Question

What number should be added to each of the numbers 12,22,42 and72 so that the resulting numbers may be in proportion

Answer 1

Answer:

The required number is 3.

Step-by-step explanation:

Given : The numbers 12,22,42 and 72.

To find : What number should be added to each of the numbers 12,22,42 and 72 so that the resulting numbers may be in proportion?

Solution :

Let, x should be added

So, first number= 12+x

Second number =22 + x

Third number = 42 + x.

Forth number = 72 + x.

So to be proportional of these numbers would be in this way

$(12 + x ): ( 22 + x ) :: ( 42 + x ) : ( 72 + x )$

Now, Product of extremes = Product of mean

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

$12\times72 + 12x + 72x + x^2 = 42\times22 + 42x + 22x + x^2$

$864 + 84x + x^2 =924+64x+x^2$

$84x - 64x + x^2- x^2 = 924−864$

$20x=60$

$x=3$

Therefore, The required number is 3.