Question

What is the least number that must be subtracted from each of the numbers $14,17,34$ and $42$ so that the remainders may be proportional?

• A. $0$
• B. $1$
• C. $2$
• D. $7$

Answer 1

The correct option is C $2$

Let the required number be $x.$
Then $(14-x):(17-x)::(34-x):(42-x)$

$\therefore \frac{14-x}{17-x}=\frac{34-x}{42-x}$

$\Rightarrow$ $(14-x)(42-x)=(17-x)(34-x)$
$\Rightarrow x^2-56x+588=x^2-51x+578$
$\Rightarrow 5x=10$ $\to x=2$
$\therefore$ Required number $=2$