25% of what amount equals 12 1/2% of ₹ 180? Find the amount.

Introduction / Context:
Here we equate two percentages of different bases. Converting the verbal statement into an equation allows solving for the unknown base amount directly.

Given Data / Assumptions:

• x is the unknown amount.
• 25% of x = 12.5% of 180.
• Percentages are standard base-100 rates.

Concept / Approach:
Write 25% as 0.25 and 12.5% as 0.125. Set 0.25x = 0.125 * 180 and solve for x. Using fractions (1/4 and 1/8) is another quick method.

Step-by-Step Solution:
0.25x = 0.125 * 1800.125 * 180 = 22.50.25x = 22.5 ⇒ x = 22.5 / 0.25 = 90

Verification / Alternative check:
Compute both sides at x = 90: 25% of 90 = 22.5; 12.5% of 180 = 22.5. Equality holds.

Why Other Options Are Wrong:
₹ 80 and ₹ 75 give too small a 25%; ₹ 120 gives 30, which is too large; ₹ 100 gives 25, not 22.5.

Common Pitfalls:
Interpreting “12 1/2 of ₹ 180” without the percent; in standard aptitude, it denotes 12.5% unless otherwise stated.

Final Answer:
₹ 90