Question

Reena is twice as old as Suneeta. Three years ago she was three times as old as Suneeta. The present age of Reena is.
a) 6
b) 7
c) 8
d) 12

Answer 1

Hint: Suppose the age of Suneeta as a variable and hence find the age of Reena in terms of that variable with the help of the given condition. Now, use the second relation between the ages of Suneeta and Reena to get a mathematical equation in a single variable. Hence, solve it to get the age of Suneeta and Reena.
Complete step-by-step answer:
Let the present age of Suneeta be x years. As it is given in the problem that Reena is twice as old as Suneeta, so Reena should be of 2x years if Suneeta is of x years. Hence, we get
Present age of Reena = 2x years
Present age of Suneeta = x years
Now, the next condition in the problem is given that 3 years ago Reena was as old as Suneeta. So, we can write
Age of Reena 3 years ago = (2x – 3) years.
Age of Suneeta 3 years ago = (x – 3) years.
Now, as it is given that three years ago Reena was three times as old as Suneeta. So, we can write an equation related to their ages before years as
2x – 3 = 3(x – 3)
2x – 3 = 3x - 9
Adding ‘3’ to both sides of the equation, we get
2x – 3 + 3 = 3x – 9 + 3
2x = 3x – 6
Adding 6 to both sides, we get
2x + 6 = 3x – 6 + 6
2x + 6 = 3x
Subtract 2x from both sides of above equation, we get
2x + 6 - 2x = 3x – 2x
6 = x or x = 6
Hence, the present age of Suneeta is 6 years. So, we get
Present age of Reena
$=2x=2\times 6=12$
So option (d) is the correct answer

Note: As we know the problem belongs to a word problem where we need to form mathematical equations with the help of the given question. So, conversion of words to mathematical equations is the key point of the problem. One may assume the age of Reena as x years as well and hence the age of Suneeta will be $\dfrac{x}{2}$ years. So, we can solve it by any approach. Don’t go wrong while writing the equation i.e. 2x – 3 = 3(x – 3) with the help of the second condition in the problem. One may write the equation as 3(2x – 3) = x – 3, which is wrong. So, be careful and don’t get confused by the words.