Question

Two numbers are in the ratio 3:5. If 8 is added to cach number , the ratio becomes 23, Find the numbers​

Answer 1

Answer:

$\bf let \: the \: rational \: between \: 2 \:$

$\bf numbers \: be \: x$

$\bf therefore \: </h2><h2>numbers$

$will \: be \: 3x$

$\bf and \: 5x \: and \: </h2><h2>their \: ratio \: 3x:5x$

$\bf if \: 8 \: is \: added \: </h2><h2>to \: both \: the \:$

$\bf numbers the \: ratio \: becomes \: 2:3$

$⇒(3x + 8) : (5x + 8) \: = \: 2:3$

$⇒\frac{3x + 8}{5x + 8} = \frac{2}{3}$

$\bf by \: cross \:$

$\bf multiplication$

$⇒2(5x + 8) = 3(3x + 8)$

$⇒10x + 16 = 9x + 24$

$⇒10x - 9x = 24 - 16$

$⇒x = 8$

$\bf thus$

$\bf the \: two \: </h2><h2>numbers \: are \:$

$⇒3x = 3 \times 8$

$⇒3x = 24$

$⇒5x = 5 \times 8$

$⇒5x = 40$

$\therefore therefore$

$\bf the \: larger \: </h2><h2>number \: is \: 40$

Answer 2

Answer:

➤Let the rational numbers between two numbers be x

⇰Then:-

• The numbers will be 3x and 5x and their ratio becomes 2:3.

➠$(3x + 8) \: (5x + 8) = 2 \: 3$

➠$\frac{(3x + 8)}{(5x + 8)} = \frac{2}{3}$

➤By cross multiplication

⇒2 (5x + 8) = 3 (3x + 8)

⇒10x + 16 = 9x + 24

⇒10x - 9x = 24 - 16

⇒x = 8

$\therefore therefore$

⇨The two numbers are 3x = 3 × 8

⇨24

And

⇨5x = 5 × 8

⇨40

HOPE IT HELPS YOU...☺