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

Hint: 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 $${\displaystyle \frac{1}{n}}$$ his present age will be $${\displaystyle \frac{x}{n}}$$ years.