Simple interest for a sum of ? 1550 for 2 yr is ? 20 more than the simple interest for X 1450 for the same duration. Find the rate of interest.

Answer

To solve the problem step by step, we will use the formula for Simple Interest (SI), which is:

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

where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time period in years

### Step 1: Calculate Simple Interest for the first sum
Given:
- Principal amount \( P_1 = 1550 \)
- Time \( T = 2 \) years

Using the formula for Simple Interest:

\[ SI_1 = \frac{1550 \times R \times 2}{100} \]

This simplifies to:

\[ SI_1 = \frac{3100R}{100} = 31R \]

### Step 2: Calculate Simple Interest for the second sum
Given:
- Principal amount \( P_2 = 1450 \)
- Time \( T = 2 \) years

Using the formula for Simple Interest:

\[ SI_2 = \frac{1450 \times R \times 2}{100} \]

This simplifies to:

\[ SI_2 = \frac{2900R}{100} = 29R \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the Simple Interest for the first sum is 20 more than the Simple Interest for the second sum. Therefore, we can write the equation:

\[ SI_1 = SI_2 + 20 \]

Substituting the values we found:

\[ 31R = 29R + 20 \]

### Step 4: Solve for \( R \)
Now, we will solve the equation:

\[ 31R - 29R = 20 \]

This simplifies to:

\[ 2R = 20 \]

Dividing both sides by 2:

\[ R = \frac{20}{2} = 10 \]

### Final Answer
The rate of interest \( R \) is \( 10\% \).

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