NIMCET 2007 — Reasoning PYQ

1. Formulating the Variables

Let us define the current ages of both individuals to form our algebraic equations:

• Let the present age of Mona be $M$ years.

• Let the present age of Radha be $R$ years.

2. Setting Up Equations Based on Given Conditions

• Condition 1: "$6$ years ago, Mona was $3$ times as old as Radha"

  Six years ago, their ages were $(M-6)$ and $(R-6)$ respectively.

  $$(M-6)=3(R-6)$$

  $$M-6=3R-18$$

  $$M=3R-18+6$$

  $$M=3R-12\text{— (Equation 1)}$$

• Condition 2: "After $6$ years, Mona will be $5/3$ times as old as Radha"

  Six years from now, their ages will be $(M+6)$ and $(R+6)$ respectively.

  $$(M+6)=\frac{5}{3}(R+6)$$

  Multiply both sides by $3$ to eliminate the fraction:

  $$3(M+6)=5(R+6)$$

  $$3M+18=5R+30\text{— (Equation 2)}$$

3. Solving the System of Equations

Now, substitute the value of $M$ from Equation 1 into Equation 2:

$$3(3R-12)+18=5R+30$$

$$9R-36+18=5R+30$$

$$9R-18=5R+30$$

Rearrange the terms to solve for $R$ by bringing all variables to one side and constants to the other:

$$9R-5R=30+18$$

$$4R=48$$

$$R=\frac{48}{4}$$

$$R=12$$

Final Answer

The present age of Radha is $12$ years.

Therefore, the correct option is (b).