Let the principal sum be denoted by \(P\). We need to find the value of \(P\).
Calculating Simple Interest Components
The formula for simple interest (SI) is given by:
$ SI = \frac{P \times R \times T}{100} $
where \(P\) is the principal sum, \(R\) is the annual interest rate (in percentage), and \(T\) is the time period (in years).
Interest for the First Scenario
For the first scenario:
- Time (\(T_1\)) = 3 years
- Rate (\(R_1\)) = 8% per annum
The simple interest (\(SI_1\)) is:
$ SI_1 = \frac{P \times 8 \times 3}{100} = \frac{24P}{100} $
Interest for the Second Scenario
For the second scenario:
- Time (\(T_2\)) = 2 years
- Rate (\(R_2\)) = 9% per annum
The simple interest (\(SI_2\)) is:
$ SI_2 = \frac{P \times 9 \times 2}{100} = \frac{18P}{100} $
Setting Up the Equation
The problem states that the simple interest in the first case (\(SI_1\)) is ₹96 more than the simple interest in the second case (\(SI_2\)). Therefore:
$ SI_1 - SI_2 = 96 $
Solving for the Sum (P)
Substitute the expressions for \(SI_1\) and \(SI_2\) into the equation:
$ \frac{24P}{100} - \frac{18P}{100} = 96 $
Combine the terms on the left side:
$ \frac{24P - 18P}{100} = 96 $
$ \frac{6P}{100} = 96 $
To solve for \(P\), multiply both sides by 100:
$ 6P = 96 \times 100 $
$ 6P = 9600 $
Now, divide by 6:
$ P = \frac{9600}{6} $
$ P = 1600 $
The principal sum is ₹1,600.
Similar Questions
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Important Questions from Simple Interest
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
