Question

If the ratio of two numbers is 2:3. If 2 is subtracted from the first number and 8 from the second number then the ratio is the reciprocal of the original ratio. Find the numbers.

Answer 1

Dear Student,

Let the no. Be x and y
x/y=2/3
3x=2y
3x-2y=0..........eq1

Now (x-2)/(y-8)=3/2
2x-4=3y-24
2x-3y=-20..........eq2

Now subtracting 3xeq2 from 2xeq1
6x-4y=0
- 6x+9y=60
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
5y=60
y=12

Now 3x=2y
x=2y/3 =24/3= 8

So x is 8 and y is12

Regards