๐ Series Info: Chapter 2: Arithmetic
Post Number: 17/76 | Topic: 2.5 Simple Interest
Previous: 2.4 Discount ✅
Chapter 2 Progress: 5/20 topics (25% complete!)
Post Number: 17/76 | Topic: 2.5 Simple Interest
Previous: 2.4 Discount ✅
Chapter 2 Progress: 5/20 topics (25% complete!)
Introduction: Simple Interest Kya Hai?
Namaste dosto! Aaj ham Simple Interest (SI) (เคธाเคงाเคฐเคฃ เคฌ्เคฏाเค) padhenge. Ye banking aur finance se related important topic hai aur SSC CGL me guaranteed 2-3 questions aate hain.
Basic Understanding
๐น Principal (P) = เคฎूเคฒเคงเคจ = Original amount borrowed/invested
๐น Rate (R) = เคฆเคฐ = Interest rate per year (%)
๐น Time (T) = เคธเคฎเคฏ = Duration (in years)
๐น Simple Interest (SI) = เคฌ्เคฏाเค = Extra money paid/earned
๐น Amount (A) = เคुเคฒ เคงเคจ = Principal + Interest
๐น Rate (R) = เคฆเคฐ = Interest rate per year (%)
๐น Time (T) = เคธเคฎเคฏ = Duration (in years)
๐น Simple Interest (SI) = เคฌ्เคฏाเค = Extra money paid/earned
๐น Amount (A) = เคुเคฒ เคงเคจ = Principal + Interest
Real-life Example:
Tumne bank se ₹10,000 loan liya
Interest rate = 5% per year
Time = 2 years
Simple Interest = ₹1000
Total amount to return = ₹11,000
(₹10,000 principal + ₹1000 interest)
Tumne bank se ₹10,000 loan liya
Interest rate = 5% per year
Time = 2 years
Simple Interest = ₹1000
Total amount to return = ₹11,000
(₹10,000 principal + ₹1000 interest)
๐ฏ Exam Importance: SSC CGL me SI questions:
- Direct SI calculations (2-3 questions)
- Finding Principal/Rate/Time
- Amount calculations
- SI vs CI comparison problems
- Two persons borrowing different amounts
- Installment problems (basic)
Simple Interest - All Formulas MUST KNOW
Main Formula
⭐ SI = (P × R × T)/100 ⭐
P = Principal (เคฎूเคฒเคงเคจ)
R = Rate % per annum (เคตाเคฐ्เคทिเค เคฆเคฐ)
T = Time in years (เคธเคฎเคฏ)
P = Principal (เคฎूเคฒเคงเคจ)
R = Rate % per annum (เคตाเคฐ्เคทिเค เคฆเคฐ)
T = Time in years (เคธเคฎเคฏ)
Example:
P = ₹5000, R = 8% per year, T = 3 years
SI = (5000 × 8 × 3)/100
SI = 120000/100
SI = ₹1200 ✓
P = ₹5000, R = 8% per year, T = 3 years
SI = (5000 × 8 × 3)/100
SI = 120000/100
SI = ₹1200 ✓
Amount Formula
⭐ Amount (A) = Principal + SI ⭐
⭐ A = P + (P × R × T)/100 ⭐
⭐ A = P[1 + (RT)/100] ⭐
⭐ A = P + (P × R × T)/100 ⭐
⭐ A = P[1 + (RT)/100] ⭐
Example:
P = ₹8000, R = 10%, T = 2 years
SI = (8000 × 10 × 2)/100 = ₹1600
Amount = 8000 + 1600 = ₹9600 ✓
Direct formula:
A = 8000[1 + (10×2)/100]
A = 8000[1 + 0.2]
A = 8000 × 1.2 = ₹9600 ✓
P = ₹8000, R = 10%, T = 2 years
SI = (8000 × 10 × 2)/100 = ₹1600
Amount = 8000 + 1600 = ₹9600 ✓
Direct formula:
A = 8000[1 + (10×2)/100]
A = 8000[1 + 0.2]
A = 8000 × 1.2 = ₹9600 ✓
Principal, Rate, Time Nikalne Ke Formulas
Formula 1: Principal (P) Nikalna
Jab SI, R, T diya ho:
P = (SI × 100)/(R × T)
Jab Amount, R, T diya ho:
P = (A × 100)/(100 + RT)
P = (SI × 100)/(R × T)
Jab Amount, R, T diya ho:
P = (A × 100)/(100 + RT)
Example 1:
SI = ₹600, R = 5%, T = 4 years. Principal?
