The marked price of a TV is 16000. After two successive discounts, it is sold for 11400. If the first discount is 5%, then the rate of second discount is

Options

A. 0.15
B. 0.2
C. 0.3
D. 0.25

Answer

To find the rate of the second discount on the TV, we can follow these steps:

### Step 1: Identify the Marked Price and First Discount
- The marked price (MP) of the TV is given as **16000**.
- The first discount (D1) is **5%**.

### Step 2: Calculate the Selling Price after the First Discount
- The selling price (SP) after the first discount can be calculated using the formula:
\[ SP_1 = MP \times (1 - \frac{D1}{100}) \]
- Plugging in the values:
\[ SP_1 = 16000 \times (1 - \frac{5}{100}) = 16000 \times 0.95 = 15200 \]

### Step 3: Identify the Final Selling Price
- The final selling price after the second discount is given as **11400**.

### Step 4: Calculate the Amount of the Second Discount
- The amount of the second discount can be calculated as:
\[ \text{Second Discount Amount} = SP_1 - \text{Final SP} \]
- Substituting the values:
\[ \text{Second Discount Amount} = 15200 - 11400 = 3800 \]

### Step 5: Calculate the Rate of the Second Discount
- To find the rate of the second discount (D2), we can use the formula:
\[ D2 = \left( \frac{\text{Second Discount Amount}}{SP_1} \right) \times 100 \]
- Plugging in the values:
\[ D2 = \left( \frac{3800}{15200} \right) \times 100 \]
- Simplifying:
\[ D2 = \left( \frac{3800 \div 3800}{15200 \div 3800} \right) \times 100 = \left( \frac{1}{4} \right) \times 100 = 25\% \]

### Step 6: Conclusion
- The rate of the second discount is **25%**.

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