Question

three number are the ratio 4:5:6 if their sum is 45 then the number are
01. 12,15,18
02. 18,15,12
03. 15,18,12
04. 10,17,18​

Answer 1

4+5+6= 15
Then 15 = 45 (given)
=3
12,15,18

Answer 2

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: ANSWER \: \: } \mid}}}}}$

$\: \: \: \: \: \: \: \text{Three number are the ratio 4:5:6. If their} \\ \text{sum is 45, then the number are : - } \\ \\ \mathtt{01) \: 12,15,18 \: \: \: \huge{\underline{ \: \checkmark}}} \\ \\ \mathtt{02) \: 18,15,12} \\ \\ \mathtt{03) \: 15,18,12} \\ \\ \mathtt{04) \: 10,17,18} \: </p><p>$

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$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \text{The ratio of the three numbers is } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{ \text{ \: 4 : 5 : 6 \: }} \\ \\ \text{And,} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \text{Sum of the numbers is = 45} \\ \\ \\ \underline{ \mathfrak{ \: \:Suppose, \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \text{The numbers are : 4x , 5x \: and \: 6x } \\ \: \: \: \: \: \: \: \: \: \: \text{respectively.}</p><p>$

$\underline{ \bold{ \: \: A.T.Q., \: \: }} \\ \\ \: \: \: \: \: \: \: \: \: \: \mathtt{4x + 5x + 6x = 45} \\ \\ \: \: \: \mathtt{\Longrightarrow 15x = 45} \\ \\ \: \: \: \mathtt{ \Longrightarrow x = \frac{45}{15} } \\ \\ \: \: \: \: \: \: \: \mathtt{\therefore \: \: \underline{ \: x = 3 \: }} \\ \\ \\ \: \: \: \: \: \mathtt{\therefore \: \: \: \: 4x = 4 \times 3 = 12} \\ \\ \: \: \: \: \: \: \: \mathtt{ : \rightsquigarrow 5x = 5 \times 3 = 15 }\\ \\ \: \: \: \: \: \: \: \mathtt{ : \rightsquigarrow 6x = 6 \times 3 = 18}$

$\bold{Hence,} \\ \: \: \: \: \: \: \bold{The \: \: three \: \: numbers \: \: are : \red{ \underline{ \: 12, 15,18 \: }}}.$