The list price of an article is ₹ 160 and a customer buys it for ₹ 122.40 after two successive discounts. If the first dis count is 10%, then second dis count is

Options

A. 0.12
B. 0.1
C. 0.14
D. 0.15

Answer

To solve the problem step by step, we need to determine the second discount given the first discount and the selling price after both discounts.

### Step 1: Identify the given values
- **List Price (MP)** = ₹160
- **Selling Price (SP)** = ₹122.40
- **First Discount (D1)** = 10%

### Step 2: Calculate the price after the first discount
The formula to calculate the selling price after the first discount is:
\[ SP = MP \times \left(1 - \frac{D1}{100}\right) \]
Substituting the values:
\[ SP = 160 \times \left(1 - \frac{10}{100}\right) = 160 \times 0.9 = 144 \]
So, after the first discount, the price is ₹144.

### Step 3: Set up the equation for the second discount
Let the second discount be \(D2\). The selling price after the second discount can be expressed as:
\[ SP = 144 \times \left(1 - \frac{D2}{100}\right) \]
We know that the selling price is ₹122.40, so we can set up the equation:
\[ 122.40 = 144 \times \left(1 - \frac{D2}{100}\right) \]

### Step 4: Solve for \(D2\)
First, divide both sides by 144:
\[ \frac{122.40}{144} = 1 - \frac{D2}{100} \]
Calculating the left side:
\[ \frac{122.40}{144} = 0.85 \]
So, we have:
\[ 0.85 = 1 - \frac{D2}{100} \]
Now, rearranging gives:
\[ \frac{D2}{100} = 1 - 0.85 = 0.15 \]
Multiplying both sides by 100:
\[ D2 = 15 \]

### Conclusion
The second discount \(D2\) is **15%**.

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