Let's work through the problem step by step.

Given:

Arnil deposited ₹73,000 in the bank. The currency notes are in denominations of ₹10, ₹50, and ₹100. The ratio of these notes is 3:4:5, respectively.

Let:

• The number of ₹10 notes be $3x$,
• The number of ₹50 notes be $4x$,
• The number of ₹100 notes be $5x$.

The total value of these notes must sum to ₹73,000.

Forming the equation:

$(3x \times 10) + (4x \times 50) + (5x \times 100) = 73,000$

Simplify the equation:

$30x + 200x + 500x = 73,000$

$730x = 73,000$

$x = \frac{73,000}{730} = 100$

So, $x = 100$.

Now, let's answer each part of the question:

a) Find the number of ₹10 notes:

The number of ₹10 notes = $3x = 3 \times 100 = 300$.

b) Find the number of ₹50 notes:

The number of ₹50 notes = $4x = 4 \times 100 = 400$.

c) Find the number of ₹100 notes:

The number of ₹100 notes = $5x = 5 \times 100 = 500$.

Final Answers:

• a) The number of ₹10 notes is 300.
• b) The number of ₹50 notes is 400.
• c) The number of ₹100 notes is 500.

Would you like more details or have any further questions?

Here are 5 related questions for further practice:

1. What would be the total deposit if the ratio was 2:3:5 for the same denominations?
2. How much money is held by the ₹50 notes alone?
3. If Arnil deposited ₹85,000 instead with the same ratio, what would be the number of ₹10 notes?
4. How does the ratio affect the total number of notes across different denominations?
5. What if one more denomination of ₹200 was included in the deposit? How would the equations change?

Tip: Always check if the total amount and the ratio match the deposit before solving the system of equations!