A number is $\dfrac{3}{4}$ of another. Their sum is $42$. The smaller is

A number is $\dfrac{3}{4}$ of another. Their sum is $42$. The smaller is
  1. $18$
  2. $24$
  3. $12$
  4. $30$

Solution

Larger $= x$. $x + \dfrac{3x}{4} = 42 \Rightarrow \dfrac{7x}{4} = 42 \Rightarrow x = 24$. Smaller $= \dfrac{3 \cdot 24}{4} = 18$.

Asked in: IMO

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