10 years ago father was seven times as old as his son. 2 years hence his age will be equal to five times his son. What is the present age of son?
Explanation
Let present care or father and son be \(x\) and 7 Son yrs ago \(=x-10\)ather ago \(y=10\), but father is 7 time older \(\Rightarrow(y\)
\(=10)=7(x-10)\)
\(\Rightarrow y-10=7 x-70\)
\(\Rightarrow \quad \mathrm{y}-7 \mathrm{x}=-60 \ldots \ldots1.\)lso \(2(y+2)=5(x+2)\)
\(\Rightarrow 2 y+4=5 x+10 \Rightarrow 2 y+5 x=6 \ldots\) 2.
Solving eqn 1. and 2. with substitution mtd
\(\mathrm{Y}=7 \mathrm{x}=-60 \ldots \ldots . .(\mathrm{i})\)
\(2 y+5 x=6 \ldots \ldots . .\) (ii)
\(y=60+7 x\)
substituting for \(y\)
from eqn (ii) \(2(-60+7 x)+5 x-6\)
\(\Rightarrow 12 x=126, x=\frac{126}{12}=14 y T \quad \Rightarrow B\)