Decimal from base-5 number – UGC NET Question

For 324₅, the digits correspond to 3×5² + 2×5¹ + 4×5⁰. This evaluates as 3×25 + 2×5 + 4×1 = 75 + 10 + 4 = 89. Hence, the decimal equivalent of 324₅ is 89.

Option A:
Option A correctly uses the powers 25, 5, and 1 for the positions and multiplies by the corresponding digits. The sum 89 matches the structure of 324₅, confirming the validity of the conversion.

Option B:
Option B, 94, would require additional value or a misinterpretation of one digit or weight, and does not equal the evaluated expression.

Option C:
Option C, 86, underestimates the correct value and would arise from a missing or misweighted term in the expansion.

Option D:
Option D, 79, is significantly lower than the correct total and thus does not represent the same base-5 number.