Question

Two numbers are in the ratio of 2 : 3, and if 6 subtracted from each, the remainders are in the ratio of 4 : 9. Find them.

Answer 1

Let the two numbers be:

2x and 3x

After subtracting 6 from each:

`(2x − 6)/(3x − 6) = 4/9`

9(2x − 6) = 4(3x − 6)

18x − 54 = 12x − 24

18x − 12x = −24 + 54

6x = 30

x = `30/6`

x = 5

Calculate the original numbers

First Number = 2x

= 2(5)

= 10

Second Number = 3x

= 3(5)

= 15

The two numbers are 10 and 15.