Question

Consider the following population and year graph.

I. Slope of $A B=\frac{1}{2}$.
II. Population in the year $2010$ is $104.5$ crore.

• A. Both I and II are true
• B. Only I is true
• C. Only II is true
• D. Both I and II are false

Answer 1

Answer: (A)

Let the population in the year $2010$ will be $k$ crore. Since, $A, B$ and $C$ are collinear.

$\therefore$ Slope of $A B=$ Slope of $B C$
$\Rightarrow \frac{y_2-y_1}{x_2-x_1}=\frac{y_3-y_2}{x_3-x_2}$
$\Rightarrow \frac{97-92}{1995-1985}=\frac{k-97}{2010-1995}$
$\left( \because x_1=1985, x_2=1995, x_3=2010, y_1=92, y_2=97, y_3=k\right)$
$\Rightarrow \frac{5}{10}=\frac{k-97}{15}$
$\Rightarrow \frac{1}{2}=\frac{k-97}{15}$
$\Rightarrow k-97=\frac{15}{2}$
$\Rightarrow k=97+\frac{15}{2}=97+7.5=104.5$
Hence, slope of $A B=\frac{1}{2}$
and population in the year $2010=104.5$ crore.