40% discount is offered on an item. By applying a promo code the customer wins 10% cash back. What is the effective discount ?

Options

A. 50.6 per cent
B. 46 per cent
C. 50 per cent
D. 14 per cent

Answer

To find the effective discount when a 40% discount is offered on an item and a 10% cash back is received, we can use the formula for effective discount:

**Effective Discount Formula:**
\[ \text{Effective Discount} = d_1 + d_2 - \left( \frac{d_1 \times d_2}{100} \right) \]

Where:
- \( d_1 \) is the first discount (40% in this case)
- \( d_2 \) is the second discount (10% cash back in this case)

**Step 1: Identify the discounts**
- \( d_1 = 40\% \)
- \( d_2 = 10\% \)

**Step 2: Substitute the values into the formula**
\[ \text{Effective Discount} = 40 + 10 - \left( \frac{40 \times 10}{100} \right) \]

**Step 3: Calculate the product \( d_1 \times d_2 \)**
- \( 40 \times 10 = 400 \)

**Step 4: Divide by 100 to find the percentage**
- \( \frac{400}{100} = 4 \)

**Step 5: Substitute back into the formula**
\[ \text{Effective Discount} = 40 + 10 - 4 \]

**Step 6: Perform the addition and subtraction**
- \( 40 + 10 = 50 \)
- \( 50 - 4 = 46 \)

**Final Answer:**
The effective discount is **46%**.

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