Question

Two numbers are in the ratio 3 :5.if 9 is subtracted from each, then they are in the ratio of 12 :23.find the second number

Answer 1

Given :

Two numbers are in ratio 3:5

So,

let one number be 3x and second be 5x

Now,

According to the question,

When 9 is subtracted from each number the ratio becomes 12:23

 

To be found :-

The second number

   

So,

here is the equation

 

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

⇒ $\bf 12(5x-9)=23(3x-9)$     [by cross multiplication]

⇒ $\bf 60x - 108 = 69x-207$

⇒ $\bf 207 - 108 = 69x - 60x$  [taking 60x to RHS and -207 to LHS]

⇒ $\bf 99=9x$

⇒ $\bf \frac{99}{9} = x$

∴ the value of x = 11

Now,

One number = 3x = 3 × 11 = 33

second number = 5x = 5 × 11 = 55

Hence

The second number is 55

Answer 2

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

Let the common multiple be x

According to the question,

$\tt\dfrac{3x \: - \: 9}{5x \: - \: 9}$ = $\tt\dfrac{12}{23}$

[m : n = m/n]

Using cross multiplication,

23(3x - 9) = 12(5x - 9)

69x - 207 = 60x - 108

60x - 69x = -207 + 108

-9x = -99

9x = 99 [minuses cancel each other]

x = 11

Hence, the first number will be,

3x = 3 × 11 = 33

The second number will be,

5x = 5 ×11 = 55