Let 'x' represent the number of ₹1 coins and 'y' represent the number of ₹2 coins.

Based on the problem statement, two linear equations can be formulated:

To solve this system of equations:

From the first equation, express x in terms of y: x = 50 - y
Substitute this expression for x into the second equation: 1(50 - y) + 2y = 75
Simplify and solve for y: 50 - y + 2y = 75 which simplifies to 50 + y = 75. Therefore, y = 75 - 50 = 25.
Substitute the value of y back into the expression for x: x = 50 - 25 = 25.

Thus, the number of ₹1 coins is 25, and the number of ₹2 coins is 25. This matches option 4.

The other options do not satisfy both conditions (total number of coins = 50 and total amount = ₹75).

Option 1 (15 and 35):
- Total coins: 15 + 35 = 50 (Satisfied)
- Total amount: 1 * 15 + 2 * 35 = 15 + 70 = 85 (Does not equal ₹75)
Option 2 (35 and 15):
- Total coins: 35 + 15 = 50 (Satisfied)
- Total amount: 1 * 35 + 2 * 15 = 35 + 30 = 65 (Does not equal ₹75)
Option 3 (30 and 20):
- Total coins: 30 + 20 = 50 (Satisfied)
- Total amount: 1 * 30 + 2 * 20 = 30 + 40 = 70 (Does not equal ₹75)