Question

If two numbers are in the ratio 10 : 13 and their difference is 33, what are the two numbers?​

Answer 1

Given data:

The Ratio of two numbers $\frac xy=10: 13$

Difference of two numbers =  $33$

To find:

$X = ?$

$Y = ?$

Explanation:

• The ratio is the kind of fraction of the whole number over the other whole number.
• The ratio can be simplified by dividing the value of both the numerator and the denominator by a larger factor.
• It indicates how many times one number has another number. to find the ratio add the ratio, find the value of each part, and multiply each part.

let assume the numbers are  $\frac xy\;=\frac{10}{13}$

then, $13x = 10y$

or $13x -10y = 0$ $\rightarrow equ\;1$

and  $x-y = 33$  $\rightarrow equ\;2$

multiplying the value $10$ in $equ\;2$

$10x-10y\;=\;330$ $\rightarrow equ\;3$

By equating the values of $\;equ\;3\;by\;equ\;1$

$\underline{\underset{\underset-\;13x\;\;\;\underset+-\;\;\;10y\;\;=\underset-\;\;\;0}{10x-10y=330}}\\\;\;-3x\;+\;o\;=\;330$

$-3x=330\\\\\\boxed{x=110}$

then for y

$13x=10y$

substitute the value of $x$ in the equation

$13(110)=10y\\y= 143$

Therefore the two numbers are $X = 110 , Y = 143$

Answer 2

Given,

Two numbers are in the ratio $10: 13$ and their difference is $33$.

We have to find the two numbers

Let, first number be $10x$ and second number be $13x$

According to the question,

The difference between the two numbers is $33$

Second number $-$ first number $=33$

$13x-10x=33$

Simplify the above expression, we get

$3x=33$

$x=11$

Substitute $x=11$ in two numbers

$10x=10\times11\\=110$

$13x=13\times11=143$

Therefore, the two numbers are $110$ and $143$.