Question

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

• A. $0$
• B. $1$
• C. $2$
• D. $7$

Answer 1

The correct option is C $2$

Let the least number subtracted from each of the numbers $14,17$

$34$ and $42$ be $x$.

$\therefore (14-x)(17-x):(34-x):(42-x)$

$\because$ Product of mean : Product of extream

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

$\Rightarrow 578-17x-34x+x^2=588-14x-42x+x^2\Rightarrow 578-51x=588-56x\Rightarrow -51x+56x=588-578\Rightarrow 5x=10\Rightarrow x=\frac{10}{5}=2$

$\therefore$ number subtracted $:x=2$