Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# Two numbers are in ratio $5:3$ . If they differ by $18$ . What are the numbers?

Last updated date: 18th Sep 2024
Total views: 431.1k
Views today: 8.31k
Verified
431.1k+ views
Hint: If a ratio of two numbers is given as $x:y$ then it can also be written in terms of fraction as $\dfrac{x}{y}$ . We can write the numbers as $xk$ and $yk$ , where $k$ is constant which is common to both numbers when the ratio $x:y$ is given.

The given ratio of two numbers is $5:3$ and difference between these two numbers is $18$
Let us consider two numbers are $x\& y$
The ratio of these number can be written as,
$\dfrac{x}{y} = \dfrac{5}{3}$
Then it can further simplified as,
$x = \dfrac{5}{3}y$ ….. (1)
The difference between these two numbers is given,
$x - y = 18$ ….. (2)
Put the value of $x$ from the equation $\left( 1 \right)$ in equation $\left( 2 \right)$ we have
$x - y = 18$
$\dfrac{5}{3}y - y = 18$
Further it can be simplified then we have,
$\dfrac{2}{3}y = 18 \Rightarrow y = 27$
Substituting the value of $y$ in equation $\left( 2 \right)$we have
$x - y = 18 \\ x - 27 = 18 \Rightarrow x = 45 \\$
Note: We can do this problem in an indifferent way which by considering numbers as $xk$ & $yk$ and putting these values in another equation and finding the value of $k$ then we can find numbers. Avoid any type of calculation mistake.