A tempo is insured to the extent of 4/5 of its original value. If the premium on it at the rate of 1.3 percent amounts to Rs 910, the original value of the tempo is

Options

A. Rs 78,500
B. Rs 80,000
C. Rs 82,500
D. Rs 87,500

Answer

To find the original value of the tempo, we can follow these steps:

### Step 1: Define the Original Value
Let the original value of the tempo be \( x \).

### Step 2: Determine the Insured Amount
The tempo is insured for \( \frac{4}{5} \) of its original value, which can be expressed as:
\[ \text{Insured Amount} = \frac{4}{5}x \]

### Step 3: Set Up the Premium Equation
The premium on the insured amount at the rate of 1.3% is given to be Rs 910. Therefore, we can write the equation:
\[ \text{Premium} = \frac{1.3}{100} \times \left(\frac{4}{5}x\right) = 910 \]

### Step 4: Simplify the Equation
Now, we can simplify the equation:
\[ \frac{1.3 \times 4}{100 \times 5}x = 910 \]
This simplifies to:
\[ \frac{5.2}{500}x = 910 \]

### Step 5: Solve for \( x \)
To isolate \( x \), we can multiply both sides by \( 500 \):
\[ 5.2x = 910 \times 500 \]
Calculating the right side:
\[ 5.2x = 455000 \]
Now, divide both sides by \( 5.2 \):
\[ x = \frac{455000}{5.2} \]

### Step 6: Perform the Division
Calculating \( \frac{455000}{5.2} \):
\[ x = 87500 \]

### Conclusion
The original value of the tempo is Rs 87500.

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