Simple Math Tricks with Solved Questions
1. Multiply by 11 quickly
1: 32 × 11 = ?
Trick: Add the digits and place in the middle.
3 _ 2 → (3 + 2 = 5) → 352
Answer: 352
2. Multiply by 5 easily
2: 48 × 5 = ?
Trick: Half the number and add a zero.
48 ÷ 2 = 24 → add 0 → 240
Answer: 240
3. Square a number ending in 5
3: 75² = ?
Trick: Take first digit (7), multiply by (7+1) → 7 × 8 = 56
Then add 25 → 5625
Answer: 5625
4. Divisibility by 9 check
4: Is 738 divisible by 9?
Trick: Add digits → 7 + 3 + 8 = 18 → 18 divisible by 9 → Yes
Answer: Yes, 738 ÷ 9 = 82
5. Multiplying by 99
5: 47 × 99 = ?
Trick: 47 × (100 – 1) = (4700 – 47) = 4653
Answer: 4653
6. Multiply even number by 6
6: 26 × 6 = ?
Trick: Half the number and put 0, then add the number.
26 ÷ 2 = 13 → 130 → +26 = 156
Answer: 156
7. Multiplying by 25
7: 64 × 25 = ?
Trick: Divide by 4 and add 2 zeros.
64 ÷ 4 = 16 → 1600
Answer: 1600
8. Checking divisibility by 11
8: Is 473 divisible by 11?
Trick: (Sum of odd digits – Sum of even digits).
(4 + 3) – (7) = 7 – 7 = 0 → divisible
Answer: Yes, 473 ÷ 11 = 43
9. Fast subtraction from 1000
9: 1000 – 487 = ?
Trick: Subtract each digit from 9, last digit from 10.
→ 1000 – 487 = (9–4)(9–8)(10–7) = 513
Answer: 513
10. Multiply by 15 quickly
10: 48 × 15 = ?
Trick: Multiply by 10 + half the number × 10.
48 × 10 = 480
Half of 48 = 24 → ×10 = 240
480 + 240 = 720
Answer: 720
📐 Areas of 2D Shapes with Examples
1. Square
Formula: Area = side × side
1: Find area of square with side 8 cm.
Solution: 8 × 8 = 64 cm²
2: Rectangle
Formula: Area = length × breadth
2: Length = 12 cm, breadth = 5 cm
Solution: 12 × 5 = 60 cm²
3. Triangle
Formula: Area = ½ × base × height
3: Base = 10 cm, height = 6 cm
Solution: ½ × 10 × 6 = 30 cm²
4. Parallelogram
Formula: Area = base × height
4: Base = 15 cm, height = 8 cm
Solution: 15 × 8 = 120 cm²
5. Rhombus
Formula: Area = ½ × d₁ × d₂
5: Diagonals = 10 cm, 8 cm
Solution: ½ × 10 × 8 = 40 cm²
6. Trapezium (Trapezoid)
Formula: Area = ½ × (a + b) × h
(a, b = parallel sides)
6: a = 12 cm, b = 8 cm, h = 5 cm
Solution: ½ × (12 + 8) × 5 = 50 cm²
7. Circle
Formula: Area = πr²
7: Radius = 7 cm, take π = 22/7
Solution: 22/7 × 7 × 7 = 154 cm²
8. Semi-Circle
Formula: Area = ½ × πr²
8: r = 14 cm
Solution: ½ × 22/7 × 14 × 14 = 308 cm²
9. Ellipse
Formula: Area = πab
(a = semi-major axis, b = semi-minor axis)
9: a = 6 cm, b = 4 cm
Solution: 3.14 × 6 × 4 ≈ 75.36 cm²
10. Sector of Circle
Formula: Area = (θ/360) × πr²
10: r = 10 cm, θ = 90°
Solution: (90/360) × 3.14 × 10² = 78.5 cm²
Practical Life Math Tricks & Solutions
1. Percentage to Find Discount
1: A shirt costs ₹800. Discount = 25%. Find price.
Answer: 25% of 800 = 800 × 25/100 = 200.
Price = 800 – 200 = ₹600
2. Fast Tip Calculation (10%, 5%)
2: Restaurant bill = ₹560. Want to give 10% tip.
