Question

the ratio of two numbers is 2/3 .if 2 is subtracted from the first and 8 is by second the ratio becomes the reciprocal of the original ratio.find the number

Answer 1

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

Answer 2

Answer:

The first number = 8 and the second number = 12

Step-by-step explanation:

Let the number be x and y

The ratio of the two numbers is given by 2 : 3

⇒ x : y = 2 : 3

$\implies\frac{x}{y}=\frac{2}{3}\\\\\implies 3x-2y =0.....(1)$

If 2 is subtracted from the first and 8 is by second the ratio becomes the reciprocal of the original ratio

$\implies\frac{x-2}{y-8}=\frac{3}{2}\\\\\implies 2x-4=3y-24\\\\\implies 2x-3y=-20......(2)$

Now, solving both the equation (1) and (2). We get,

x = 8 and y = 12

Therefore, The first number = 8 and the second number = 12