What will come in the place of lsquo rsquo in the following question 125 times 55 5 times 25 2 ........

What will come in the place of ‘?’ in the following question?

125 × 5⁵ = 5^? × (25)²

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RRB Clerk Prelims (13 Aug, 2022 Shift 1)

-4

None of these

To find the value that replaces '?', let's solve the equation step-by-step:

- The given equation is $ 125 \times 5^5 = 5^? \times (25)^2 $.

- Rewrite 125 as $ 5^3 $ since $ 125 = 5 \times 5 \times 5 $.

- Rewrite 25 as $ 5^2 $. Thus, $(25)^2 = (5^2)^2 = 5^4$.

- Substitute these values into the equation:

$$ 5^3 \times 5^5 = 5^? \times 5^4 $$.

- Simplify the left side:

$$ 5^{3+5} = 5^8 $$.

- Simplifying further:

$$ 5^8 = 5^? \times 5^4 $$.

- According to properties of exponents:

$$ 5^8 = 5^{?+4} $$.

- Therefore, $ ?+4 = 8 $. Solving for '?':

$$ ? = 4 $$.

- Correct Answer: Option 4, 4

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