Question

If $$a, b, c$$ and $$d$$ are points on a number line such that $$a < b < c < d, b$$ is twice as far from $$c$$ as from $$a,$$ and $$c$$ is twice as far from $$b$$ as from $$d,$$ then what is the value of $$\dfrac{c-a}{d-b}$$ ?

A
13
B
23
C
12
D
1

Solution

The correct option is D $$1$$Let distance between ab be $$x$$$$\therefore$$ distance between $$bc = 2x$$Let distance between $$cd$$ be $$y$$$$\therefore$$ distance between $$bc=2x$$$$\therefore 2x = 2y$$$$\therefore x = y$$$$\cfrac { c-a }{ d-b } =\cfrac { 2x+x }{ y+2x } =\cfrac { 3x }{ 3x } =1$$Mathematics

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