Q1): Find the simple interest on ₹5,000 at 6% per annum for 2 years.
A) ₹500
B) ₹600
C) ₹650
D) ₹700
Answer: B) ₹600
Explanation:
- Step 1: Formula: SI = (P × R × T) / 100
- Step 2: Symbols: P = principal, R = rate (% p.a.), T = time (years)
- Step 3: Substitute: SI = (5000 × 6 × 2) / 100
- Step 4: Calculate: 5000×12 = 60000; 60000/100 = 600
- Final: SI = ₹600, so option B is correct
Q2): The amount on ₹8,000 at 5% per annum simple interest for 3 years is:
A) ₹8,800
B) ₹9,000
C) ₹9,200
D) ₹9,600
Answer: C) ₹9,200
Explanation:
- Step 1: Formula: SI = (P × R × T) / 100
- Step 2: Symbols: P = 8000, R = 5, T = 3
- Step 3: SI = (8000 × 5 × 3) / 100 = 1200
- Step 4: Amount formula: A = P + SI = 8000 + 1200
- Final: A = ₹9,200, so option C is correct
Q3): Simple interest is ₹450 on a sum at 9% per annum for 1 year. The principal is:
A) ₹4,500
B) ₹5,000
C) ₹5,500
D) ₹6,000
Answer: B) ₹5,000
Explanation:
- Step 1: Formula: SI = (P × R × T) / 100
- Step 2: Rearrange: P = (SI × 100) / (R × T)
- Step 3: Substitute: P = (450 × 100) / (9 × 1)
- Step 4: Calculate: 45000/9 = 5000
- Final: P = ₹5,000, so option B is correct
Q4): The simple interest on ₹6,000 for 2 years is ₹720. The rate of interest is:
A) 5%
B) 6%
C) 7%
D) 8%
Answer: B) 6%
Explanation:
- Step 1: Formula: SI = (P × R × T) / 100
- Step 2: Rearrange: R = (SI × 100) / (P × T)
- Step 3: Substitute: R = (720 × 100) / (6000 × 2)
- Step 4: Calculate: 72000/12000 = 6
- Final: R = 6% p.a., so option B is correct
Q5): The simple interest on ₹2,000 at 5% per annum is ₹300. The time period is:
A) 2 years
B) 3 years
C) 4 years
D) 5 years
Answer: B) 3 years
Explanation:
- Step 1: Formula: SI = (P × R × T) / 100
- Step 2: Rearrange: T = (SI × 100) / (P × R)
- Step 3: Substitute: T = (300 × 100) / (2000 × 5)
- Step 4: Calculate: 30000/10000 = 3
- Final: T = 3 years, so option B is correct
Q6): Find the simple interest on ₹2,400 at 10% per annum for 9 months.
A) ₹160
B) ₹180
C) ₹200
D) ₹240
Answer: B) ₹180
Explanation:
- Step 1: Convert time: 9 months = 9/12 years = 0.75 years
- Step 2: Formula: SI = (P × R × T) / 100
- Step 3: Substitute: SI = (2400 × 10 × 0.75) / 100
- Step 4: Calculate: 2400×7.5 = 18000; 18000/100 = 180
- Final: SI = ₹180, so option B is correct
Q7): A machine worth ₹20,000 depreciates at 5% per annum (simple depreciation) for 2 years. Its value becomes:
A) ₹17,500
B) ₹18,000
C) ₹18,500
D) ₹19,000
Answer: B) ₹18,000
Explanation:
- Step 1: Simple depreciation works like simple interest (decrease)
- Step 2: Decrease = (P × R × T) / 100
- Step 3: Decrease = (20000 × 5 × 2) / 100 = 2000
- Step 4: New value = 20000 − 2000
- Final: Value = ₹18,000, so option B is correct
Q8): Find the compound interest on ₹10,000 at 10% per annum for 1 year.
A) ₹900
B) ₹1,000
C) ₹1,100
D) ₹1,200
Answer: B) ₹1,000
Explanation:
- Step 1: For 1 year, CI = interest for that year
- Step 2: Formula (amount): A = P(1 + R/100)^T
- Step 3: A = 10000(1 + 10/100)^1 = 10000 × 1.10 = 11000
- Step 4: CI = A − P = 11000 − 10000
- Final: CI = ₹1,000, so option B is correct
Q9): The compound amount on ₹5,000 at 10% per annum for 2 years is:
A) ₹6,000
B) ₹6,050
C) ₹6,100
D) ₹6,200
Answer: B) ₹6,050
Explanation:
- Step 1: Formula: A = P(1 + R/100)^T
- Step 2: Symbols: P = 5000, R = 10, T = 2
- Step 3: A = 5000(1.10)^2 = 5000 × 1.21
- Step 4: Calculate: 5000 × 1.21 = 6050
- Final: Amount = ₹6,050, so option B is correct
Q10): Find the compound interest on ₹4,000 at 5% per annum for 2 years.
