NIMCET 2011 — Reasoning PYQ

1. Define Variables:

Let Pushpa's current age be $P$.

Let Rita's current age be $R$.

2. Formulate Equations:

• From the first statement: "Pushpa is twice as old as Rita was two years ago."

  $$P=2(R-2)\text{— (Eq. 1)}$$
  $$P=2R-4$$

• From the second statement: "The difference between their ages is $2$ years."

  Since Pushpa's age is related to twice of Rita's past age, Pushpa is older.

  $$P-R=2\text{— (Eq. 2)}$$
  $$R=P-2$$

3. Solve the Equations:

Substitute the value of $R$ from (Eq. 2) into (Eq. 1):

4. Verification:

If Pushpa is $8$, Rita is $6$ (difference is $2$).

Two years ago, Rita was $4$.

Pushpa ($8$) is twice Rita's age two years ago ($4$). The condition holds.

Correct Option: (b) $8$ years