Question

9. What number should be added to each of the numbers 12, 22, 42 and 72 so that the resulting numbers may be in proportion?​

Answer 1

Given the four proportional numbers 12:22::42:72

Let x be the number added to each of these numbers, so the new number become

First number =12+x

Second number =22+x

Third number =42+x

Fourth number =72+x

12+x:22+x::42+x:72+x

:72+x(12+x)×(72+x)=(22+x)×(42+x)

12×72+12x+72x+x2=22×42+22x+42x+x2⇒864+8

4x-64x = 924 - 864 = 20x= 60

⇒x=3

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Answer 2

Answer:

2

Let the required number be x then

According to given

Proportion a:b::c:d

Then => a/b = c/d

Applying above rule

=> (12 + x) /(22 + x) = (42 + x) /(72 + x)

By cross multiplication

=> (42 + x) (22 + x) = (72 + x) (12 + x)

=> 924 + x² + 64x = 864 + x² + 84x

=> 30x = 60

=> x = 2

Hence required number is 2