The sum lent at 5 % per annum (i.e. 365 days) simple interest, that produces interest of Rs 2.00 a day, is

Options

A. Rs 1,400
B. Rs 14, 700
C. Rs 14, 600
D. Rs 7,300

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Calculate the total interest for one year
Given that the interest produced is Rs 2.00 per day, we can calculate the total interest for one year (365 days).

\[ \text{Total Interest for 1 year} = \text{Interest per day} \times \text{Number of days} \]
\[ \text{Total Interest for 1 year} = 2 \, \text{Rs/day} \times 365 \, \text{days} = 730 \, \text{Rs} \]

**Hint for Step 1:** Multiply the daily interest by the total number of days in a year to find the annual interest.

### Step 2: Use the formula for Simple Interest
The formula for Simple Interest (SI) is given by:

\[ SI = \frac{P \times R \times T}{100} \]

Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount (the sum lent)
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

From Step 1, we know \( SI = 730 \, \text{Rs} \), \( R = 5\% \), and \( T = 1 \, \text{year} \).

### Step 3: Rearranging the formula to find the Principal (P)
We can rearrange the formula to find \( P \):

\[ P = \frac{SI \times 100}{R \times T} \]

Substituting the known values:

\[ P = \frac{730 \times 100}{5 \times 1} \]

### Step 4: Calculate the Principal
Now we perform the calculation:

\[ P = \frac{73000}{5} = 14600 \, \text{Rs} \]

### Final Answer
The sum lent at 5% per annum that produces interest of Rs 2.00 a day is **Rs 14,600**.

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