Mukesh got series of discount 30%, 25%, 15% on his shirt. Find out the single equivalent discount.
A. 52.34%
B. 38.35%
C. 55.38%
D. 57.38%

Options

A. B
B. C
C. D
D. A

Answer

To find the single equivalent discount when Mukesh receives a series of discounts of 30%, 25%, and 15%, we can follow these steps:

### Step 1: Understand the Discounts
When a series of discounts is applied, the final price is calculated based on the remaining amount after each discount is applied sequentially.

### Step 2: Assume an Initial Price
Let’s assume the initial price of the shirt is ₹100. This makes calculations easier since we can directly use percentages.

### Step 3: Apply the First Discount (30%)
The first discount is 30%.
- Amount after the first discount = Initial Price - (30% of Initial Price)
- Amount after the first discount = ₹100 - (30/100 * ₹100) = ₹100 - ₹30 = ₹70

### Step 4: Apply the Second Discount (25%)
Now, we apply the second discount of 25% on the new amount (₹70).
- Amount after the second discount = ₹70 - (25% of ₹70)
- Amount after the second discount = ₹70 - (25/100 * ₹70) = ₹70 - ₹17.5 = ₹52.5

### Step 5: Apply the Third Discount (15%)
Next, we apply the third discount of 15% on the new amount (₹52.5).
- Amount after the third discount = ₹52.5 - (15% of ₹52.5)
- Amount after the third discount = ₹52.5 - (15/100 * ₹52.5) = ₹52.5 - ₹7.875 = ₹44.625

### Step 6: Calculate the Total Discount
Now we need to find out how much discount was applied in total.
- Total discount = Initial Price - Final Amount
- Total discount = ₹100 - ₹44.625 = ₹55.375

### Step 7: Calculate the Equivalent Discount Percentage
To find the equivalent discount percentage, we use the formula:
- Equivalent Discount Percentage = (Total Discount / Initial Price) * 100
- Equivalent Discount Percentage = (₹55.375 / ₹100) * 100 = 55.375%

### Step 8: Round the Result
Rounding off to two decimal places, we get 55.38%.

### Conclusion
Thus, the single equivalent discount is **55.38%**, which corresponds to option **C**.

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