All questions of Simple & Compound Interest for SSC CGL Exam

Understanding the Problem
When a sum of money triples itself in 5 years under simple interest, it means that the interest earned is equal to two times the principal amount. We need to find out how many years it will take for the same sum to become five times under simple interest.
Given Information
- Initial amount (Principal, P) = P
- Amount after 5 years = 3P
- Therefore, Interest for 5 years = 3P - P = 2P
Calculating the Rate of Interest
Using the formula for simple interest:
- Simple Interest (SI) = P * r * t
Here, SI = 2P, t = 5 years, and we need to find the rate (r).
- 2P = P * r * 5
Cancelling P from both sides (assuming P is not zero):
- 2 = r * 5
Thus,
- r = 2/5 = 0.4 or 40% per annum.
Finding Time to Become Five Times
Now, we want to find out the time (t) when the sum becomes five times the principal:
- Amount after t years = 5P
- Interest earned = 5P - P = 4P
Using the simple interest formula again:
- 4P = P * r * t
Cancelling P:
- 4 = r * t
Substituting the value of r (0.4):
- 4 = 0.4 * t
Now, solve for t:
- t = 4 / 0.4 = 10 years.
Conclusion
Thus, it will take 10 years for the sum of money to become five times itself under simple interest. The correct answer is option 'C'.

Understanding Compound Interest
When an amount of money is placed at compound interest, it grows exponentially over time. In this case, we know that the amount doubles in 2 years. To find out how long it will take for the amount to quadruple (become 4 times), we can use the concept of doubling time.
Doubling Time
- Doubling in 2 Years: If the initial amount doubles in 2 years, this means that the growth rate is effective enough to double the principal amount.
- Growth Factor: After 2 years, the amount is 2 times the principal (P). In mathematical terms:
- After 2 years: A = P * (1 + r)^2 = 2P
Quadrupling the Amount
- Quadrupling: To quadruple the amount means to get 4 times the principal amount:
- A = 4P
- Using Doubling Principle: Since the amount doubles every 2 years, we can deduce:
- After 2 years: Amount = 2P
- After another 2 years (total of 4 years): Amount = 2 * 2P = 4P
Conclusion
Thus, it takes a total of 4 years for the initial amount to quadruple. Therefore, the correct answer is:
- 4 years (Option B)
This approach demonstrates the relationship between doubling time and the time required for an amount to grow fourfold.

Understanding Simple Interest and Compound Interest
To solve the problem, we need to differentiate between simple interest (SI) and compound interest (CI).
Formula for Simple Interest
- Simple Interest (SI) = P * r * t / 100
Where P = Principal amount, r = rate of interest, t = time (in years).
Formula for Compound Interest
- Compound Interest (CI) = P * (1 + r/100)^t - P
This represents the interest earned on both the principal and the interest that has been added.
Given Information
- Rate of interest (r) = 15% per annum
- Time (t) = 2 years
- Difference between CI and SI = 9
Calculating Simple Interest
- SI = x * 15 * 2 / 100
- SI = (30x) / 100 = 0.3x
Calculating Compound Interest
- CI = x * (1 + 0.15)^2 - x
- CI = x * (1.15)^2 - x
- CI = x * (1.3225) - x
- CI = 1.3225x - x = 0.3225x
Setting Up the Equation
- The difference between CI and SI is given as 9:
0.3225x - 0.3x = 9
0.0225x = 9
Finding x
- x = 9 / 0.0225
- x = 400
Thus, the value of x is 400. Therefore, the correct answer is option 'B'.

Understanding Compound Interest
To determine the principal sum that will amount to 12,100 in 2 years at a 10% annual compound interest, we can use the formula for compound interest:
Amount (A) = Principal (P) × (1 + r)^n
Where:
- A = Amount after n years
- P = Principal amount (the sum we need to find)
- r = Rate of interest (in decimal form)
- n = Number of years
Given Values
- A = 12,100
- r = 10% = 0.10
- n = 2 years
Setting Up the Equation
Using the compound interest formula:
12,100 = P × (1 + 0.10)^2
This simplifies to:
12,100 = P × (1.10)^2
Next, calculate (1.10)^2:
- (1.10)^2 = 1.21
Now, substitute back into the equation:
12,100 = P × 1.21
Solving for Principal (P)
To find P, rearrange the equation:
P = 12,100 / 1.21
Now, perform the division:
P = 10,000
Conclusion
The principal sum that will amount to 12,100 in 2 years at a 10% compound interest is:
- 10,000
Thus, the correct answer is option 'D'.