Question

After $12$ years, Pravallika will be $3$ times as old as she was $4$ years ago. What is the present age of her?
A. $16{\text{ years}}$
B. $15{\text{ years}}$
C. $14{\text{ years}}$
D. $12{\text{ years}}$

Answer 1

Here we will solve this question by assuming the ages of a person by applying a rule that if a person’s present age is $x$ then after $n$ the number of years, that person’s age will be $x + n$. Also, before $n$ the number of years the age will be $x - n$.

Complete step-by-step answer:
Step 1: Assume that the present age of Pravallika is $a$ years. So her age after $12$ years will be $a + 12$ and before $4$ years was $a - 4$. So, as given in the question that after $12$ years she will be three times as old as she was $4$ years ago, so we get the below equation: $a + 12 = 3\left( {a - 4} \right)$
Step 2: By doing the multiplication in the RHS side of the equation
$a + 12 = 3\left( {a - 4} \right)$ we get:
$\Rightarrow a + 12 = 3a - 12$
By bringing $3a$ into the LHS side and $12$ on the RHS side of the above equation we get:
$\Rightarrow a - 3a = - 12 - 12$
By doing the simple addition and subtraction on both sides of the above equation we get:
$\Rightarrow - 2a = - 24$
By eliminating the negative symbol from both sides we get:
$\Rightarrow 2a = 24$
By bringing
$2$ into the RHS side of the above equation and after dividing we get:
$\Rightarrow a = 12$

$\because$ The present age of Pravallika is $12$ years. So, option D is correct.

Note:
Students needs to remember some important formulas for solving these types of questions:
If you are assuming the present age of a person as $x$then his age after $n$years will be $x + n$ years. If you are assuming the present age of a person as $x$then his age before $n$years will be $x - n$ years. If you are assuming the present age of a person $x$, then $n$times of present age will be $nx$ years. If you are assuming the present age of a person $x$, then $\dfrac{1}{n}$ his present age will be $\dfrac{x}{n}$ years.