Question 1

The population of a city increased by 20% in each of two successive years and then decreased by 10% in the third year. If the present population is 51,840, what was the population three years ago?

IUC Academy · Accepted Answer

40,000 — Net multiplier = 1.2 x 1.2 x 0.9 = 1.296. Original = 51840 / 1.296 = 40000. Check: 40000 -> 48000 -> 57600 -> 51840. Dividing by 1.2 only gives the wrong 43,200.

Question 2

The population of a town is 40,000. It increases by 10% in the first year, decreases by 5% in the second year and increases by 20% in the third year. The population at the end of the third year is:

IUC Academy · Accepted Answer

50,160 — Population = 40000 x 11/10 x 19/20 x 6/5. 40000 x 1.1 = 44000; 44000 x 0.95 = 41800; 41800 x 1.2 = 50160. Adding 10 - 5 + 20 = 25% (giving 50,000) ignores compounding.

Question 3

The price of an article is first increased by 20%, then decreased by 25% and finally increased by 10%. The net change in its price is:

IUC Academy · Accepted Answer

1% decrease — Take price = 100. After +20%: 120. After -25%: 90. After +10%: 99. Net change = 99 - 100 = -1, i.e. 1% decrease. Multiplier method: 1.2 x 0.75 x 1.1 = 0.99.

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