NIMCET 2009 — Reasoning PYQ

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Question

NIMCET 2009 — Reasoning PYQ

NIMCET | Reasoning | 2009

Reena visited her High School friend, Natasha after their 25th school reunion. “what a nice pair of children you have, are they twins?” Reena asked.
“No my sister is older than I”, said Natasha’s son Rahul. “The square of my age plus the cube of her age is 7148”. “The square of my age plus the cube of his age is 5274”, said Preeti, Natasha;s daughter.
How old were they?

Choose the correct answer:

Explanation

Let the age of Preeti be $P$ and the age of Rahul be $R$ .

Step 1: Formulate the equations from the given statements

From Rahul's statement: "The square of my age plus the cube of her age is 7148."

R^2 + P^3 = 7148 \quad \dots \text{(Equation 1)}

From Preeti's statement: "The square of my age plus the cube of his age is 5274."

P^2 + R^3 = 5274 \quad \dots \text{(Equation 2)}

We are also told that Preeti is older than Rahul ( $P > R$ ).

Step 2: Use the options to find the correct ages

Instead of solving high-degree polynomial equations, we can test the given options in Equation 1.

Testing Option (a): $P = 23, R = 14$

$14^2 + 23^3 = 196 + 12167 = 12363 \neq 7148$
Testing Option (b): $P = 18, R = 16$

$16^2 + 18^3 = 256 + 5832 = 6088 \neq 7148$
Testing Option (d): $P = 19, R = 17$

$17^2 + 19^3 = 289 + 6859 = 7148$

This satisfies Equation 1.

Step 3: Verify Option (d) with Equation 2

Substitute $P = 19$ and $R = 17$ into Equation 2:

19^2 + 17^3 = 361 + 4913 = 5274

This also satisfies Equation 2.

Conclusion:

The ages of Preeti and Rahul are 19 and 17 respectively.

Correct Option: (d)