Question

What least number 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 $2$

To be in proportion, we subtract $x$ from each number

$14-x:17-x=34-x:42-x$

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

$\Rightarrow (14-x)(42-x)=(34-x)(17-x)$

$\Rightarrow x^2-56x+588=x^2-51x+578$

$\Rightarrow 5x=10$

$\Rightarrow x=2$