28.00% decrease