Question

In an examination, the ratio of passes to failures was 4:1. Had 30 less appeared , and 20 less passed, the ratio of passes to failures would have been 5:1.Represent this situation algebraically and graphically

Answer 1

Step1: Algebraic representation

Let the number of candidates passed=$x$

Number of candidates failed = $y$

Given that $\frac{x}{y}$=$x$ $\frac{4}{1}$

$x=4y$…………………(1)

If the number of students appeared are $30$ less then the total students appeared are $x+y-30$

The number of students passed when $20$ less pass $=$$x-20$

The number of students failed $=$$x+y-30-(x-20)$

= $y-10$

From the second condition,

$$\begin{gathered} \frac{x-20}{y-10}=\frac{5}{1} \\ x-20=5\left(y-10\right) \\ x-20=5y-50 \\ x-5y=-30..........\left(2\right) \end{gathered}$$

pair of equations (1) and (2) represent the given situation algebraically.

Step2: Geometrical representation:

$x=4y$ …………………(1)

$x-5y=-30.........\left(2\right)$

Substituting different values for $x$ in equation (1) ,we get different values for $y$ as follows.

$x$	$0$	$2$	$4$
$y$	$0$	$0.5$	$1$

Substituting different values for $x$ in equation two we get.

$x$	$0$	$-5$	$5$
$y$	$6$	$5$	$7$

Plotting the points on a graph we get the geometrical representation of the situation as follows.

Hence the situation is represented algebraically and graphically.