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The sum of the present ages of a father and son is 52 years. Four years hence, the son's age will be $$\frac{1}{4}$$ that of the father. What will be the ratio of the ages of the son and father, 10 years from now?
Answer & Solution
Correct Answer:
Option
C
\[\begin{array}{*{20}{c}}
{{\text{After four years}} \to }&{{\text{Father}}}&:&{{\text{Son}}} \\
{}&4&:&1
\end{array}\]
Four years ago → 4x - 4, x - 4
4x - 4 + x - 4 = 52
5x - 8 = 52
x = 12
\[\begin{array}{*{20}{c}} {{\text{Present age}} \to }&{{\text{Father}}}&:&{{\text{Son}}} \\ {}&{44}&:&8 \\ {{\text{After 10 years}} \to }&{{\text{Father}}}&:&{{\text{Son}}} \\ {}&{54}&:&{18} \\ {}&3&:&1 \end{array}\]
Four years ago → 4x - 4, x - 4
4x - 4 + x - 4 = 52
5x - 8 = 52
x = 12
\[\begin{array}{*{20}{c}} {{\text{Present age}} \to }&{{\text{Father}}}&:&{{\text{Son}}} \\ {}&{44}&:&8 \\ {{\text{After 10 years}} \to }&{{\text{Father}}}&:&{{\text{Son}}} \\ {}&{54}&:&{18} \\ {}&3&:&1 \end{array}\]
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