Question

two numbers are in the ratio 3 is to 5. if 9 is subtracted from each the new numbers are in the ratio of 12 to 23. find the smallest number ​

Answer 1

$\sf{\large{\underline{\pink{Question:-}}}}$

Two numbers are in the ratio 3 is to 5. if 9 is subtracted from each the new numbers are in the ratio of 12 to 23. find the smallest number.

$\sf{\large{\underline{\blue{Answer:-}}}}$

➠ $\bf{\red{Ratio \:of \:original\: numbers\: =\: 3 \::\: 5 }}$

Let the numbers be 3x and 5x

$\sf{\underline{\orange{Subtracting\: 9 \:from \:each\: number:}}}$

• 3x - 9
• 5x - 9

➠ $\red{\bf{Ratio \:of \:new \:numbers\: =\: 12\: :\: 23}}$

$\bold{\underline{A/q}}$

$\frac{3x - 9}{5x - 9} = \frac{12}{23}$

$⟶$ 23(3x - 9) = 12(5x - 9)

$⟶$ 69x - 207 = 60x - 108

$⟶$ 69x - 60x = 207 - 108

$⟶$ 9x = 99

$⟶$ x = 99/9

$⟶$ x = 11

➠$\green{\bf{Original \:numbers:}}$

• 3x = 3 * 11 = 33
• 5x = 5 * 11 = 55

33 < 55

$\sf{\red{\boxed{\boxed{Smallest\:number\:=\:33}}}}$