The ratio of prices of Cello and Rotomac pens is 2000 were in the ratio of 3:5. In 2005 the price of Cello pen trebles itself and the price of Rotomac pen is increased by Rs. 100, then the new ratio of prices of the same pens becomes 4:5. What was the original price ofthe Rotomac pen is 2000?

Options

A. Rs. 6000
B. Rs. 80
C. Rs. 100
D. Rs. 120

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the initial ratio of prices
The prices of Cello and Rotomac pens are in the ratio 3:5. Let's denote the price of the Cello pen as \(3x\) and the price of the Rotomac pen as \(5x\).

### Step 2: Write down the prices in 2000
From the ratio, we have:
- Price of Cello pen = \(3x\)
- Price of Rotomac pen = \(5x\)

### Step 3: Determine the price changes in 2005
According to the problem:
- The price of the Cello pen trebles, so the new price of the Cello pen = \(3 \times 3x = 9x\).
- The price of the Rotomac pen increases by Rs. 100, so the new price of the Rotomac pen = \(5x + 100\).

### Step 4: Set up the new ratio
In 2005, the new ratio of the prices of the Cello and Rotomac pens becomes 4:5. Therefore, we can write the equation:
\[ \frac{9x}{5x + 100} = \frac{4}{5} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives us:
\[ 9x \cdot 5 = 4 \cdot (5x + 100) \]
This simplifies to:
\[ 45x = 20x + 400 \]

### Step 6: Solve for \(x\)
Now, we will isolate \(x\):
\[ 45x - 20x = 400 \]
\[ 25x = 400 \]
\[ x = \frac{400}{25} = 16 \]

### Step 7: Find the original price of the Rotomac pen
Now that we have \(x\), we can find the original price of the Rotomac pen:
\[ \text{Price of Rotomac pen} = 5x = 5 \times 16 = 80 \]

### Final Answer
The original price of the Rotomac pen in 2000 was Rs. 80.

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