# Which number must be added to each term of the ratio 5 : 12, so that the ratio becomes 2 : 3?

• September 26, 2020

Terms are in the ratio 5 : 12,  Number that must be added to each term of the ratio 5: 12, so that the ratio becomes 2 : 3

At first, numbers are in the ratio 5 : 12.

Now,

Let the number which must be added to this ratio to make it equal to 2 : 3 = x

Then, below proportion is true

(5 + x) : (12 + x) :: 2 : 3

So, using the below property of proportion we can find the value of a.

Product of extremes = Product of means

(5 + x) times 3 = (12 + x) times 2

15+ 3x = 24 + 2x

3x-2x=24-15

x = 9

So, 9 must be added to each term of the ratio 5 : 12, so that the ratio becomes 2 : 3.

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