Two third of a consignment was sold at a profit of 5% and the remainder at a loss of 2%. If the total profit was Rs. 400, then value of the consignment (in rupees) was:

Options

A. 15000
B. 20000
C. 10000
D. 12000

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the total value of the consignment be \( X \) rupees.

### Step 2: Calculate the Value Sold at Profit
Two-thirds of the consignment is sold at a profit of 5%. Therefore, the value sold at profit is:
\[ \text{Value sold at profit} = \frac{2}{3}X \]
The profit earned from this portion is:
\[ \text{Profit from this portion} = \frac{5}{100} \times \frac{2}{3}X = \frac{10}{300}X = \frac{1}{30}X \]

### Step 3: Calculate the Value Sold at Loss
The remaining one-third of the consignment is sold at a loss of 2%. Therefore, the value sold at loss is:
\[ \text{Value sold at loss} = \frac{1}{3}X \]
The loss incurred from this portion is:
\[ \text{Loss from this portion} = \frac{2}{100} \times \frac{1}{3}X = \frac{2}{300}X = \frac{1}{150}X \]

### Step 4: Calculate the Total Profit
The total profit from the consignment is given as Rs. 400. The total profit can be calculated as:
\[ \text{Total Profit} = \text{Profit from sold portion} - \text{Loss from sold portion} \]
Substituting the values we calculated:
\[ 400 = \frac{1}{30}X - \frac{1}{150}X \]

### Step 5: Find a Common Denominator
To simplify the equation, we need a common denominator for the fractions. The least common multiple of 30 and 150 is 150. Therefore, we can rewrite the equation as:
\[ 400 = \frac{5}{150}X - \frac{1}{150}X \]
This simplifies to:
\[ 400 = \frac{4}{150}X \]

### Step 6: Solve for \( X \)
Now, we can solve for \( X \):
\[ 400 = \frac{4}{150}X \]
Multiplying both sides by 150 to eliminate the fraction:
\[ 400 \times 150 = 4X \]
\[ 60000 = 4X \]
Dividing both sides by 4:
\[ X = \frac{60000}{4} = 15000 \]

### Conclusion
The value of the consignment is Rs. 15,000.

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