P = (600 × 100)/(5 × 4)
P = 60000/20
P = ₹3000 ✓
Example 2:
Amount = ₹1200, R = 10%, T = 2 years. Principal?
P = (1200 × 100)/(100 + 10×2)
P = 120000/120
P = ₹1000 ✓
SI = ₹600, R = 5%, T = 4 years. Principal?
P = (600 × 100)/(5 × 4)
P = 60000/20
P = ₹3000 ✓
Example 2:
Amount = ₹1200, R = 10%, T = 2 years. Principal?
P = (1200 × 100)/(100 + 10×2)
P = 120000/120
P = ₹1000 ✓
Formula 2: Rate (R) Nikalna
R = (SI × 100)/(P × T)
Example:
P = ₹4000, SI = ₹800, T = 5 years. Rate?
R = (800 × 100)/(4000 × 5)
R = 80000/20000
R = 4% per annum ✓
P = ₹4000, SI = ₹800, T = 5 years. Rate?
R = (800 × 100)/(4000 × 5)
R = 80000/20000
R = 4% per annum ✓
Formula 3: Time (T) Nikalna
T = (SI × 100)/(P × R)
Example:
P = ₹6000, SI = ₹1800, R = 6%. Time?
T = (1800 × 100)/(6000 × 6)
T = 180000/36000
T = 5 years ✓
P = ₹6000, SI = ₹1800, R = 6%. Time?
T = (1800 × 100)/(6000 × 6)
T = 180000/36000
T = 5 years ✓
Time Conversions (Important!)
SI formula เคฎें time เคนเคฎेเคถा YEARS เคฎें เคนोเคจा เคाเคนिเค!
Agar months เคฏा days เคฎें diya ho, convert karo:
Agar months เคฏा days เคฎें diya ho, convert karo:
| Given Time | Conversion to Years |
|---|---|
| Months | T = Months/12 |
| Days | T = Days/365 |
| Years + Months | T = Years + (Months/12) |
Example 1: 6 months = ?
T = 6/12 = 0.5 years ✓
Example 2: 2 years 3 months = ?
T = 2 + (3/12) = 2.25 years ✓
Example 3: 73 days = ?
T = 73/365 = 0.2 years ✓
T = 6/12 = 0.5 years ✓
Example 2: 2 years 3 months = ?
T = 2 + (3/12) = 2.25 years ✓
Example 3: 73 days = ?
T = 73/365 = 0.2 years ✓
Complete Problem:
P = ₹5000, R = 12% per year, T = 9 months. SI?
Step 1: Convert time
T = 9/12 = 0.75 years
Step 2: Calculate SI
SI = (5000 × 12 × 0.75)/100
SI = 45000/100
SI = ₹450 ✓
P = ₹5000, R = 12% per year, T = 9 months. SI?
Step 1: Convert time
T = 9/12 = 0.75 years
Step 2: Calculate SI
SI = (5000 × 12 × 0.75)/100
SI = 45000/100
SI = ₹450 ✓
Special Cases & Important Concepts
Case 1: When SI = Principal
Agar SI = P (amount doubles), toh:
Time = 100/R years
Time = 100/R years
Example:
Kitne years me amount double hoga at 5% SI?
T = 100/5 = 20 years ✓
Verification:
P = 100, R = 5%, T = 20
SI = (100 × 5 × 20)/100 = 100
Amount = 100 + 100 = 200 (doubled!) ✓
Kitne years me amount double hoga at 5% SI?
