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

Options

A. `20%`
B. `17.5%`
C. `16.67 %`
D. `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 two successive discounts on the marked price (MP) can be expressed as:
\[ SP = MP \times (1 - d_1) \times (1 - d_2) \]
where \( d_1 \) is the first discount and \( d_2 \) is the second discount.

### Step 2: Substitute the known values.
Given:
- Marked Price (MP) = Rs 150
- Selling Price (SP) = Rs 105
- Second Discount (d2) = 12.5% = 0.125

Substituting these values into the formula:
\[ 105 = 150 \times (1 - d_1) \times (1 - 0.125) \]

### Step 3: Simplify the equation.
First, calculate \( (1 - 0.125) \):
\[ 1 - 0.125 = 0.875 \]

Now substitute this back into the equation:
\[ 105 = 150 \times (1 - d_1) \times 0.875 \]

### Step 4: Isolate \( (1 - d_1) \).
Divide both sides by 0.875:
\[ \frac{105}{0.875} = 150 \times (1 - d_1) \]

Calculating \( \frac{105}{0.875} \):
\[ \frac{105}{0.875} = 120 \]

Now, we have:
\[ 120 = 150 \times (1 - d_1) \]

### Step 5: Solve for \( (1 - d_1) \).
Divide both sides by 150:
\[ 1 - d_1 = \frac{120}{150} \]

Calculating \( \frac{120}{150} \):
\[ \frac{120}{150} = 0.8 \]

### Step 6: Find \( d_1 \).
Now, rearranging gives:
\[ d_1 = 1 - 0.8 = 0.2 \]

### Step 7: Convert \( d_1 \) to percentage.
To convert \( d_1 \) into percentage:
\[ d_1 = 0.2 \times 100 = 20\% \]

### Conclusion:
The first discount is **20%**.

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