Three numbers are in the ratio of 4 : 5 : 6.

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 .

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