For a certain sum, the simple interest in 2 yr at 8% per annum is ? 90 more than the simple interest in 1.5 yr at the rate of 10% per annum for the same sum. Find the sum

Answer

To solve the problem, we need to find the principal sum (let's denote it as \( P \)) based on the information given about simple interest.

### Step 1: Write the formula for Simple Interest (SI)
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
where \( P \) is the principal amount, \( R \) is the rate of interest per annum, and \( T \) is the time in years.

### Step 2: Calculate the Simple Interest for 2 years at 8%
Using the formula for SI, we can calculate the simple interest for 2 years at 8%:
\[ SI_1 = \frac{P \times 8 \times 2}{100} = \frac{16P}{100} = 0.16P \]

### Step 3: Calculate the Simple Interest for 1.5 years at 10%
Now, we calculate the simple interest for 1.5 years at 10%:
\[ SI_2 = \frac{P \times 10 \times 1.5}{100} = \frac{15P}{100} = 0.15P \]

### Step 4: Set up the equation based on the problem statement
According to the problem, the simple interest for 2 years at 8% is 90 more than the simple interest for 1.5 years at 10%. Therefore, we can set up the equation:
\[ 0.16P = 0.15P + 90 \]

### Step 5: Solve the equation for \( P \)
Now, we will solve the equation:
\[ 0.16P - 0.15P = 90 \]
\[ 0.01P = 90 \]
\[ P = \frac{90}{0.01} = 9000 \]

### Conclusion
The principal sum \( P \) is \( 9000 \).

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