Equal count of three note types: A man has ₹480 in ₹1, ₹5, and ₹10 notes. The count of notes of each denomination is equal. What is the total number of notes he has?

Introduction / Context:
This is a neat arithmetic application of equal counts across denominations. The total value is a simple multiple of the sum of the denominations, scaled by the common count. We then multiply by three to get the total number of notes.

Given Data / Assumptions:

• Total money = ₹480.
• Denominations: ₹1, ₹5, ₹10.
• Let n be the equal count for each denomination.

Concept / Approach:
Total value = n*(1 + 5 + 10) = 16n. Solve 16n = 480, then compute total notes = 3n. This linear setup avoids any need for trial and error.

Step-by-Step Solution:

Verification / Alternative check:
Compute value by denomination: 30*₹1 + 30*₹5 + 30*₹10 = ₹30 + ₹150 + ₹300 = ₹480, exactly the given total.

Why Other Options Are Wrong:

• 45, 60, 75, 120: Do not correspond to 3n with n an integer satisfying 16n = 480.

Common Pitfalls:
Confusing equal value with equal count, or summing denominations incorrectly (1 + 5 + 10 = 16, not 15).

Final Answer:
90