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Question

Answers

A) $9:7$

B) $7:9$

C) $3:5$

D) $2:7$

Answer
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It can be observed that the whole question revolves around two numbers, whose ratio is to be found.

We can replace their values with variables so that we will be able to apply mathematical approach to solve this problem.

Let the first number$ = x$

Let second number$ = y$

Now it is given that the sum of the two numbers is $20$. This can be mathematically written as,

Sum of $x$ and $y = 20$

$x + y = 20………...(1)$

Further, it is written that their difference is $2.5$. The fact that the numbers have a difference means the numbers are not equal. We can safely assume one of them to be larger than the other. So, let $x$ be greater than $y$.

So, now,

Difference of $x$ and $y = 2.5$

$x - y = 2.5………...(2)$

We can achieve the original values of $x$ and $y$ by simply solving the simultaneous equations (1) and (2)

$x + y = 20$ and $x - y = 2.5$

On adding both equations,

We will get

$

\left( {x + y} \right) + \left( {x - y} \right) = 20 + 2.5 \\

x + y + x - y = 22.5 \\

2x = 22.5 \\

x = \dfrac{{22.5}}{2} \\

x = 11.25 \\

$

Also, $x + y = 20$

$

11.25 + y = 20 \\

y = 20 - 11.25 = 8.75 \\

$

The required numbers are $11.25$ and $8.75$

Their ratio$ = \dfrac{x}{y} = \dfrac{{11.25}}{{8.75}} = \dfrac{9}{7}$

Hence the ratio of the numbers is $9:7$.

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