Question

The ratio of two numbers is. If 2 is subtracted from the first and 8 from the second,
the ratio becomes the reciprocal of the original ratio. Find the numbers.
3​

Answer 1

Let us consider the two numbers as x and y respectively

As per the given ratio

x/y=2/3

3x=2y

3x-2y=0—————-(i)

The second condition

(x-2)/(y-8)=3/2

2x-4=3y-24

2x-3y=-20———————-(ii)

Multiplying equation (i) by 2 and (ii) by 3 we get,

6x-4y=0

– 6x+9y=60

¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On solving these equations we get

5y=60

y=12

Now 3x=2y

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

So x = 8 and y =12

So the two numbers are 8 and 12