Question

The ratio of two numbers is $5:4$ and their sum is $54$. The greater of the two numbers is

• A. $36$
• B. $24$
• C. $30$
• D. None of these

Answer 1

The correct option is C $30$

Let the number be $x$ and $y$

From the given data,

$x+y=54$

$x:y=5:4$

$\frac{x}{y}=\frac{5}{4}$

$4x=5y$

$4x-5y=0$

$x+y=54-------\times 5$

$4x-5y=0$

$5x+5y=270$

$9x=270$

$x=\frac{270}{9}$

$x=30$

$30+y=54$

$y=24$

The greatest number is $30$