The cost of an earaser is 80 paise and the cost of a pencil is Rs 2. What is the ratio of their costs in simplest form?

Answer

To find the ratio of the costs of an eraser and a pencil in simplest form, follow these steps:

### Step 1: Convert the costs to the same unit
The cost of the eraser is given as 80 paise, and the cost of the pencil is given as Rs 2. Since 1 Rupee is equal to 100 paise, we can convert the cost of the pencil into paise.

Cost of pencil in paise:
\[ \text{Cost of pencil} = 2 \text{ Rs} \times 100 \text{ paise/Rs} = 200 \text{ paise} \]

### Step 2: Write the costs in paise
Now we have:
- Cost of eraser = 80 paise
- Cost of pencil = 200 paise

### Step 3: Set up the ratio
The ratio of the cost of the eraser to the cost of the pencil can be written as:
\[ \text{Ratio} = \frac{\text{Cost of eraser}}{\text{Cost of pencil}} = \frac{80 \text{ paise}}{200 \text{ paise}} \]

### Step 4: Simplify the ratio
To simplify the ratio, we can divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 80 and 200 is 40.

So, we divide both by 40:
\[ \frac{80 \div 40}{200 \div 40} = \frac{2}{5} \]

### Step 5: Write the final answer
Thus, the ratio of the cost of the eraser to the cost of the pencil in simplest form is:
\[ \text{Ratio} = 2 : 5 \]

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