Rakesh finds (gets) his profit percentage on selling price and Ramesh finds his profit percentage on cost price. If the difference between their profits is Rs 150 and the selling price of both is same, find the selling price of each where Rakesh gets a profit of 25% and Ramesh earn a profit of 20%.

Options

A. a)Rs 1800
B. b)Rs 1600
C. c)Rs 1900
D. d)Rs 1700

Answer

To solve the problem step by step, we will denote the selling price of both Rakesh and Ramesh as \( SP \).

### Step 1: Define the Selling Price
Let the selling price of both Rakesh and Ramesh be \( SP \).

### Step 2: Calculate Rakesh's Profit
Rakesh earns a profit of 25% on the selling price. Therefore, his profit can be calculated as:
\[ \text{Profit}_{Rakesh} = 25\% \text{ of } SP = \frac{25}{100} \times SP = \frac{SP}{4} \]

### Step 3: Calculate Ramesh's Profit
Ramesh earns a profit of 20% on the cost price. Let \( CP_R \) be the cost price of Ramesh. Since he earns a profit of 20%, we can express the selling price in terms of his cost price:
\[ SP = CP_R + 20\% \text{ of } CP_R = CP_R + \frac{20}{100} \times CP_R = CP_R + \frac{CP_R}{5} = \frac{6}{5} CP_R \]
From this, we can find \( CP_R \):
\[ CP_R = \frac{5}{6} SP \]

### Step 4: Calculate Ramesh's Profit in Terms of Selling Price
Now, Ramesh's profit can be calculated as:
\[ \text{Profit}_{Ramesh} = SP - CP_R = SP - \frac{5}{6} SP = \frac{1}{6} SP \]

### Step 5: Set Up the Equation for the Difference in Profits
According to the problem, the difference between their profits is Rs 150:
\[ \text{Profit}_{Rakesh} - \text{Profit}_{Ramesh} = 150 \]
Substituting the values we calculated:
\[ \frac{SP}{4} - \frac{1}{6} SP = 150 \]

### Step 6: Solve the Equation
To solve the equation, we need a common denominator. The least common multiple of 4 and 6 is 12. Thus, we can rewrite the equation:
\[ \frac{3SP}{12} - \frac{2SP}{12} = 150 \]
This simplifies to:
\[ \frac{1SP}{12} = 150 \]
Multiplying both sides by 12 gives:
\[ SP = 150 \times 12 = 1800 \]

### Conclusion
The selling price of each, Rakesh and Ramesh, is Rs 1800.