A shop provides flat 50% discount on one shirt, while another shop provides two successive discounts of 30% and 30%. If the difference in the bill is ₹ 43 , then find the cost of the shirt.

Shop 1 provides a flat 50% discount.

Shop 2 provides two successive discounts of 30% and 30%.

The difference in the bill is ₹43.

Price after a flat discount:
For a flat discount, the final price = $$\text{Cost Price} \times \left(1 - \frac{\text{Discount Percentage}}{100} \right).$$​

For successive discounts, the final price = $$\text{Cost Price} \times (1 - \frac{\text{First Discount}}{100}) \times (1 - \frac{\text{Second Discount}}{100})$$​

The cost of the shirt be x (in ₹).

Final price at Shop 1 = $$x \times (1 - 0.50) = x \times 0.50 = \frac{x}{2}$$​

Final price at Shop 2 = $$x \times (1 - 0.30) \times (1 - 0.30) = x \times 0.70 \times 0.70 = x \times 0.49$$​

Difference between the bill at Shop 1 and Shop 2 is ₹43:

​$$\frac{x}{2} - 0.49x = 43.\frac{x}{2} - 0.49x = 43, \\\frac{x}{2} - \frac{49x}{100} = 43 \\\frac{50x}{100} - \frac{49x}{100} = 43, \\\frac{x}{100} = 43. \\x = 43 \times 100 = ₹4300$$​​

The cost of the shirt is ₹4,300