When a discount of 25% is given on a cruise trip, the profit is 41%. If the discount is 26%, then the profit is

Options

A. 39.12 per cent
B. 67 per cent
C. 94.88 per cent
D. 11.24 per cent

Answer

To solve the problem step by step, we will follow the reasoning laid out in the video transcript.

### Step 1: Understand the Given Information
We know that when a discount of 25% is given, the profit is 41%. We need to find the profit when the discount is increased to 26%.

### Step 2: Establish the Relationships
Let:
- CP = Cost Price
- MP = Marked Price
- SP = Selling Price

From the information given:
- When a discount of 25% is given, the Selling Price (SP) can be expressed as:
\[ SP = MP \times (1 - 0.25) = MP \times 0.75 \]
- The profit of 41% means:
\[ SP = CP \times (1 + 0.41) = CP \times 1.41 \]

### Step 3: Set Up the Equations
From the above relationships, we can set up the equation:
\[ MP \times 0.75 = CP \times 1.41 \]
This can be rearranged to find the ratio of CP to MP:
\[ \frac{CP}{MP} = \frac{0.75}{1.41} \]

### Step 4: Calculate the Ratio
Calculating the ratio:
\[ \frac{CP}{MP} = \frac{0.75}{1.41} \approx \frac{75}{141} \]

### Step 5: Find the New Selling Price with a 26% Discount
Now, if the discount is increased to 26%, the new Selling Price becomes:
\[ SP = MP \times (1 - 0.26) = MP \times 0.74 \]

### Step 6: Relate the New Selling Price to the Cost Price
Using the same relationship for profit:
\[ SP = CP \times (1 + p) \]
Where \( p \) is the new profit percentage we want to find. Therefore:
\[ MP \times 0.74 = CP \times (1 + p) \]

### Step 7: Substitute the CP in Terms of MP
Substituting \( CP \) from the earlier ratio:
\[ MP \times 0.74 = \left(\frac{75}{141} \times MP\right) \times (1 + p) \]

### Step 8: Cancel MP and Solve for p
Cancelling \( MP \) from both sides (assuming \( MP \neq 0 \)):
\[ 0.74 = \frac{75}{141} \times (1 + p) \]

### Step 9: Solve for (1 + p)
Rearranging gives:
\[ 1 + p = \frac{0.74 \times 141}{75} \]
Calculating the right-hand side:
\[ 1 + p \approx \frac{104.94}{75} \approx 1.3992 \]

### Step 10: Calculate p
Thus:
\[ p \approx 1.3992 - 1 = 0.3992 \]
To express this as a percentage:
\[ p \approx 39.92\% \]

### Final Answer
Therefore, the profit when a discount of 26% is given is approximately **39.92%**.

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