Question

The ratio between two numbers is 12: 13. If
each number is reduced by 20, the ratio become 2:3 . Find the number.
(a) 30, 26
(C) 24, 26
(b) 26, 28
(d) 25, 27​

Answer 1

Answer:

Let the ratios be = 12x,13x

$\frac{12x - 20}{13x - 20} = \frac{2}{3} \\ \\ = 3(12x - 20) = 2(13x - 20) \\ \\ = 36x - 60 = 26x - 40 \\ \\ = 36x - 26x = - 40 + 60 \\ \\ 10x = 20 \\ \\ x = \frac{20}{10} \\ \\ x = 10$

So, numbers are -

$\rightarrow$12x=120

$\rightarrow$13x= 130

Answer 2

Answer:

Let the two number be x and y.

So, given

$\frac{x}{y} = \frac{12}{13} \\ 13x = 12y..........i)$

According to question

$\frac{x - 20}{y - 20} = \frac{2}{3} \\ 3(x - 20) = 2(y - 20) \\ 3x - 60 = 2y - 40 \\ 3x - 2y = - 40 + 60 \\ 3x - 2y = 20 \\ 6(3x - 2y) = 6 \times 20 \\ 18x - 12y = 120 \\ by \: equation \: i) \: 13x = 12y \\ \\ subtituting \: value \: we \: get \\ 18x - 13x = 120 \\ 5x = 120 \\ x = 24 \\ now \\ 13x = 12y \\ 13 \times 24 = 12y \\ 312 = 12y \\ y = 26 \\ x = 24 \: \: and \: \: y = 26$

So. Option(C)= 24,26 is correct answer.