Haryana Police Constable Model Paper 8

Given:
Sum of the ages of a mother and daughter $=56$ years.
The age of the mother will be three times that of her daughter's.
Concept Used:
Linear equation is used.
Calculation:
Let the mother's age be ' $\mathrm{x}$ ' years.
So, Daughter's age $=56-\mathrm{x}$.
After four years,
Mother's age $=\left(\mathrm{x}+4\right)$ years
Daughter's age $=56-\mathrm{x}+4=\left(60-\mathrm{x}\right)$ years
According to the question,
$\left(\mathrm{x}+4\right)=3\left(60-\mathrm{x}\right)$
$\Rightarrow \mathrm{x}+4=180-3\mathrm{x}$
$\Rightarrow 4\mathrm{x}=176$
$\Rightarrow \mathrm{x}=44$
Mother's age $=\mathrm{x}=44$ years.
Daughter's age $=56-\mathrm{x}=56-44=12$ years
∴ Their respective ages are $44$ years and $12$ years.