The length and breadth of a steel tape are 10m and 2.4cm, respectively. The ratio of the length to the breadth is

Options

A. `5 : 1 . 2`
B. `25 :6`
C. `625 : 6 `
D. `1250 : 3`

Answer

To find the ratio of the length to the breadth of the steel tape, we can follow these steps:

### Step 1: Convert the units to be the same
The length is given as 10 meters and the breadth is given as 2.4 centimeters. We need to convert the length from meters to centimeters for consistency.

- **Conversion**:
\[ 1 \text{ meter} = 100 \text{ centimeters} \]
Therefore,
\[ 10 \text{ meters} = 10 \times 100 = 1000 \text{ centimeters} \]

### Step 2: Write the ratio of length to breadth
Now that both measurements are in centimeters, we can write the ratio of length to breadth.

- **Ratio**:
\[ \text{Length} : \text{Breadth} = 1000 \text{ cm} : 2.4 \text{ cm} \]

### Step 3: Simplify the ratio
To simplify the ratio, we can express it as a fraction:
\[ \frac{1000}{2.4} \]

To eliminate the decimal, we can multiply both the numerator and the denominator by 10:
\[ \frac{1000 \times 10}{2.4 \times 10} = \frac{10000}{24} \]

Now, we simplify \(\frac{10000}{24}\) by finding the greatest common divisor (GCD) of 10000 and 24.

### Step 4: Divide by the GCD
The GCD of 10000 and 24 is 8. Now we can divide both the numerator and the denominator by 8:
\[ \frac{10000 \div 8}{24 \div 8} = \frac{1250}{3} \]

### Step 5: Write the final ratio
Thus, the simplified ratio of length to breadth is:
\[ 1250 : 3 \]

### Final Answer:
The ratio of the length to the breadth is \(1250 : 3\).

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