Currency note mix: A man has 170 currency notes consisting of ₹100 and ₹50 denominations totaling ₹10000. How much money is in ₹50 notes?

Introduction / Context:
This is a standard system-of-equations problem involving two denominations. We know the total number of notes and the total value, and we must determine the value tied to one denomination (₹50 notes).

Given Data / Assumptions:

• Total notes = 170
• Denominations: ₹100 and ₹50
• Total value = ₹10000

Concept / Approach:
Let x be the number of ₹100 notes and y be the number of ₹50 notes. Then x + y = 170 and 100x + 50y = 10000. Solve this linear system to find y and compute 50y.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• ₹ 4000: Implies only 80 fifty-rupee notes; would not total ₹10000 with 170 notes.
• ₹ 9000: Exceeds the maximum possible given only 170 notes.
• ₹ 6000: Leads to inconsistent counts with the total number of notes.

Common Pitfalls:

• Forgetting to divide the value equation by 50 to simplify.
• Arithmetic slips when subtracting equations.

Final Answer: