The population of a town is decreased by 20 % | vedclass

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Question

(B) Let the initial population of the town be $100$.After the first year,the population decreases by $20 \%$,so the new population is $100 - 20 = 80$.

Vedclass · Accepted Answer

$40 \%$

Vedclass · Answer

(B) Let the initial population of the town be $100$.After the first year,the population decreases by $20 \%$,so the new population is $100 - 20 = 80$.After the second year,the population decreases by $25 \%$ of the remaining $80$. The decrease is $\frac{25}{100} 	imes 80 = 20$.The final population is $80 - 20 = 60$.The total decrease in population is $100 - 60 = 40$.Therefore,the percentage decrease is $\frac{40}{100} 	imes 100 = 40 \%$.Alternatively,using the formula for successive percentage change: $	ext{Net } \% 	ext{ change} = \left(x + y + \frac{xy}{100}ight) \%$.Here,$x = -20$ and $y = -25$.Net change $= -20 - 25 + \frac{(-20) 	imes (-25)}{100} = -45 + 5 = -40 \%$.The negative sign indicates a decrease of $40 \%$.

The population of a town is decreased by $20 \%$ and $25 \%$ in two successive years. What per cent population is decreased after two years?

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