Question

two nubers are given in the ratio 5:6 if 7 is subtracted from each of the numbers the ratio becomes 4:5 find the numbers

Answer 1

I hope this answer will help you.

Answer 2

$\sf\underline{Step-by-step \: explanation}$

Let the common number be x

Ratio, before subtracting 7 to each number,

$\dfrac{5x}{6x}$

[m : n = m/n]

$\sf\underline{According \: to \: the \: question...}$

$\dfrac{5x - 7}{6x - 7} \: = \: \dfrac{4}{5}$

● 4(6x - 7) = 5(5x - 7) [Cross multiplication]

● 24x - 28 = 25x - 35

● 24x - 25x = (-35) + 28

● -x = -7

● x = 7 (Minuses cancel each other)

Hence, the numbers are,

● First number, ${\sf{\boxed{\boxed{35}}}}$

[5x = 5×7 = 35]

● Second number, ${\sf{\boxed{\boxed{42}}}}$

[6x = 6×7 = 42]