T = 100/5 = 20 years ✓
Verification:
P = 100, R = 5%, T = 20
SI = (100 × 5 × 20)/100 = 100
Amount = 100 + 100 = 200 (doubled!) ✓
Case 2: When Amount becomes n times
Agar Amount = n × P, toh:
Time = [(n - 1) × 100]/R
Time = [(n - 1) × 100]/R
Example:
8% SI pe kitne years me amount triple hoga?
n = 3 (triple)
T = [(3 - 1) × 100]/8
T = 200/8
T = 25 years ✓
8% SI pe kitne years me amount triple hoga?
n = 3 (triple)
T = [(3 - 1) × 100]/8
T = 200/8
T = 25 years ✓
Case 3: Two Different Rates
Example:
Ek person ne ₹5000 me se kuch amount 8% pe aur baki 10% pe invest kiya. Total SI 1 year me ₹460 mili. 10% pe kitna invest kiya?
Let 10% pe invested = x
8% pe invested = (5000 - x)
SI from 8% = (5000-x) × 8 × 1/100
SI from 10% = x × 10 × 1/100
Total SI = 460
(5000-x)×8/100 + x×10/100 = 460
40000 - 8x + 10x = 46000
2x = 6000
x = ₹3000 ✓
Ek person ne ₹5000 me se kuch amount 8% pe aur baki 10% pe invest kiya. Total SI 1 year me ₹460 mili. 10% pe kitna invest kiya?
Let 10% pe invested = x
8% pe invested = (5000 - x)
SI from 8% = (5000-x) × 8 × 1/100
SI from 10% = x × 10 × 1/100
Total SI = 460
(5000-x)×8/100 + x×10/100 = 460
40000 - 8x + 10x = 46000
2x = 6000
x = ₹3000 ✓
Case 4: SI on Two Different Principals
Example:
₹800 ka 3 years me SI = ₹144
Same rate pe ₹1200 ka 4 years me SI kya hoga?
Step 1: Rate nikalo
144 = (800 × R × 3)/100
R = 6%
Step 2: New SI calculate
SI = (1200 × 6 × 4)/100
SI = ₹288 ✓
₹800 ka 3 years me SI = ₹144
Same rate pe ₹1200 ka 4 years me SI kya hoga?
Step 1: Rate nikalo
144 = (800 × R × 3)/100
R = 6%
Step 2: New SI calculate
SI = (1200 × 6 × 4)/100
SI = ₹288 ✓
Ratio-Based SI Problems
Key Concept: SI is directly proportional to P, R, and T
SI₁/SI₂ = (P₁R₁T₁)/(P₂R₂T₂)
SI₁/SI₂ = (P₁R₁T₁)/(P₂R₂T₂)
Example:
Do sums ka ratio 2:3 hai. Rate 5% aur 4% hai. Time 4 years aur 5 years hai. SIs ka ratio?
SI₁/SI₂ = (P₁R₁T₁)/(P₂R₂T₂)
= (2 × 5 × 4)/(3 × 4 × 5)
= 40/60
= 2/3 ✓
Do sums ka ratio 2:3 hai. Rate 5% aur 4% hai. Time 4 years aur 5 years hai. SIs ka ratio?
SI₁/SI₂ = (P₁R₁T₁)/(P₂R₂T₂)
= (2 × 5 × 4)/(3 × 4 × 5)
= 40/60
= 2/3 ✓
SSC CGL Level Practice Questions
Q1. ₹4000 pe 5% SI, 3 years me kitna interest milega?
(A) ₹500
(B) ₹600
(C) ₹700
(D) ₹800
Answer: (B) ₹600
Solution:
SI = (4000 × 5 × 3)/100 = ₹600 ✓
(A) ₹500
(B) ₹600
(C) ₹700
(D) ₹800
Answer: (B) ₹600
Solution:
SI = (4000 × 5 × 3)/100 = ₹600 ✓
Q2. ₹5000 pe 2 years me SI = ₹800. Rate kya hai?
