The cost price of a product is ₹1800. The cost of the product is three times the cost of the impurities in it. The cost of the impurities increased in the ratio of 3:7 and that of pure material increased in the ratio of 4:9. What is the present cost price of the product?

Options

A. ₹3000
B. ₹4100
C. ₹4000
D. ₹4500

Answer

To solve the problem step by step, we will break down the information given and perform the necessary calculations.

### Step 1: Understand the Cost Price (CP) of the Product
The cost price of the product is given as ₹1800.

### Step 2: Define the Cost of Impurities
Let the cost of impurities be denoted as \( x \). According to the problem, the cost of the product (CP) is three times the cost of the impurities:
\[ CP = 3 \times \text{Cost of Impurities} \]
Thus, we can express this as:
\[ 1800 = 3x \]

### Step 3: Calculate the Cost of Impurities
To find \( x \), we can rearrange the equation:
\[ x = \frac{1800}{3} = 600 \]
So, the cost of impurities is ₹600.

### Step 4: Calculate the Cost of Pure Material
The cost of pure material can be calculated by subtracting the cost of impurities from the total cost price:
\[ \text{Cost of Pure Material} = 1800 - 600 = 1200 \]

### Step 5: Determine the Increase in Cost of Impurities
The cost of impurities increased in the ratio of 3:7. If the initial cost of impurities is ₹600, we can find the new cost:
- The value of 3 corresponds to ₹600, so the value of 1 is:
\[ \text{Value of 1} = \frac{600}{3} = 200 \]
- The new cost corresponding to the value of 7 is:
\[ \text{New Cost of Impurities} = 7 \times 200 = 1400 \]

### Step 6: Determine the Increase in Cost of Pure Material
The cost of pure material increased in the ratio of 4:9. If the initial cost of pure material is ₹1200, we can find the new cost:
- The value of 4 corresponds to ₹1200, so the value of 1 is:
\[ \text{Value of 1} = \frac{1200}{4} = 300 \]
- The new cost corresponding to the value of 9 is:
\[ \text{New Cost of Pure Material} = 9 \times 300 = 2700 \]

### Step 7: Calculate the Present Cost Price of the Product
Now, we can find the present cost price of the product by adding the new costs of impurities and pure material:
\[ \text{Present Cost Price} = \text{New Cost of Impurities} + \text{New Cost of Pure Material} \]
\[ \text{Present Cost Price} = 1400 + 2700 = 4100 \]

### Final Answer
The present cost price of the product is ₹4100.

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