NIMCET 2014 — Reasoning PYQ

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Question

NIMCET 2014 — Reasoning PYQ

NIMCET | Reasoning | 2014

Ajith is three times older than Babita. Chetu is half the age of Das. Babita is older than Chetu. Which of the following additional information is needed to estimate the age of Ajith?

I. Chetu is $10$ yr old.

II. Both Babita and Das are older than Chetu by the same number of years.

Choose the correct answer:

Explanation

Solution

1. Equation Formulation:

Let the ages of Ajith, Babita, Chetu, and Das be $A, B, C,$ and $D$ respectively.

From the question:

$A = 3B$
$C = \frac{1}{2}D$ or $D = 2C$
$B > C$

2. Evaluating Statement I:

$C = 10 \text{ yr}$
Then $D = 2 \times 10 = 20 \text{ yr}$
Since $B > C$ , we only know $B > 10$ .
We cannot find the exact value of $B$ , so $A$ cannot be determined.
Statement I alone is not sufficient.

3. Evaluating Statement II:

Let the "same number of years" be $k$ .
$B = C + k$
$D = C + k$
From the original data, $D = 2C$ .
So, $2C = C + k \Rightarrow C = k$ .
This means $B = C + C = 2C$ .
However, without a numerical value for $C$ , we cannot find $B$ or $A$ .
Statement II alone is not sufficient.

4. Combining I and II:

From Statement I: $C = 10 \text{ yr}$ .
From Statement II: $B = 2C$ (as derived above).
Therefore, $B = 2 \times 10 = 20 \text{ yr}$ .
Now, find Ajith's age: $A = 3B = 3 \times 20 = 60 \text{ yr}$ .
Both statements together are sufficient.

Final Answer: Option 3 is correct.