(A) 6%
(B) 7%
(C) 8%
(D) 10%
Answer: (C) 8%
Solution:
R = (800 × 100)/(5000 × 2)
R = 80000/10000 = 8% ✓
(A) 6%
(B) 7%
(C) 8%
(D) 10%
Answer: (C) 8%
Solution:
R = (800 × 100)/(5000 × 2)
R = 80000/10000 = 8% ✓
Q3. 10% SI pe kitne years me amount double hoga?
(A) 8 years
(B) 10 years
(C) 12 years
(D) 15 years
Answer: (B) 10 years
Solution:
T = 100/R = 100/10 = 10 years ✓
(A) 8 years
(B) 10 years
(C) 12 years
(D) 15 years
Answer: (B) 10 years
Solution:
T = 100/R = 100/10 = 10 years ✓
Q4. ₹6000 pe 6 months, 12% SI. Interest kitna?
(A) ₹300
(B) ₹360
(C) ₹400
(D) ₹450
Answer: (B) ₹360
Solution:
T = 6/12 = 0.5 years
SI = (6000 × 12 × 0.5)/100 = ₹360 ✓
(A) ₹300
(B) ₹360
(C) ₹400
(D) ₹450
Answer: (B) ₹360
Solution:
T = 6/12 = 0.5 years
SI = (6000 × 12 × 0.5)/100 = ₹360 ✓
Q5. Principal = ₹8000, Amount = ₹10,000, Time = 5 years. Rate?
(A) 4%
(B) 5%
(C) 6%
(D) 8%
Answer: (B) 5%
Solution:
SI = Amount - Principal = 10000 - 8000 = ₹2000
R = (2000 × 100)/(8000 × 5)
R = 200000/40000 = 5% ✓
(A) 4%
(B) 5%
(C) 6%
(D) 8%
Answer: (B) 5%
Solution:
SI = Amount - Principal = 10000 - 8000 = ₹2000
R = (2000 × 100)/(8000 × 5)
R = 200000/40000 = 5% ✓
Exam Shortcuts & Quick Tricks
๐ Trick 1: Mental Calculation for Simple Rates
10% of ₹1000 for 1 year = ₹100 (direct 10% calculation)
5% = half of 10%
20% = double of 10%
10% of ₹1000 for 1 year = ₹100 (direct 10% calculation)
5% = half of 10%
20% = double of 10%
๐ Trick 2: Doubling Time
Amount double hone ka time = 100/R
เคฏाเคฆ เคฐเคो: 5% → 20 years, 10% → 10 years, 20% → 5 years
Amount double hone ka time = 100/R
เคฏाเคฆ เคฐเคो: 5% → 20 years, 10% → 10 years, 20% → 5 years
๐ Trick 3: Quick Amount Calculation
Amount = P[1 + RT/100]
Example: ₹1000 at 10% for 2 years
= 1000[1 + 20/100] = 1000 × 1.2 = ₹1200
Amount = P[1 + RT/100]
Example: ₹1000 at 10% for 2 years
= 1000[1 + 20/100] = 1000 × 1.2 = ₹1200
๐ Trick 4: Percentage Method
3 years at 5% SI = 15% of Principal
Direct multiply: P × 0.15 = SI
3 years at 5% SI = 15% of Principal
Direct multiply: P × 0.15 = SI
Common Mistakes (เคฏे เคเคฒเคคिเคฏां เคฎเคค เคเคฐเคจा)
❌ Mistake 1: Time months เคฎें เคนोเคจे เคชเคฐ convert เคจ เคเคฐเคจा
Wrong: 6 months เคो directly use เคเคฐเคจा ✗
Right: 6/12 = 0.5 years convert เคเคฐो ✓
Wrong: 6 months เคो directly use เคเคฐเคจा ✗
Right: 6/12 = 0.5 years convert เคเคฐो ✓
❌ Mistake 2: SI เคเคฐ Amount confuse เคเคฐเคจा
SI = Interest only
Amount = Principal + Interest
Dono different hain!
