Question

Which number should be subtracted from each of the numbers 13, 25 and 55 so that the resulting numbers would be in continued proportion.

• A. $4$
• B. $5$
• C. $12$
• D. $10$

Answer 1

The correct option is B $5$

Let the number to be subtracted be $a$.
So, $13-a,25-a,55-a$ are in continued proportion.
If $a:b::b:c$, then we say that $a,b,c$ are in continued proportion, and c is the third proportional of a and b.
Here, $b^2=ac$
$=>{(25-a)}^2=(13-a)\times (55-a)$
$a^2-50a+625=a^2-68a+715$

$-50a+625=-68a+715$

$18a=90$

$a=5$

Hence, $5$ needs to be subtracted from $13,25,55$ such that they are in continued proportion.