Question

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

Answer 1

Answer:

The numbers are 8 and 12

Step-by-step explanation:

Given :

• The ratio of two numbers 2:3

• If two is subtracted from the first number and 8 from the second the ratio becomes the reciprocal of the original ratio

To find :

the numbers

Solution :

Let the two numbers be 2x and 3x

first number = 2x

second number = 3x

If two is subtracted from the first number,

 the first number becomes = 2x - 2

If 8 is subtracted from the second number,

 the second number becomes = 3x - 8

The new ratio = reciprocal of the original ratio

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

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

4x - 4 = 9x - 24

9x - 4x = 24 - 4

 5x = 20

  x = 20/5

  x = 4

The first number = 2(4) = 8

The second number = 3(4) = 12

Answer 2

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$\huge\bf{Solution:-}$

Given That:

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

We need to find the numbers

Solution

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

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