Question

Two numbers are in the ratio 5:6. If 6 is subtracted from each, the
the ratio becomes 2:3. Find the numbers.

Answer 1

Let the numbers be 5x and 6x respectively

and the resultant numbers be 2x and 3x Respectively .

Now , According to question ,

(5x-6)/(6x-6) = 2x/3x

=> (5x-6) × 3x = 2x × (6x-6)

=> 15x² - 18x = 12x² - 12x

=> 15x² - 12x² - 18x + 12x = 0

=> 3x² - 6x = 0

=> 3x ( x - 2 ) = 0

therefore , 3x = 0 , or , (x-2) = 0

=> x = 0 and x = 2

but , if x = 0 , the fraction would become 0/0 , which is an indeterminable form .

So , x ≠ 0

=> x = 2

Now , the numbers are , 5x = 5(2) = 10

and 6x = 6(2) = 12

Hope this helps !

Answer 2

Let the no. be 5x and 6x
According the question
5x-6/6x-6= 2/3
3(5x-6)=2(6x-6)
15x-18=12x-12
-18+12=12x-15x
-6=-3x
-6/-3=x
2=x
then the no. will be 5×2=10
6×2=12