Veer purchased two mobiles for Rs. 36,000 and he sold first mobile at 30% profit and second mobile at 20% loss. If in this transaction Veer gets no profit no loss, then by how much rupees more than the previous selling price, the second mobile must be sold in order to make a profit of 25% on it?

Options

A. A)Rs 9720
B. B)Rs 9700
C. C)Rs 9750
D. D)Rs 9690

Answer

To solve the problem step by step, let's break down the information given and calculate the required values.

### Step 1: Determine the Cost Price of Each Mobile
Let the cost price of the first mobile be \( A \) and the cost price of the second mobile be \( B \). According to the problem, we know:

\[ A + B = 36,000 \]

### Step 2: Calculate Selling Price of First Mobile
Veer sold the first mobile at a 30% profit. Therefore, the selling price (SP) of the first mobile can be calculated as:

\[ SP_A = A + 0.3A = 1.3A \]

### Step 3: Calculate Selling Price of Second Mobile
Veer sold the second mobile at a 20% loss. Therefore, the selling price of the second mobile can be calculated as:

\[ SP_B = B - 0.2B = 0.8B \]

### Step 4: Set Up the No Profit No Loss Condition
Since Veer made no profit and no loss overall, the total selling price of both mobiles must equal the total cost price:

\[ SP_A + SP_B = A + B \]

Substituting the expressions for \( SP_A \) and \( SP_B \):

\[ 1.3A + 0.8B = 36,000 \]

### Step 5: Substitute \( B \) in Terms of \( A \)
From the first equation \( A + B = 36,000 \), we can express \( B \) as:

\[ B = 36,000 - A \]

Now substitute this into the equation from Step 4:

\[ 1.3A + 0.8(36,000 - A) = 36,000 \]

### Step 6: Simplify the Equation
Expanding the equation gives:

\[ 1.3A + 28,800 - 0.8A = 36,000 \]

Combining like terms:

\[ 0.5A + 28,800 = 36,000 \]

### Step 7: Solve for \( A \)
Subtract 28,800 from both sides:

\[ 0.5A = 36,000 - 28,800 \]
\[ 0.5A = 7,200 \]

Now, multiply both sides by 2 to find \( A \):

\[ A = 14,400 \]

### Step 8: Calculate \( B \)
Using the value of \( A \) to find \( B \):

\[ B = 36,000 - 14,400 = 21,600 \]

### Step 9: Calculate Selling Price of Second Mobile
Now, we need to find the selling price of the second mobile after the 20% loss:

\[ SP_B = 0.8B = 0.8 \times 21,600 = 17,280 \]

### Step 10: Calculate Required Selling Price for 25% Profit
To achieve a 25% profit on the second mobile, we need to find the new selling price:

\[ \text{New SP} = B + 0.25B = 1.25B \]
\[ \text{New SP} = 1.25 \times 21,600 = 27,000 \]

### Step 11: Calculate the Difference
Now, we need to find out by how much more the second mobile must be sold compared to the previous selling price:

\[ \text{Difference} = \text{New SP} - \text{Previous SP} \]
\[ \text{Difference} = 27,000 - 17,280 = 9,720 \]

### Final Answer
Veer must sell the second mobile for Rs. 9,720 more than the previous selling price to achieve a 25% profit.

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