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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
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B
23
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C
12
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D
1
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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 $$bc=2x$$
$$\therefore  2x = 2y$$
$$\therefore  x = y$$
$$\cfrac { c-a }{ d-b } =\cfrac { 2x+x }{ y+2x } =\cfrac { 3x }{ 3x } =1$$

983325_1038230_ans_9f9caff37c0f4056addc66883f923971.png

Mathematics

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