A jacket is marked at ₹4,000. During a festive sale, it is given two successive discounts of 32% and 22%. What is the final price after both discounts, and what is the effective percentage discount?

The correct option is ₹2,121.6 ; 46.96%.

Step 1: Understand the given data
Marked Price (MP) of the jacket = ₹4,000
First discount (d₁) = 32%
Second discount (d₂) = 22%

Step 2: Calculate the price after the first discount
The price after applying a 32% discount is calculated as:

Price after 1st discount = MP × (1 - d₁/100)

Price after 1st discount = 4000 × (1 - 32/100) = 4000 × 0.68

Price after 1st discount = ₹2,720

Step 3: Calculate the final price after the second discount
Applying a successive discount of 22% on ₹2,720:

Final Price = 2720 × (1 - d₂/100)

Final Price = 2720 × (1 - 22/100) = 2720 × 0.78

Final Price = ₹2,121.6

Step 4: Calculate the effective single percentage discount
The formula for the effective percentage discount of two successive discounts d₁ and d₂ is:

$\text{Effective Discount \%}=d_1+d_2-\frac{d_1\times d_2}{100}$

Substituting the values:

Effective Discount % = 32 + 22 - (32 × 22)/100

Effective Discount % = 54 - 704/100 = 54 - 7.04

Effective Discount % = 46.96%

Conclusion:
The final price of the jacket after both discounts is ₹2,121.6, and the total effective percentage discount is 46.96%.