Theory & Concepts
SSC CGL SI and CI Questions, Formulas & Short Tricks
Prepare SI and CI for SSC CGL with formulas, short tricks, solved examples, practice questions, PYQs, and free PDF notes for faster exam preparation.
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28 min readDifficulty: Advanced
Ssc cgl Tier-2 frequently tests the interplay between Simple Interest (SI) and Compound Interest (CI). Understanding the relationship between the two is the key to solving complex difference and installment queries.
This module focuses on the specialized formulas required to find the difference between CI and SI over 2 and 3 years, alongside the logic for annual installments—a high-weightage topic for the Mains exam.
Learning path
- CI - SI difference formulas
- Combined installment logic
- Rate comparison techniques
- 10 standard solved problems
- Mixed frequency compounding
1. Difference between CI and SI
For a principal at a rate per annum, the differences are:
For 2 Years (D2):
For 3 Years (D3):
2. The Installment Logic
In CI, each installment is seen as a present value calculation. For a debt cleared in installments of each:
CI Installment formula
3. 10 Solved examples
Question 01Standard pattern
The difference between SI and CI on a certain sum for 2 years at 10% per annum is rs. 631. Find the sum.
rs. 63,100
rs. 6,310
rs. 60,000
rs. 65,000
Correct answer: a) rs. 63,100
Solution
Use the 2-year difference formula: \( D = P(R/100)^2 \).
Substitute: \( 631 = P(10/100)^2 = P/100 \).
Calculation: \( P = 631 \times 100 = 63,100 \).
Result = \( rs. 63,100 \).
Question 02Standard pattern
Find the difference between CI and SI on rs. 8,000 for 3 years at 5% per annum.
rs. 61
rs. 60
rs. 62
rs. 58
Correct answer: a) rs. 61
Solution
Use the 3-year difference formula: \( D = P(R/100)^2 \times (300+R)/100 \).
Substitute values: \( 8000 \times (5/100)^2 \times (305/100) \).
Simplification: \( 8000 \times \frac{1}{400} \times \frac{305}{100} = 20 \times 3.05 \).
Result = \( rs. 61 \).
Question 03Standard pattern
A sum of money invested at CI triple itself in 5 years. It will become 27 times itself in:
15 years
20 years
10 years
25 years
Correct answer: a) 15 years
Solution
Factor of change = \( 3 \).
Target change = \( 27 = 3^3 \).
Time taken = \( 3 \times 5 = 15 \text{ years} \).
Question 04Standard pattern
What is the difference between CI and SI on rs. 5000 for 2 years at 8% per annum?
rs. 32
rs. 35
rs. 30
rs. 40
Correct answer: a) rs. 32
Solution
Calculation: \( 5000 \times (8/100)^2 = 5000 \times \frac{64}{10000} \).
\( \frac{1}{2} \times 64 = 32 \).
Question 05Standard pattern
A sum of rs. 12,600 is to be paid back in two equal annual installments of CI at 10% rate. Find each installment.
rs. 7,260
rs. 7,000
rs. 7,500
rs. 6,300
Correct answer: a) rs. 7,260
Solution
Equation: \( \frac{x}{1.1} + \frac{x}{1.21} = 12600 \).
Calculation: \( \frac{1.1x + x}{1.21} = 12600 \implies 2.1x = 15246 \).
Result: \( x = 7260 \).
Question 06Standard pattern
The ratio of CI difference for 3 years to 2 years is 25:8. Find rate.
12.5%
10%
15%
20%
Correct answer: a) 12.5%
Solution
Ratio logic: \( \frac{D3}{D2} = \frac{300+R}{100} = \frac{25}{8} \).
\( 8(300+R) = 2500 \implies 2400 + 8R = 2500 \).
Calculation: \( 8R = 100 \implies R = 12.5\% \).
Question 07Standard pattern
If SI on a sum for 2 years at 5% is rs. 50, what is CI for same period?
rs. 51.25
rs. 52
rs. 50.50
rs. 55
Correct answer: a) rs. 51.25
Solution
SI for 1 yr = 25. CI for 2nd yr starts on Principal + 1st yr interest.
CI = \( 25 + (25 + 5\% \text{ of } 25) = 25 + 26.25 = 51.25 \).
Question 08Standard pattern
Effective annual rate of 10% p.a. compounded half-yearly is?
10.25%
10.50%
10.00%
10.15%
Correct answer: a) 10.25%
Solution
Compounded half-yearly: \( r=5\%, n=2 \).
Equivalent: \( 5 + 5 + \frac{25}{100} = 10.25\% \).
Question 09Standard pattern
Sum rs. 2520 to be paid in 3 equal installments at 5% CI. Installment?
rs. 926.10
rs. 900
rs. 840
rs. 950
Correct answer: a) rs. 926.10
Solution
Ratio for 5\% is \( 20:21 \).
Eq: \( x(20/21) + x(20/21)^2 + x(20/21)^3 = 2520 \).
Calculation: \( x = 926.10 \).
Question 010Standard pattern
Difference for 3 years at 10% is rs. 155. Find sum.
rs. 5,000
rs. 6,000
rs. 4,500
rs. 5,500
Correct answer: a) rs. 5,000
Solution
\( 155 = P \times (1/100) \times 3.1 \implies P = 5000 \).
4. Strategy errors to avoid
Error 01Denominator error: Mixing (300+R)/100 with (R/100) and losing track of the exponents.
Error 02Installment sum: Adding installments directly without discounting them back to the present value.
Error 03Frequency mismatch: Using annual rate for half-yearly compounding without halving the R and doubling the N.
Error 04Ratio overlap: Forgetting that CI and SI are identical for the first year of any investment.
