Question

Q(4) The population of a certain town was 50,000. In a year, male population was increased
by 5% and female population was increased by 3%. Now the population became
52020. Then what was the number of males and females in the previous year?​

Answer 1

$\sf\Large{\underline{\underline{Answer:-}}}$

• Male = 26000
• Female = 24000

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$\huge\color{pink}{\textbf{\textsf{explaination}}}$

★ Given

• Initially the population town is 50000.

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let the population of male and female of previous year be x and y respectively.

• x + y = 50000
• Female = y
• Male = x = 50000 – y. Equation ❶

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It is given that the male population increased by 5% and female population has increased by 3% so the increase in population is,

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$\begin{gathered}\\\;\sf{:\rightarrow\;\;(x + 5\% \: of \: x) + (\;\bf{{y+ 3\% \: of \: y})\: = 52020}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{\bigg({x + \frac{5}{100} \times x}\bigg) +\bigg({y + \frac{3}{100} \times y}\bigg) \: = 52020}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{{\frac{100x + 5x + 100y + 3y}{100}} \: = 52020}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;105x + \;\bf{{103y}\: = 52020 \times 100}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;105x + \;\bf{{103y}\: = 5202000 ⠀⠀⠀⠀Equation ⠀❷}}\end{gathered}$

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★ Now,

Putting Equation ❶ with Equation ❷.

Multiply 105 by Equation ❶ and Subtract it from ❷, we get

$\begin{gathered}\\\;\sf{:\rightarrow\;\;105(50000 - y) + \;\bf{{103y}\: = 5202000}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;5250000 - 105y + \;\bf{{103y}\: = 5202000}}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;5250000 - 2y = 5202000}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;- 2y = 5202000 - 5250000}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;- 2y = - 48000}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;2y = 48000}\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;y = \frac{48000}{2} }\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;y = 24000 }\end{gathered}$

➥ The number of female = y = 24000

Now, we have the value of y i.e., 24000 and now let us find the value of x.

According to Equation ❶

$\begin{gathered}\\\;\sf{:\rightarrow\;\;x = 50000 - y }\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;x = 50000 - 24000 }\end{gathered}$

$\begin{gathered}\\\;\sf{:\rightarrow\;\;x = 26000 }\end{gathered}$

∴ The number of male and female in previous year was 2400 and 2600 respectively.