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RRB Group D 1 Dec 2025 Shift 1 Solved Paper

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Question : 48 of 100

Marks: +1, -0

Simplify the following:

\frac{5^{3x+4}+125^{x+1}}{125^{x+1}-5^{3x+2}}

8
7.5
5
10

Solution:

Concept:

Rewrite all terms with base

5

and factor to simplify the fraction.

Explanation:

Write

125

as

5^3

.

Numerator becomes

5^{3x+4} + (5^3)^{x+1} = 5^{3x+4} + 5^{3x+3}

.

Denominator becomes

(5^3)^{x+1} - 5^{3x+2} = 5^{3x+3} - 5^{3x+2}

.

Factor

5^{3x+2}

from both numerator and denominator.

Numerator:

5^{3x+2}(5^2 + 5^1) = 5^{3x+2}(25+5) = 5^{3x+2}\times 30

.

Denominator:

5^{3x+2}(5^1 - 5^0) = 5^{3x+2}(5-1) = 5^{3x+2}\times 4

.

Cancel

5^{3x+2}

.

Result:

\frac{30}{4} = 7.5

.

Answer:

7.5

(Option B).

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