Question

If the difference between two numbers is 48 and one number is five times the other then find the numbers

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{The difference between two numbers is 48 and one number}$
$\textsf{is five times the other}$

$\underline{\textbf{To find:}}$

$\textsf{The two numbers}$

$\underline{\textbf{Solution:}}$

$\textsf{Let the two numbers be x and y}\;\mathsf{(x\,>\,y)}$

$\textsf{As per given data,}$

$\mathsf{x-y=48\;\;\;\&\;\;\;x=5y}$

$\implies\mathsf{5y-y=48}$

$\implies\mathsf{4y=48}$

$\implies\mathsf{y=\dfrac{48}{4}}$

$\implies\boxed{\mathsf{y=12}}$

$\mathsf{Now,}$

$\mathsf{x-y=48}$

$\implies\mathsf{x-12=48}$

$\implies\mathsf{x=48+12}$

$\implies\boxed{\mathsf{x=60}}$

$\therefore\textbf{The required two numbers are 60 and 12}$