What should be added to each term of the ratio 7:13 so that their ratio becomes 2:3?

Given:

Terms are in the ratio 7:13.

To find: 

We have to find the number that must be added to each term of the ratio 7:13 so that the ratio becomes 2:3.

Solution:

At first, the numbers are in the ratio 7:13.

Now,

Let the number that must be added to this ratio to make it equal to 2:3 be $a$.

Then, below proportion is true

(7 $+$ a) : (13 $+$ a) :: 2 : 3

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

Product of extremes $=$ Product of means

(7 $+$ a) $\times$ 3 = (13 $+$ a) $\times$ 2

21 $+$ 3a = 26 $+$ 2a

3a $-$ 2a = 26 $-$ 21

a = 5

So, 5 must be added to each term of the ratio 7:13, so that the ratio becomes 2:3. 

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Updated on: 10-Oct-2022

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