Two articles - A and B are sold at 25% profit and 40% profit respectively. If total profit is Rs 178 and the cost price of A is Rs 120 less than B. find the CP of B.

Options

A. A)Rs 310
B. B)Rs 370
C. C)Rs 320
D. D)Rs 430

Answer

To solve the problem step by step, we will define the variables and set up equations based on the information provided.

### Step 1: Define Variables
Let the cost price of article B be \( CP_B \). According to the problem, the cost price of article A, \( CP_A \), is Rs 120 less than that of article B. Therefore, we can express this as:
\[ CP_A = CP_B - 120 \]

### Step 2: Express the Profits
The profit from article A is 25% of its cost price, and the profit from article B is 40% of its cost price. We can express these profits mathematically:
- Profit from A:
\[ \text{Profit}_A = 0.25 \times CP_A = 0.25 \times (CP_B - 120) \]
- Profit from B:
\[ \text{Profit}_B = 0.40 \times CP_B \]

### Step 3: Set Up the Total Profit Equation
According to the problem, the total profit from both articles is Rs 178. Therefore, we can set up the following equation:
\[ \text{Profit}_A + \text{Profit}_B = 178 \]
Substituting the expressions for the profits:
\[ 0.25 \times (CP_B - 120) + 0.40 \times CP_B = 178 \]

### Step 4: Simplify the Equation
Now, let's simplify the equation:
1. Distribute the 0.25:
\[ 0.25 \times CP_B - 30 + 0.40 \times CP_B = 178 \]
2. Combine like terms:
\[ (0.25 + 0.40) \times CP_B - 30 = 178 \]
\[ 0.65 \times CP_B - 30 = 178 \]

### Step 5: Solve for \( CP_B \)
Now, we will isolate \( CP_B \):
1. Add 30 to both sides:
\[ 0.65 \times CP_B = 178 + 30 \]
\[ 0.65 \times CP_B = 208 \]
2. Divide both sides by 0.65:
\[ CP_B = \frac{208}{0.65} \]
\[ CP_B = 320 \]

### Conclusion
The cost price of article B is Rs 320.