SI = Interest only
Amount = Principal + Interest
Dono different hain!
❌ Mistake 3: Rate เคो decimal เคฎें directly use เคเคฐเคจा
Wrong: 5% = 0.05 direct formula เคฎें ✗
Right: Formula เคฎें 5 use เคเคฐो, /100 already hai ✓
Wrong: 5% = 0.05 direct formula เคฎें ✗
Right: Formula เคฎें 5 use เคเคฐो, /100 already hai ✓
❌ Mistake 4: Principal find เคเคฐเคคे waqt galat formula
Agar Amount diya ho toh: P = (A × 100)/(100 + RT)
Sirf SI diya ho toh: P = (SI × 100)/(RT)
Agar Amount diya ho toh: P = (A × 100)/(100 + RT)
Sirf SI diya ho toh: P = (SI × 100)/(RT)
Homework Practice (เคुเคฆ Try เคเคฐो)
- ₹7500 pe 8% SI, 4 years เคฎें เคिเคคเคจा interest?
- SI = ₹1200, Rate = 6%, Time = 5 years. Principal?
- ₹10,000 pe 9 months, 16% SI. Total amount?
- 6% SI เคชे เคिเคคเคจे years เคฎें amount triple เคนोเคा?
- Principal = ₹5000, Amount = ₹6500, Time = 3 years. Rate เคจिเคाเคฒो
Quick Reference - All Formulas
Main Formulas:
SI = (P × R × T)/100
Amount = P + SI
Amount = P[1 + (RT)/100]
Finding Values:
P = (SI × 100)/(R × T)
R = (SI × 100)/(P × T)
T = (SI × 100)/(P × R)
Special:
Doubling time = 100/R
Tripling time = 200/R
n times = [(n-1) × 100]/R
SI = (P × R × T)/100
Amount = P + SI
Amount = P[1 + (RT)/100]
Finding Values:
P = (SI × 100)/(R × T)
R = (SI × 100)/(P × T)
T = (SI × 100)/(P × R)
Special:
Doubling time = 100/R
Tripling time = 200/R
n times = [(n-1) × 100]/R
Next Topic Preview
๐ เค
เคเคฒे Post เคฎें: 2.6 Compound Interest (เคเค्เคฐเคตृเคฆ्เคงि เคฌ्เคฏाเค)
CI formulas, SI vs CI difference, compound interest annually/half-yearly/quarterly, เคเคฐ SSC level questions!
CI เคฎें SI เคे concepts directly use เคนोंเคे, isliye aaj ka topic clear เคฐเคो!
CI formulas, SI vs CI difference, compound interest annually/half-yearly/quarterly, เคเคฐ SSC level questions!
CI เคฎें SI เคे concepts directly use เคนोंเคे, isliye aaj ka topic clear เคฐเคो!
Conclusion
Simple Interest SSC CGL เคा scoring topic เคนै। Formula เคธीเคงा เคนै เคเคฐ calculation เคญी เคเคธाเคจ। P, R, T เคฎें เคธे koi bhi find เคเคฐเคจा ho, formula directly apply เคนोเคคा เคนै। Time conversion เคฏाเคฆ เคฐเคो - months เคो years เคฎें convert เคเคฐเคจा เค़เคฐूเคฐी เคนै!
Practice Strategy: Daily 15-20 SI problems solve เคเคฐो। Different types practice เคเคฐो - basic calculations, finding P/R/T, amount problems, ratio-based questions। Calculator เคे เคฌिเคจा practice เคเคฐो เคคाเคि exam เคฎें speed เค เค्เคी เคนो!
✅ Post Complete!
Chapter 2: Arithmetic - 5/20 done (25% - Quarter Complete! ๐)
Total Progress: 17/76 posts complete (22.4%)
Next: 2.6 Compound Interest ๐ฏ
Chapter 2: Arithmetic - 5/20 done (25% - Quarter Complete! ๐)
Total Progress: 17/76 posts complete (22.4%)
Next: 2.6 Compound Interest ๐ฏ