Answer: Shift decimal → 560 → 56.
Tip = ₹56
(For 5%, take half of 10% → 28)
3. Simple Interest (SI)
Formula: SI = (P × R × T) / 100
3: ₹5000 at 8% for 2 years.
Solution: (5000 × 8 × 2)/100 = ₹800
4. Compound Interest (CI)
Formula: A = P(1 + R/100)ⁿ
4: ₹1000 at 10% for 2 years.
A = 1000(1.1)² = 1210 → CI = 1210 – 1000 = ₹210
5. Unitary Method (Daily Rates)
5: 5 pens = ₹75. Cost of 1 pen?
75 ÷ 5 = ₹15
Cost of 12 pens = 15 × 12 = ₹180
6. Fast Square Trick
6: 47² = ?
Trick: (50 – 3)² = 50² – (2×50×3) + 3²
= 2500 – 300 + 9 = 2209
7. Time & Work
7: A can do a job in 10 days. B in 20 days. Together?
Work/day = 1/10 + 1/20 = 3/20.
So time = 20/3 = 6.67 days
8. Speed, Distance, Time
Formula: Speed = Distance ÷ Time
8: Distance = 180 km, Time = 3 hr.
Speed = 180 ÷ 3 = 60 km/h
9. Quick Multiplication by 25
9: 84 × 25 = ?
Trick: Divide by 4 → 84 ÷ 4 = 21 → add “00” → 2100
10. Rule of 72 (Money Doubling)
10: At 12% interest, how many years to double money?
72 ÷ 12 = 6 years
11. Ratio in Cooking
11: Rice:Water = 1:2. If rice = 3 cups?
Water = 6 cups
12. Currency Conversion (Estimation)
12: $1 = ₹83. How much is $120?
Trick: 120 × 80 = 9600 (approx),
120 × 3 = 360 → 9960
1. Shopping Discount
A jacket costs ₹1200. Shopkeeper gives 20% discount. What is the selling price?
Solution:
20% of 1200 = 1200 × 20/100 = 240
Selling Price = 1200 – 240 = ₹960
2. Restaurant Bill (Tip)
A bill is ₹750. You want to give a 10% tip. How much?
Solution:
10% of 750 = 750 ÷ 10 = ₹75
3. Simple Interest
Principal = ₹4000, Rate = 9% per year, Time = 3 years. Find SI.
Solution:
SI = (P × R × T) / 100
= (4000 × 9 × 3)/100 = 1080
SI = ₹1080
4. Compound Interest
₹2000 at 5% compound interest for 2 years. Find CI.
Solution:
A = P(1 + R/100)² = 2000(1.05)² = 2000 × 1.1025 = 2205
CI = A – P = 2205 – 2000 = ₹205
5. Unitary Method (Shopping)
If 6 apples cost ₹150, what is the cost of 15 apples?
Solution:
1 apple = 150 ÷ 6 = 25
15 apples = 25 × 15 = ₹375
6. Time & Work
A can finish a job in 12 days. B can do it in 18 days. How many days together?
Solution:
Work per day = 1/12 + 1/18 = (3 + 2)/36 = 5/36
Total time = 36/5 = 7.2 days
7. Speed, Distance, Time
A car travels 240 km in 4 hours. Find its speed.
Solution:
Speed = Distance ÷ Time = 240 ÷ 4 = 60 km/h
8. Cooking Ratio
Milk:Water = 3:1. If you need 12 liters mixture, how much milk and water?
Solution:
Total parts = 3 + 1 = 4
Milk = (3/4) × 12 = 9 L
Water = (1/4) × 12 = 3 L
Milk = 9 L, Water = 3 L
9. Rule of 72 (Money Doubling)
At 8% interest, in how many years will money double?
Solution:
72 ÷ 8 = 9 years
10. Currency Conversion
$1 = ₹83. Find value of $250.
Solution:
250 × 83 = 250 × (80 + 3)
= 250 × 80 + 250 × 3
= 20,000 + 750 = ₹20,750
More daily life related maths trics
Shopping & Money
1. A mobile costs ₹15,000. Shopkeeper offers 10% discount. