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 \[\dfrac{1}{n}\] his present age will be \[\dfrac{x}{n}\] years.