Q1): An item is given two successive discounts of 20% and 10%. What is the single equivalent discount?
A) 28%
B) 30%
C) 32%
D) 18%
Answer: A) 28%
Explanation:
- Step 1: Successive discounts apply on the reduced price.
- Step 2: Remaining after 20% discount = 80% = 0.80.
- Step 3: Remaining after 10% discount = 90% = 0.90.
- Step 4: Combined remaining = 0.80 × 0.90 = 0.72 = 72%.
- Final: Equivalent discount = 100% − 72% = 28%, so option A is correct.
Q2): After a 25% discount, a jacket is sold for ₹900. What was its marked price?
A) ₹1100
B) ₹1150
C) ₹1200
D) ₹1250
Answer: C) ₹1200
Explanation:
- Step 1: After 25% discount, selling price is 75% of marked price.
- Step 2: So, 0.75 × MP = 900.
- Step 3: MP = 900 ÷ 0.75.
- Step 4: 900 ÷ 0.75 = 1200.
- Final: Marked price is ₹1200, so option C is correct.
Q3): A price is increased by 15% and then discounted by 10% on the increased price. What is the net percentage change?
A) 3.5% increase
B) 5% increase
C) 1.5% decrease
D) No change
Answer: A) 3.5% increase
Explanation:
- Step 1: Increase by 15% means multiply by 1.15.
- Step 2: Discount by 10% means multiply by 0.90.
- Step 3: Net factor = 1.15 × 0.90 = 1.035.
- Step 4: 1.035 means final is 103.5% of original.
- Final: Net change = 103.5% − 100% = 3.5% increase, so option A is correct.
Q4): 40% of a number is 96. What is the number?
A) 220
B) 240
C) 260
D) 280
Answer: B) 240
Explanation:
- Step 1: Let the number be N.
- Step 2: 40% of N = 96 means 0.40N = 96.
- Step 3: N = 96 ÷ 0.40.
- Step 4: 96 ÷ 0.40 = 240.
- Final: The number is 240, so option B is correct.
Q5): A is 25% more than B. B is what percent less than A?
A) 15%
B) 20%
C) 25%
D) 30%
Answer: B) 20%
Explanation:
- Step 1: “A is 25% more than B” means A = 1.25B.
- Step 2: So B = A ÷ 1.25.
- Step 3: A ÷ 1.25 = 0.8A, so B is 80% of A.
- Step 4: Decrease from A to B = 100% − 80% = 20%.
- Final: B is 20% less than A, so option B is correct.
Q6): A person spends 30% of salary on rent and 20% on food. If the remaining amount is ₹25,200, what is the salary?
A) ₹45,000
B) ₹50,400
C) ₹52,000
D) ₹56,000
Answer: B) ₹50,400
Explanation:
- Step 1: Total spent = 30% + 20% = 50%.
- Step 2: Remaining = 100% − 50% = 50% of salary.
- Step 3: 50% of salary = 25,200 means 0.5S = 25,200.
- Step 4: S = 25,200 ÷ 0.5 = 50,400.
- Final: Salary is ₹50,400, so option B is correct.
Q7): The selling price of an item is ₹720 after a discount of 28%. Find the marked price.
A) ₹900
B) ₹950
C) ₹1000
D) ₹1050
Answer: C) ₹1000
Explanation:
- Step 1: Discount 28% means customer pays 72% of marked price.
- Step 2: So, 0.72 × MP = 720.
- Step 3: MP = 720 ÷ 0.72.
- Step 4: 720 ÷ 0.72 = 1000.
- Final: Marked price is ₹1000, so option C is correct.
Q8): Successive discounts of 12% and 8% are given. What is the equivalent single discount (approx.)?
A) 19.04%
B) 20.00%
C) 18.00%
D) 16.00%
Answer: A) 19.04%
Explanation:
- Step 1: Remaining after 12% discount = 88% = 0.88.
- Step 2: Remaining after 8% discount = 92% = 0.92.
- Step 3: Combined remaining = 0.88 × 0.92 = 0.8096 = 80.96%.
- Step 4: Equivalent discount = 100% − 80.96% = 19.04%.
- Final: Equivalent discount is 19.04%, so option A is correct.
Q9): A value is decreased by 10% and then increased by 10%. What is the net change?
A) 1% increase
B) 1% decrease
C) No change
D) 2% decrease
Answer: B) 1% decrease
Explanation:
- Step 1: Decrease by 10% means multiply by 0.90.
- Step 2: Increase by 10% means multiply by 1.10.
- Step 3: Net factor = 0.90 × 1.10 = 0.99.
- Step 4: 0.99 means final is 99% of original.
- Final: Net change = 1% decrease, so option B is correct.
Q10): A shopkeeper sells an item for ₹1500 after giving a discount of 25% on marked price. What is the marked price?
A) ₹1800
B) ₹1900
C) ₹2000
D) ₹2100
Answer: C) ₹2000
Explanation:
- Step 1: After 25% discount, selling price is 75% of marked price.
- Step 2: So, 0.75 × MP = 1500.
- Step 3: MP = 1500 ÷ 0.75.
- Step 4: 1500 ÷ 0.75 = 2000.
