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Mathematics

If a carton containing a dozen mirrors is dropped, then which of the following cannot be the ratio of broken mirrors to unbroken mirrors?

  1. 2 : 1

  2. 7 : 5

  3. 3 : 2

  4. 3 : 1

Ratio Proportion

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Answer

Let ratio of broken mirrors to unbroken mirrors = p : q

Number of mirrors in dozen = 12

Number of broken mirrors = pp+q×12\dfrac{p}{p + q} \times 12

Number of broken mirrors = qp+q×12\dfrac{q}{p + q} \times 12

If we consider 3 : 2,

3 + 2 = 5

35×12=7.2\dfrac{3}{5} \times 12 = 7.2

Since 7.2 is not integer. Thus, 3 : 2 is the ratio that cannot exist.

Hence, option 3 is the correct option.

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