If the interest on Rs. 2,400 be more than the interest on Rs. 2,000 by Rs. 60 in 3 years at the same rate per cent, find the rate.

Answer

To solve the problem step by step, we will follow the same approach as described in the video transcript.

### Step 1: Understand the problem
We need to find the rate of interest (let's denote it as \( r \)) such that the interest on Rs. 2400 is Rs. 60 more than the interest on Rs. 2000 over a period of 3 years.

### Step 2: Set up the formula for Simple Interest
The formula for calculating Simple Interest (SI) is:
\[ SI = \frac{P \times r \times t}{100} \]
where:
- \( P \) = Principal amount
- \( r \) = Rate of interest
- \( t \) = Time in years

### Step 3: Calculate the interest for Rs. 2400
Let’s calculate the interest for the principal amount of Rs. 2400 over 3 years:
- Principal (\( P_1 \)) = Rs. 2400
- Time (\( t \)) = 3 years
- Rate (\( r \)) = \( x \) (we will find this)

Using the formula:
\[ SI_1 = \frac{2400 \times x \times 3}{100} = \frac{7200x}{100} = 72x \]

### Step 4: Calculate the interest for Rs. 2000
Now, we calculate the interest for the principal amount of Rs. 2000 over the same period:
- Principal (\( P_2 \)) = Rs. 2000
- Time (\( t \)) = 3 years
- Rate (\( r \)) = \( x \)

Using the formula:
\[ SI_2 = \frac{2000 \times x \times 3}{100} = \frac{6000x}{100} = 60x \]

### Step 5: Set up the equation based on the problem statement
According to the problem, the interest on Rs. 2400 is Rs. 60 more than the interest on Rs. 2000:
\[ SI_1 = SI_2 + 60 \]
Substituting the values we calculated:
\[ 72x = 60x + 60 \]

### Step 6: Solve the equation
Now, we will solve for \( x \):
\[ 72x - 60x = 60 \]
\[ 12x = 60 \]
\[ x = \frac{60}{12} = 5 \]

### Step 7: Conclusion
The rate of interest is \( 5\% \).