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."
From Preeti's statement: "The square of my age plus the cube of his age is 5274."
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.
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Testing Option (a): P=23,R=14
142+233=196+12167=12363=7148
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Testing Option (b): P=18,R=16
162+183=256+5832=6088=7148
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Testing Option (d): P=19,R=17
This satisfies Equation 1.
Step 3: Verify Option (d) with Equation 2
Substitute P=19 and R=17 into Equation 2:
This also satisfies Equation 2.
Conclusion:
The ages of Preeti and Rahul are 19 and 17 respectively.
Correct Option: (d)
