Question

Rekha is 24 years older than her daughter Ishita. After eight years she will be twice as old as Ishita. Find their present ages

Answer 1

Hint: In this question initially it is said that age of Rekha is 24 year more than the age of Ishita and after 8 years age of Rekha will be double than her daughter age so we will form two equation for both the condition and then we will solve them to find their present ages.

Complete step-by-step answer:
Let the present age of Rekha be x
The present age of her daughter be y
Now since it is said that Rekha is 24 years older than her daughter this means Rekha age more than her daughter age by 24 years hence we can write
  \[x = 24 + y - - (i)\]
Now it is said that after 8 year she will be twice as old as Ishita this means that after 8 year from now the age of Rekha will be double the age of Ishita, hence we can write this as
 \[x + 8 = 2\left( {y + 8} \right) - - (ii)\]
Now we will further solve this equation (ii), hence we get
 \[
  x + 8 = 2y + 16 \\
  x = 2y + 16 - 8 \\
  x = 2y + 8 \;
 \]
Now comparing equation (ii) with equation (i) we get
 \[
  2y + 8 = 24 + y \\
  y = 16 \;
 \]
Now substitute the value of y in the equation (i), hence we get
 \[
  x = 24 + (16) \\
   = 40 \;
 \]
Hence the present age of Rekha is \[x = 40\;years\]
The present age of her daughter Ishita is \[y = 16\;years\]
So, the correct answer is “x=40 years, y=16 years”.

Note: In this type of problems, the key factor is to develop the mathematical equation such that it should satisfy all the given conditions of the problem. Students must note that when we say that x is 6 year older than y this means age of x is more than the age of y by 6 years and when we say 6 year younger this means age x is less than the age of y by 6 years.