Question:
Three numbers are in the ratio of 4 : 5 : 6. If the sum of the largest and the smallest equals the sum of the third and 55, find the numbers.
Solution:
Let the common multiple for the given three numbers be $x$.
Then, the three numbers would be $4 \mathrm{x}, 5 \mathrm{x}$ and $6 \mathrm{x}$.
$\therefore 4 x+6 x=5 x+55$
$\Rightarrow 10 x=5 x+55$
$\Rightarrow 10 x-5 x=55$
$\Rightarrow 5 x=55$
$\Rightarrow x=\frac{55}{5}=11$
$\therefore S$ mallest number $=4 \mathrm{x}=4(11)=44$
$L$ argest number is $=6 \mathrm{x}=6(11)=66$
$T$ hird number $=5 \mathrm{x}=5(11)=55$
Therefore, the three numbers are 44,55 and 66 .