A shopkeeper allows two successive discounts on an article whose marked price is Rs. 150 and selling price is 105. What is first discount if second discount is 12.5% ?

Options

A. 0.2
B. 0.175
C. 0.1667
D. 0.25

Answer

To find the first discount when the second discount is 12.5%, we can follow these steps:

### Step 1: Understand the relationship between marked price, selling price, and discounts.
The selling price (SP) after applying successive discounts can be calculated using the formula:
\[ SP = MP \times (1 - D_1/100) \times (1 - D_2/100) \]
where:
- \( MP \) = Marked Price
- \( D_1 \) = First Discount Percentage
- \( D_2 \) = Second Discount Percentage

### Step 2: Substitute the known values into the formula.
Given:
- Marked Price (MP) = Rs. 150
- Selling Price (SP) = Rs. 105
- Second Discount (D2) = 12.5%

We can substitute these values into the formula:
\[ 105 = 150 \times (1 - D_1/100) \times (1 - 12.5/100) \]

### Step 3: Calculate the value of \( (1 - D_2/100) \).
First, calculate \( (1 - D_2/100) \):
\[ 1 - 12.5/100 = 1 - 0.125 = 0.875 \]

### Step 4: Substitute this value back into the equation.
Now, substitute \( 0.875 \) into the equation:
\[ 105 = 150 \times (1 - D_1/100) \times 0.875 \]

### Step 5: Simplify the equation.
Divide both sides by 0.875:
\[ \frac{105}{0.875} = 150 \times (1 - D_1/100) \]
Calculating \( \frac{105}{0.875} \):
\[ 105 \div 0.875 = 120 \]

So, we have:
\[ 120 = 150 \times (1 - D_1/100) \]

### Step 6: Solve for \( (1 - D_1/100) \).
Now, divide both sides by 150:
\[ 1 - D_1/100 = \frac{120}{150} \]
Calculating \( \frac{120}{150} \):
\[ \frac{120}{150} = 0.8 \]

### Step 7: Solve for \( D_1 \).
Now we have:
\[ 1 - D_1/100 = 0.8 \]
Subtract 0.8 from 1:
\[ D_1/100 = 1 - 0.8 = 0.2 \]
Multiply both sides by 100:
\[ D_1 = 0.2 \times 100 = 20 \]

### Conclusion:
The first discount \( D_1 \) is **20%**.

---