Question

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

Answer 1

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.

Complete step-by-step answer:
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.