Question

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

Answer 1

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

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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

Answer 2

Answer given as an attachment above.

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