Question

Two years ago, the age of a father was three and a half times the age
daughter then. Six years hence, the age of father will be ten years more than twice
the age of his daughter then. Find their present ages.
(1) Let the present age of the father be x years and that of his daughter be y years.
(2) Form two equations from the given conditions.
(3) Solve the equations and find the ​

Answer 1

Answer:  The required present ages of the father and daughter are 16 years and  years respectively.

Step-by-step explanation:  Given that two hen. Six years hence, the age of father will be ten years more than twice  the age of his daughter then.

We are to find the present ages of the father and daughter.

Let x yrs and y yrs represents the present ages of the father and daughter respectively.

Then, according to the given information, the system of equations can be written as :

$x-2=3\frac{1}{2}(y-2)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x+6=y+6+10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equation (ii), we have  

$x+6=y+6+10\\\\\Rightarrow x=y+10~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)$

Substituting the value of x from equation (iii) in equation (i), we get

$y+10-2=\dfrac{7}{2}(y-2)\\\\\Rightarrow 2(y+8)=7(y-2)\\\\\Rightarrow 2y+16=7y-14\\\\\Rightarrow 7y-2y=16+14\\\\\Rightarrow 5y=30\\\\\Rightarrow y=6.$

From equation (iii), we get

$x=6+10=16.$

Thus, the required present ages of the father and daughter are 16 years and  years respectively.