Question

"In 1985, the population of town A and town B were the same.From 1985 to 1995 the population of town A increased by 60% while the population of town B decreased by 60%.What percentage of the population of town A was the population of town B in 1995?" plz help me by answering the problem.​

Answer 1

AnswEr :

• Let the Population of town A and town B be 100 in Year 1985.

⋆ Population of town A in 1995

$\longrightarrow \mathsf{New \: Population = 100 \times \dfrac{(100 + Incr\%)}{100}}$

$\longrightarrow \mathsf{New \: Population = 100 \times \dfrac{(100 + 60\%)}{100}}$

$\longrightarrow \mathsf{New \: Population = \cancel{100} \times \dfrac{160}{ \cancel{100}}}$

$\longrightarrow \mathsf{New \: Population = 160}$

⋆ Population of town B in 1995

$\longrightarrow \mathsf{New \: Population = 100 \times \dfrac{(100 - Decr\%)}{100}}$

$\longrightarrow \mathsf{New \: Population = 100 \times \dfrac{(100 - 60\%)}{100}}$

$\longrightarrow \mathsf{New \: Population = \cancel{100} \times \dfrac{40}{ \cancel{100}}}$

$\longrightarrow \mathsf{New \: Population = 40}$

⠀

⋆ Let the Percentage of the Population of town A of town B be x%.

$\longrightarrow \mathsf{x\% \times New \: Population_A=New \: Population_B}$

$\longrightarrow \mathsf{ \dfrac{x}{100} \times \cancel{160} = \cancel{40}}$

$\longrightarrow \mathsf{ \dfrac{x}{ \cancel{100}} \times \cancel{4} = 0}$

$\longrightarrow \mathsf{ \dfrac{x}{25} = 0}$

$\longrightarrow \boxed{\mathsf{x = 25\%}}$

⠀

$\therefore$ The population of town A was 25% of the population of town B in 1995.