Question

Number of oranges	Cost in rupees
2	8
6	$p$
$q$	84

$Findthenumericalvalueofp\text{and}q$.

• A. $p=24q=21$
• B. $p=21q=24$
• C. $p=12q=17$
• D. $p=24q=20$

Answer 1

The correct option is A $p=24q=21$

Given,
Cost of 2 oranges is ₹8.

We know that more the number of oranges, more the cost.

$\text{So, Number of oranges}\left(x\right)\propto \text{Cost}\left(y\right)$
$\therefore \frac{x_1}{y_1}=\frac{x_2}{y_2}$

Given,
$x_1=2oranges$
$y_1=₹8$
$x_2=6oranges$
$\text{and}{y}_2=p=\text{cost of 6 oranges}$

$\Rightarrow y_2=\frac{x_2\times y_1}{x_1}$

$\Rightarrow p=\frac{6\times 8}{2}=₹24$

Again,
$x_1=2oranges$
$y_1=₹8$
$y_2=₹84$
$\text{and}{x}_2=q=\text{no. of oranges}$

$\Rightarrow x_2=\frac{x_1\times y_2}{y_1}$

$\Rightarrow q=\frac{2\times 84}{8}=21oranges$