4 Mark Question

Question 14 Marks

The population of a place increased to $54,000$ in $2003$ at a rate of $5\%$ per annum.
$(i)$ Find the population in $2001.$
$(ii)$ What would be its population in $2005?$

Answer

$(i)$ Given: Population in $2003=54,000$
$\begin{aligned}
& \text { Rate }=5 \% \text { pa } \\
& \text { Time }=2003-2001=2 \text { years } \\
& \text { Population in } 2003=\text { Population in } 2001 \times\left(1+\frac{ R }{100}\right)^n \\
& 54,000=\text { Population in } 2001 \times\left(1+\frac{5}{100}\right)^2 \\
& \begin{array}{r}
\Rightarrow \quad 54,000=\text { Population in } 2001 \times\left(\frac{21}{20}\right)^2 \\
\Rightarrow \quad 54,000=\text { Population in } 2001 \times \frac{441}{400} \\
\therefore \text { Population in } 2001=\frac{54,000 \times 400}{441} \\
\quad=\frac{21,6,00,000}{441}=48,979.59 \\
\quad=48,980 \text { (approximately) }
\end{array}
\end{aligned}$
$\begin{aligned}
& \text { (ii) Population in } 2005=\text { Population in } 2003 \times\left(1+\frac{ R }{100}\right)^n \\
& =54,000 \times\left(1+\frac{5}{100}\right)^2 \\
& =54000 \times\left(\frac{21}{20}\right)^2 \\
& ={54000} \times \frac{441}{400} \\
& =135 \times 441=59,535
\end{aligned}$

View full question & answer→

Question 24 Marks

If $60\%$ of people in a city like a cricket, $30\%$ like football and the remaining like other games, then what per cent of the people like other games$?$ If the total number of people are $50$ lakh, find the exact number who like each type of game.

Answer

Total number of people $=50,00,000$
Number of people who like cricket $=60 \%$ of $50,00,000$
$\begin{aligned}
& =\frac{60}{100} \times 50,00,000 \\
& =30,00,000
\end{aligned}$
Number of people who like football $=30 \%$ of $50,00,000$
$\begin{aligned}
& =\frac{30}{100} \times 50,00,000 \\
& =15,00,000
\end{aligned}$
Number of people who like other games $=50,00,000-(30,00,000+15,00,000)$
$\begin{aligned}
& =50,00,000-45,00,000 \\
& =5,00,000
\end{aligned}$
Percentage of the people who like other games $=\frac{500000}{5000000} \times 100=10 \%$ Hence, $10 \%$ of people like other game.

View full question & answer→

MATHS 4 Mark Question

Test yourself on this topic