On a machine there is 10% trade discount on the marked price of Rs 2,50,000. But the machine is sold at ? 2,16,000 after givinga cash discount. How much is this cash discount (in%)?

Options

A. 5
B. 4
C. 6
D. 7

Answer

To find the cash discount percentage on the machine, we can follow these steps:

### Step 1: Calculate the Trade Discount
The marked price of the machine is Rs. 2,50,000, and there is a trade discount of 10%.

**Formula for Trade Discount:**
\[ \text{Trade Discount} = \text{Marked Price} \times \frac{\text{Trade Discount Percentage}}{100} \]

**Calculation:**
\[ \text{Trade Discount} = 2,50,000 \times \frac{10}{100} = 2,50,000 \times 0.10 = 25,000 \]

### Step 2: Calculate the Selling Price after Trade Discount
To find the selling price after the trade discount, subtract the trade discount from the marked price.

**Formula for Selling Price after Trade Discount:**
\[ \text{Selling Price after Trade Discount} = \text{Marked Price} - \text{Trade Discount} \]

**Calculation:**
\[ \text{Selling Price after Trade Discount} = 2,50,000 - 25,000 = 2,25,000 \]

### Step 3: Calculate the Cash Discount
The machine is sold for Rs. 2,16,000. To find the cash discount, we need to subtract the selling price after the trade discount from the actual selling price.

**Formula for Cash Discount:**
\[ \text{Cash Discount} = \text{Selling Price after Trade Discount} - \text{Selling Price} \]

**Calculation:**
\[ \text{Cash Discount} = 2,25,000 - 2,16,000 = 9,000 \]

### Step 4: Calculate the Cash Discount Percentage
Now, we need to find out what percentage this cash discount is of the selling price after the trade discount.

**Formula for Cash Discount Percentage:**
\[ \text{Cash Discount Percentage} = \left( \frac{\text{Cash Discount}}{\text{Selling Price after Trade Discount}} \right) \times 100 \]

**Calculation:**
\[ \text{Cash Discount Percentage} = \left( \frac{9,000}{2,25,000} \right) \times 100 \]

Calculating this gives:
\[ \text{Cash Discount Percentage} = \left( \frac{9,000}{2,25,000} \right) \times 100 = \left( \frac{9}{225} \right) \times 100 = 4\% \]

### Final Answer
The cash discount is **4%**.

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