What number must be added to each term of the ratio 7 : 12, so that the ratio becomes 4 : 5?

Given: Terms are in the ratio 7 : 12.

To find: Number that must be added to each term of the ratio 7 : 12, so that the ratio becomes 4 : 5.

Solution:

At first numbers are in the ratio 7 : 12.

Now,

Let the number which must be added to this ratio to make it equal to 4 : 5 = a

Then, below proportion is true

(7 $+$ a) : (12 $+$ a) :: 4 : 5

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

Product of extremes = Product of means

(7 $+$ a) $\times$ 5 = (12 $+$ a) $\times$ 4

35 $+$ 5a = 48 $+$ 4a

5a $-$ 4a = 48 $-$ 35

a = 13

So, 13 must be added to each term of the ratio 7 : 12, so that the ratio becomes 4 : 5.

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Updated on: 10-Oct-2022

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