A shopkeeper marks up price of T.V. `50%` above its cost price and gives three successive discounts of `12 1/2%, d%` and `40%`. If shopkeeper made a loss `37%` on T.V. Find the second discount allowed by shop?

Options

A. `15%`
B. `20%`
C. `25%`
D. `17.5%`

Answer

To solve the problem step by step, we will follow the outline provided in the video transcript and add clarity to each step.

### Step 1: Define the Cost Price (CP)
Let the cost price (CP) of the TV be `100` (this is a convenient assumption to simplify calculations).

### Step 2: Calculate the Marked Price (MP)
The shopkeeper marks up the price of the TV by `50%` above its cost price.
- Marked Price (MP) = CP + 50% of CP
- MP = 100 + (50/100) * 100 = 100 + 50 = `150`

### Step 3: Calculate the Selling Price (SP) after Loss
The shopkeeper incurs a loss of `37%`. Therefore, the selling price can be calculated as:
- Loss = 37% of CP = (37/100) * 100 = `37`
- Selling Price (SP) = CP - Loss = 100 - 37 = `63`

### Step 4: Apply the First Discount
The first discount is `12.5%`.
- After the first discount, the price becomes:
- Price after first discount = MP * (1 - 12.5/100) = 150 * (1 - 0.125) = 150 * 0.875 = `131.25`

### Step 5: Apply the Second Discount (d%)
Let the second discount be `d%`. The price after the second discount becomes:
- Price after second discount = Price after first discount * (1 - d/100) = 131.25 * (1 - d/100)

### Step 6: Apply the Third Discount
The third discount is `40%`.
- Price after third discount = Price after second discount * (1 - 40/100) = Price after second discount * 0.6

### Step 7: Set Up the Equation for Selling Price
We know that the final selling price (after all discounts) is equal to `63`. Therefore, we can set up the equation:
\[ 63 = 131.25 * (1 - \frac{d}{100}) * 0.6 \]

### Step 8: Solve for d
1. Simplify the equation:
\[ 63 = 131.25 * 0.6 * (1 - \frac{d}{100}) \]
\[ 63 = 78.75 * (1 - \frac{d}{100}) \]

2. Divide both sides by `78.75`:
\[ \frac{63}{78.75} = 1 - \frac{d}{100} \]
\[ 0.8 = 1 - \frac{d}{100} \]

3. Rearranging gives:
\[ \frac{d}{100} = 1 - 0.8 = 0.2 \]
\[ d = 0.2 * 100 = 20 \]

### Conclusion
The second discount allowed by the shopkeeper is `20%`.

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