The population of a town is 25,000. It increases by 8% in the first year and decreases by 5% in the second year.
Consider the following statements:
I. The population at the end of the second year is 25,650.
II. Over the two years, the population increases by 2.6%.
III. If the 5% decrease had come in the first year and the 8% increase in the second year, the final population would have been larger.
Which of the above statements is/are correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → I and II only
Each year’s change is taken on the population at the start of that year, so the multipliers \(1.08\) and \(0.95\) are multiplied.
I. The population at the end of the second year is 25,650. — Correct. Applying the two changes in turn gives 25,650.
After the first year: \(25000\times1.08=27000\)
After the second year: \(27000\times0.95=25650\)
II. Over the two years, the population increases by 2.6%. — Correct. The overall multiplier is 1.026.
Overall multiplier \(=1.08\times0.95=1.026\)
Increase \(=1.026-1=0.026=2.6\%\)
Check: \(25650-25000=650\) and \(\displaystyle\frac{650}{25000}\times100=2.6\%\)
III. If the 5% decrease had come in the first year and the 8% increase in the second year, the final population would have been larger. — Incorrect. The order of multiplication does not matter: \(0.95\times1.08=1.08\times0.95=1.026\), so the final population would again be 25,650.