Question

031. Three numbers are in the ratio 4:5:6. If the sum of the largest and the smallest number equals to the sum of the third number and
55. find the numbers.​

Answer 1

$\large\underline\blue{\bold{Given - }}$

• Three numbers are in the ratio 4:5:6

• The sum of the largest and the smallest number equals to the sum of the third number and 55.

$\large\underline\blue{\bold{To\:Find:-}}$

• The three numbers

$\large\underline{\bold{Solution :- }}$

$\begin{gathered}\begin{gathered}\bf \: Let \: the \: numbers\: be - \begin{cases} &\sf{4x} \\ &\sf{5x}\\ &\sf{6x} \end{cases}\end{gathered}\end{gathered}$

So,

$\large \underline{\tt \:{ According \: to \: statement }}$

• The sum of the largest and the smallest number equals to the sum of the third number and 55.

$\rm :\longmapsto\:4x + 6x = 5x + 55$

$\rm :\longmapsto\:10x - 5x = 55$

$\rm :\longmapsto\:5x = 55$

$\rm :\longmapsto\: \boxed{ \bf \: x \: = \: 11}$

$\begin{gathered}\begin{gathered}\bf \:Hence, \: the \: numbers \: are - \begin{cases} &\sf{4x = 4 \times 11 = 44} \\ &\sf{5x = 5 \times 11 = 55}\\ &\sf{6x = 6 \times 11 = 66} \end{cases}\end{gathered}\end{gathered}$