SSC CPO 2022 PYQ — Question 129

The correct answer is Option 2 i.e. 17.

According to the question,

{(5 × 5 × 5 × 5 × 5 × 5)⁵ × (5 × 5 × 5 × 5 × 5)⁸} ÷ (5 × 5) = (625)^a

⇒ {(5⁶)⁵ × (5⁵)⁸} + (5²) = (625)^a

⇒ {5³⁰ × 5⁴⁰) + (5²) = (5⁴)^a

⇒ {5⁷⁰) + (5²) = 5^4a [a^m × aⁿ = a^{(m + n)}]

⇒ 5⁷⁰/5² = 5^4a

⇒ 5⁶⁸ = 5^4a [a^m/aⁿ = a^{(m - n)}]

Comparing the powers in the above equation

⇒ 68 = 4a

⇒ a = 17

Therefore, the value of a is 17.