Question

In a span of 50 years, out of the 6 main cities in a country, the population of cities A, B and C doubles while the population of cities D, E and F becomes 4 times as much as their initial population. If the population in each city is as given in the table, choose the line plot that correctly represent their populations 50 years later.

City	$A$	$B$	$C$	$D$	$E$	$F$
Initial population (in millions)	$\frac{1}{8}$	$\frac{1}{4}$	$\frac{1}{4}$	$\frac{1}{8}$	$\frac{1}{8}$	$\frac{1}{16}$

• A. Plot 1
• B. Plot 2
• C. Plot 3
• D. None of the above

Answer 1

The correct option is B Plot 2

$\text{From the question, we have:}$

$\text{City}$	$\text{Initial}\text{population}\text{(millions)}$	$\text{Population}\text{after 50 years}$ $\text{(millions)}$
A	$\frac{1}{8}$	$\frac{1}{8}+\frac{1}{8}=\frac{2}{8}$
B	$\frac{1}{4}$	$\frac{1}{4}+\frac{1}{4}=\frac{2}{4}$
C	$\frac{1}{4}$	$\frac{1}{4}+\frac{1}{4}=\frac{2}{4}$
D	$\frac{1}{8}$	$\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}=\frac{4}{8}$
E	$\frac{1}{8}$	$\frac{1}{8}+\frac{1}{8}+\frac{1}{8}+\frac{1}{8}=\frac{4}{8}$
F	$\frac{1}{16}$	$\frac{1}{16}+\frac{1}{16}+\frac{1}{16}+\frac{1}{16}=\frac{4}{16}$

$\text{Now,}\frac{2}{8}\text{can be written as:}$

$\frac{2}{8}=\frac{2÷2}{8÷2}=\frac{1}{4}$

$⟹\frac{1}{4}\text{is an equivalent fraction of}\frac{2}{8}$

$\frac{2}{4}\text{can be written as:}$

$\frac{2}{4}=\frac{2÷2}{4÷2}=\frac{1}{2}$

$⟹\frac{1}{2}\text{is an equivalent fraction of}\frac{2}{4}$

$\text{Similarly,}\frac{4}{8}\text{can be written as:}$

$\frac{4}{8}=\frac{4÷4}{8÷4}=\frac{1}{2}$

$⟹\frac{1}{2}\text{is an equivalent fraction of}\frac{4}{8}$

$\text{Finally,}\frac{4}{16}\text{can be written as:}$

$\frac{4}{16}=\frac{4÷4}{16÷4}=\frac{1}{4}$

$⟹\frac{1}{4}\text{is an equivalent fraction of}\frac{4}{16}$

$\text{Tabulating the equivalent fractions, we get:}$

$\text{City}$	$\text{Population}\text{after 50 years}$ $\text{(millions)}$	$\text{Equivalent}\text{fraction}$
A	$\frac{2}{8}$	$\frac{1}{4}$
B	$\frac{2}{4}$	$\frac{1}{2}$
C	$\frac{2}{4}$	$\frac{1}{2}$
D	$\frac{4}{8}$	$\frac{1}{2}$
E	$\frac{4}{8}$	$\frac{1}{2}$
F	$\frac{4}{16}$	$\frac{1}{4}$

$\text{Plotting this data on a line plot, we get:}$


$\therefore \text{Line plot 2 correctly represents the}$ $\text{population of the cities after 50 years.}$