What least number must be sub tracted from each of the numbers 14 17 34 and 42 so that the re Mainders may be proportional?

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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

  $$7$$

$$ 14-x:17-x=34-x:42-x$$ 

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

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

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

$$\Rightarrow 5x=10$$ 

$$\Rightarrow x=2$$