If the simple interest on Rs. 1400 be more than the interset on Rs. 1000 by Rs. 60 in 5 years, find the rate percent per annum.

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the problem
We need to find the rate of interest per annum (R) given that the simple interest on Rs. 1400 is more than the simple interest on Rs. 1000 by Rs. 60 over a period of 5 years.

### Step 2: Write the formula for Simple Interest
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 3: Calculate the Simple Interest for both amounts
1. **For Rs. 1400:**
\[ SI_1 = \frac{1400 \times R \times 5}{100} = \frac{7000R}{100} = 70R \]

2. **For Rs. 1000:**
\[ SI_2 = \frac{1000 \times R \times 5}{100} = \frac{5000R}{100} = 50R \]

### Step 4: Set up the equation based on the information given
According to the problem, the simple interest on Rs. 1400 is more than that on Rs. 1000 by Rs. 60:
\[ SI_1 = SI_2 + 60 \]
Substituting the values we calculated:
\[ 70R = 50R + 60 \]

### Step 5: Solve for R
Now, we will solve the equation:
\[ 70R - 50R = 60 \]
\[ 20R = 60 \]
\[ R = \frac{60}{20} = 3 \]

### Step 6: Conclusion
The rate of interest per annum is \( R = 3\% \).

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