Marked price of an item is Rs 400. On purchase of 1 item discount is 6% and on purchase of 4 items discount is 24% Rachita buys 5 items. What is the effice discount ?

Options

A. 0.34
B. 0.204
C. 0.128
D. 0.2325

Answer

To find the effective discount when Rachita buys 5 items, we will follow these steps:

### Step 1: Calculate the discount on the first item
The marked price (MP) of one item is Rs 400. The discount on purchasing one item is 6%.

\[ \text{Discount on 1 item} = \text{MP} \times \left(\frac{\text{Discount Percentage}}{100}\right) = 400 \times \left(\frac{6}{100}\right) = 24 \text{ Rs} \]

### Step 2: Calculate the discount on the four items
When purchasing four items, the discount is 24%.

\[ \text{Total MP for 4 items} = 4 \times \text{MP} = 4 \times 400 = 1600 \text{ Rs} \]

\[ \text{Discount on 4 items} = 1600 \times \left(\frac{24}{100}\right) = 384 \text{ Rs} \]

### Step 3: Calculate the total discount for 5 items
Now, we need to find the total discount when Rachita buys 5 items (1 item with 6% discount and 4 items with 24% discount).

\[ \text{Total Discount} = \text{Discount on 1 item} + \text{Discount on 4 items} = 24 + 384 = 408 \text{ Rs} \]

### Step 4: Calculate the total marked price for 5 items
The total marked price for 5 items is:

\[ \text{Total MP for 5 items} = 5 \times \text{MP} = 5 \times 400 = 2000 \text{ Rs} \]

### Step 5: Calculate the effective discount percentage
To find the effective discount percentage, we use the formula:

\[ \text{Effective Discount Percentage} = \left(\frac{\text{Total Discount}}{\text{Total MP}}\right) \times 100 \]

Substituting the values:

\[ \text{Effective Discount Percentage} = \left(\frac{408}{2000}\right) \times 100 = 20.4\% \]

### Step 6: Convert the effective discount percentage to decimal form
To express the effective discount as a decimal:

\[ \text{Effective Discount in Decimal} = \frac{20.4}{100} = 0.204 \]

### Final Answer
The effective discount when Rachita buys 5 items is **0.204**.

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