Question

5 47. Find a number such that the ratio of 5/2 to that number is the same as the ratio of the number to 5/8​

Answer 1

$•\huge\bigstar{\underline{{\red{A}{\pink{n}{\color{blue}{s}{\color{gold}{w}{\color{aqua}{e}{\color{lime}{r}}}}}}}}}\huge\bigstar•$

s = 45, which answers the question. To check, g = 8s/5 = 8(45)/5 = 360/5 = 72. This checks since 72/45 = 8/5, the correct ratio, and (72 + 8)/(45 - 5) = 80/40 = 2.

Answer 2

ANSWER :-

Let the two numbers be “$\sf x$” for greater and “$\sf y$” for smaller.

We are given,

$\sf \frac{x}{y} = \frac{8}{5} \: or \: x = \frac{8y}{ 5} --\:eq\:(1)$

$\sf and \: \frac{(x + 8)}{(y - 5)} = 2 \: or \: x + 8 = 2y - 10 \: --\:eq\:(2)$

Substituting the value of $\sf x$ from the first equation into the second,

$\sf \frac{8x}{5} + 8 = 2y - 10$

$\sf 8x + 40 = 10y - 50$

So, $\sf 2y = 90$

$\sf \: y = \frac{90}{2}$

$\sf \fbox \pink {y \: = \: 45}$

Now substituting the value of $\sf y$ in equation (1),

$\sf x = \frac{8y}{5}$

$\sf = \frac{8(45)}{5}$

$\sf = \frac{360}{5}$

$\sf \fbox \pink{x \: = \: 72}$

Formula for ratio,

$\sf \fbox {\star Ratio = \frac{x}{y}}$

So, $\sf \frac{72}{45} = \frac{8}{5}$

is the correct ratio as per given in question.