Question

Which number when added to each of the numbers 24, 32 and 42 would make the sums to be in continued proportion?

• A. $8$
• B. $5$
• C. $10$
• D. $6$

Answer 1

The correct option is A $8$

Let the number to be added is $x$

$\Rightarrow 24+x,32+x$ and $42+x$ are in continued proportion.

$\therefore \frac{24+x}{32+x}=\frac{32+x}{42+x}$

$\Rightarrow \frac{x+24}{x+32}=\frac{x+32}{x+42}$

$\Rightarrow (x+24)(x+42)=(x+32)(x+32)$

$\Rightarrow x(x+42)+24(x+42)={(x+32)}^2$

$\Rightarrow x^2+42x+24x+1,008‬=x^2+64x+1,024‬$

$\Rightarrow 66x+1,008‬-64x-1,024=0‬$

$\Rightarrow 2x-16‬=0‬$

$\Rightarrow 2(x-8)‬=0‬$

$\Rightarrow x-8‬=0‬$

$\therefore x=8$

Hence $8$ has to be added to make the sum to be in continued proportion.