Question

The sum of three numbers is $123$. If the ratio between first and second number is $2:5$ and that of between second and third is $3:4$ then find the difference between second and third number.

Answer 1

Let the three numbers be $a$, $b$, and $c$.

Given that

$a:b=2:5$

We can also write it as

$a:b=6:15$

Also second given condition is

$b:c=3:4$

We can also write it as

$b:c=15:20$

Hence from above equations

$a:b:c=6:15:20$

Let us assume that $a=6x$, $b=15x$ and $c=20x$.

Given sum of all the three numbers = $123$

On adding all the three numbers we get,

$a+b+c=123$

$6x+15x+20x=123$

$41x=123$

$x=3$

Hence $a=18$, $b=45$ and $c=60$.

The difference between the second and the third number is $60–45=15$.

Hence, the difference between the second and the third number is $15$.