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# Two numbers are in the ratio 3:5. If the sum of numbers is 144, then what is the value of the smallest number?${\text{A}}{\text{. 54}} \\ {\text{B}}{\text{. 72}} \\ {\text{C}}{\text{. 90}} \\ {\text{D}}{\text{. 48}} \\$

Last updated date: 15th Mar 2023
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Hint: Here, we will proceed by assuming the two numbers as x and y and then according to the problem statements we will obtain some equations which will be solved by using the substitution method.

Given the sum of the two numbers is 144 i.e., $x + y = 144 \\ \Rightarrow y = 144 - x{\text{ }} \to {\text{(1)}} \\$
Also, the ratio of these two numbers is 3:5 i.e., $\dfrac{x}{y} = \dfrac{3}{5}$
$5x = 3y{\text{ }} \to {\text{(2)}}$
$\Rightarrow 5x = 3\left( {144 - x} \right) \\ \Rightarrow 5x = 432 - 3x \\ \Rightarrow 8x = 432 \\ \Rightarrow x = 54 \\$
$\Rightarrow y = 144 - 54 = 90$