A) ₹400
B) ₹405
C) ₹410
D) ₹420
Answer: C) ₹410
Explanation:
- Step 1: Formula: A = P(1 + R/100)^T
- Step 2: A = 4000(1.05)^2 = 4000 × 1.1025
- Step 3: Calculate amount: A = 4410
- Step 4: CI = A − P = 4410 − 4000
- Final: CI = ₹410, so option C is correct
Q11): For 2 years, CI exceeds SI by ₹80 at 10% per annum. The principal is:
A) ₹6,000
B) ₹7,000
C) ₹8,000
D) ₹9,000
Answer: C) ₹8,000
Explanation:
- Step 1: For 2 years: CI − SI = P × (R/100)^2
- Step 2: Symbols: P = principal, R = rate
- Step 3: 80 = P × (10/100)^2 = P × (0.1)^2 = P × 0.01
- Step 4: P = 80 / 0.01 = 8000
- Final: P = ₹8,000, so option C is correct
Q12): For 2 years at 4% per annum, compound interest exceeds simple interest on ₹2,500 by:
A) ₹2
B) ₹3
C) ₹4
D) ₹5
Answer: C) ₹4
Explanation:
- Step 1: For 2 years: CI − SI = P × (R/100)^2
- Step 2: P = 2500, R = 4
- Step 3: CI − SI = 2500 × (4/100)^2 = 2500 × (0.04)^2
- Step 4: (0.04)^2 = 0.0016; 2500 × 0.0016 = 4
- Final: Difference = ₹4, so option C is correct
Q13): ₹10,000 becomes ₹12,100 in 2 years at compound interest (annual). The rate is:
A) 8%
B) 9%
C) 10%
D) 11%
Answer: C) 10%
Explanation:
- Step 1: Formula: A = P(1 + R/100)^2
- Step 2: Divide both sides by P: A/P = (1 + R/100)^2
- Step 3: A/P = 12100/10000 = 1.21
- Step 4: √1.21 = 1.10 ⇒ 1 + R/100 = 1.10 ⇒ R = 10
- Final: Rate = 10% p.a., so option C is correct
Q14): The compound amount after 2 years at 10% per annum is ₹2,420. The principal is:
A) ₹1,800
B) ₹2,000
C) ₹2,200
D) ₹2,400
Answer: B) ₹2,000
Explanation:
- Step 1: Formula: A = P(1 + R/100)^T
- Step 2: Here, R = 10 and T = 2 ⇒ A = P(1.10)^2 = P × 1.21
- Step 3: So, P = A/1.21 = 2420/1.21
- Step 4: 1.21 × 2000 = 2420, so P = 2000
- Final: Principal = ₹2,000, so option B is correct
Q15): Find the compound interest on ₹1,000 at 10% per annum for 3 years.
A) ₹300
B) ₹310
C) ₹331
D) ₹350
Answer: C) ₹331
Explanation:
- Step 1: Formula: A = P(1 + R/100)^T
- Step 2: A = 1000(1.10)^3
- Step 3: (1.10)^3 = 1.331, so A = 1000 × 1.331 = 1331
- Step 4: CI = A − P = 1331 − 1000
- Final: CI = ₹331, so option C is correct
Q16): The compound amount on ₹5,000 at 20% per annum for 2 years is:
A) ₹6,800
B) ₹7,000
C) ₹7,200
D) ₹7,500
Answer: C) ₹7,200
Explanation:
- Step 1: Formula: A = P(1 + R/100)^T
- Step 2: A = 5000(1.20)^2
- Step 3: (1.20)^2 = 1.44
- Step 4: A = 5000 × 1.44 = 7200
- Final: Amount = ₹7,200, so option C is correct
Q17): ₹2,000 is invested at 10% for the first year and 5% for the second year (compounded yearly). The compound interest is:
A) ₹300
B) ₹310
C) ₹320
D) ₹330
Answer: B) ₹310
Explanation:
- Step 1: Successive compounding: A = P(1 + r1)(1 + r2)
- Step 2: Symbols: P = 2000, r1 = 10% = 0.10, r2 = 5% = 0.05
- Step 3: A = 2000 × 1.10 × 1.05 = 2000 × 1.155
- Step 4: A = 2310, so CI = 2310 − 2000 = 310
- Final: Compound interest = ₹310, so option B is correct
Q18): Compound interest for 1 year on a sum at 9% per annum is ₹450. The principal is:
A) ₹4,500
B) ₹5,000
C) ₹5,500
D) ₹6,000
Answer: B) ₹5,000
Explanation:
- Step 1: For 1 year: CI = (P × R) / 100
- Step 2: Rearrange: P = (CI × 100) / R
- Step 3: Substitute: P = (450 × 100) / 9
- Step 4: Calculate: 45000/9 = 5000
- Final: Principal = ₹5,000, so option B is correct
Q19): Which statement is always true for a positive rate of interest?
A) SI is always greater than CI
B) CI is always less than SI for 2 years
C) CI is greater than SI when time is more than 1 year
D) SI and CI are never equal
Answer: C) CI is greater than SI when time is more than 1 year
Explanation (Line-by-Line):
- Step 1: For 1 year, SI and CI give the same interest (no “interest on interest” yet)
- Step 2: From the 2nd year onward, CI adds interest on the previous year’s interest
- Step 3: That extra “interest on interest” makes CI larger than SI for the same P, R, T (> 1 year)
- Step 4: Example idea: in CI, the base increases after year 1; in SI, base stays the same
- Final: So, statement C is always true for positive rate
Q20): A sum becomes ₹6,050 in 2 years at 10% compound interest (annual). The principal is:
A) ₹4,500
B) ₹5,000
C) ₹5,500
D) ₹6,000
Answer: B) ₹5,000
Explanation:
- Step 1: Formula: A = P(1 + R/100)^T
- Step 2: Here, R = 10 and T = 2 ⇒ A = P(1.10)^2 = P × 1.21
- Step 3: So, P = A/1.21 = 6050/1.21
- Step 4: 1.21 × 5000 = 6050, so P = 5000
- Final: Principal = ₹5,000, so option B is correct