Question

Which number should be added to each of the numbers 1, 9, 13 and 45 so that the resulting numbers would be in proportion.

Answer 1

Let the number to be added be $a$
So, $1+a,9+a,13+a$ and $45+a$ are in proportion.
$=>1+a:9+a::13+a:45+a$
Applying the rule product of extremes $=$ product of means

$(1+a)\times (45+a)=(9+a)\times (13+a)$
$a^2+46a+45=a^2+22a+117$

$46a+45=22a+117$

$24a=72$

$a=3$

Hence, $3$ needs to be added to $1,9,13$ and $45$, such that they are in proportion.