- Final: Marked price is ₹2000, so option C is correct.
Q11): The number of students increases from 50 to 65. Find the percentage increase.
A) 25%
B) 30%
C) 35%
D) 40%
Answer: B) 30%
Explanation:
- Step 1: Increase = 65 − 50 = 15.
- Step 2: Percentage increase = (Increase/Original) × 100.
- Step 3: (15/50) × 100 = 0.30 × 100.
- Step 4: 0.30 × 100 = 30%.
- Final: Percentage increase is 30%, so option B is correct.
Q12): Last year’s marks were 450. This year the marks are 20% less. What are this year’s marks?
A) 340
B) 350
C) 360
D) 370
Answer: C) 360
Explanation:
- Step 1: 20% less means this year is 80% of last year.
- Step 2: This year’s marks = 0.80 × 450.
- Step 3: 0.80 × 450 = 360.
- Step 4: 360 matches the required reduced value.
- Final: This year’s marks are 360, so option C is correct.
Q13): 70% of a number is 80 more than 30% of the same number. Find the number.
A) 180
B) 200
C) 220
D) 240
Answer: B) 200
Explanation:
- Step 1: Let the number be N.
- Step 2: Given 0.70N = 0.30N + 80.
- Step 3: Subtract 0.30N: 0.40N = 80.
- Step 4: N = 80 ÷ 0.40 = 200.
- Final: The number is 200, so option B is correct.
Q14): A bill becomes ₹1050 after adding 5% extra charges. What was the original bill?
A) ₹950
B) ₹980
C) ₹1000
D) ₹1020
Answer: C) ₹1000
Explanation:
- Step 1: Adding 5% means final = 105% of original.
- Step 2: So, 1.05 × Original = 1050.
- Step 3: Original = 1050 ÷ 1.05.
- Step 4: 1050 ÷ 1.05 = 1000.
- Final: Original bill is ₹1000, so option C is correct.
Q15): In a class, 40% are girls. If there are 18 girls, what is the total number of students?
A) 40
B) 45
C) 48
D) 50
Answer: B) 45
Explanation:
- Step 1: Let total students be T.
- Step 2: 40% of T = 18 means 0.40T = 18.
- Step 3: T = 18 ÷ 0.40.
- Step 4: 18 ÷ 0.40 = 45.
- Final: Total students are 45, so option B is correct.
Q16): Three successive discounts of 10%, 10%, and 10% are given. What is the equivalent single discount (approx.)?
A) 27.1%
B) 30%
C) 25%
D) 21%
Answer: A) 27.1%
Explanation:
- Step 1: Each 10% discount leaves 90% = 0.90.
- Step 2: Combined remaining = 0.90 × 0.90 × 0.90 = 0.729.
- Step 3: 0.729 means 72.9% of the original remains.
- Step 4: Equivalent discount = 100% − 72.9% = 27.1%.
- Final: Equivalent discount is about 27.1%, so option A is correct.
Q17): A price is reduced by 20%. By what percent should the reduced price be increased to get back the original price?
A) 20%
B) 22%
C) 25%
D) 30%
Answer: C) 25%
Explanation:
- Step 1: After 20% reduction, price becomes 80% of original.
- Step 2: To return to 100%, increase needed is on the reduced base (80%).
- Step 3: Required increase% = (20/80) × 100.
- Step 4: (20/80) × 100 = (1/4) × 100 = 25%.
- Final: Increase needed is 25%, so option C is correct.
Q18): Marked price is ₹1500. A discount of 20% is given, then 5% tax is added on the discounted price. What is the final amount paid?
A) ₹1200
B) ₹1250
C) ₹1260
D) ₹1300
Answer: C) ₹1260
Explanation:
- Step 1: After 20% discount, price becomes 80% of 1500.
- Step 2: Discounted price = 0.80 × 1500 = 1200.
- Step 3: Add 5% tax on 1200 means multiply by 1.05.
- Step 4: Final amount = 1200 × 1.05 = 1260.
- Final: Amount paid is ₹1260, so option C is correct.
Q19): A shopkeeper marks an item 25% above cost price and then gives a 10% discount on the marked price. What is the profit percent?
A) 10%
B) 12.5%
C) 15%
D) 17.5%
Answer: B) 12.5%
Explanation:
- Step 1: Let cost price be 100.
- Step 2: Marked price = 100 × 1.25 = 125.
- Step 3: After 10% discount, selling price = 125 × 0.90 = 112.5.
- Step 4: Profit = 112.5 − 100 = 12.5 on base 100.
- Final: Profit percent = 12.5%, so option B is correct.
Q20): Pass percentage rises from 60% to 75%. What is the percent increase in pass percentage (not percentage points)?
A) 20%
B) 25%
C) 30%
D) 15%
Answer: B) 25%
Explanation:
- Step 1: Old pass% = 60, new pass% = 75.
- Step 2: Increase = 75 − 60 = 15 (percentage points).
- Step 3: Percent increase = (Increase/Old) × 100.
- Step 4: (15/60) × 100 = (1/4) × 100 = 25%.
- Final: Percent increase is 25%, so option B is correct.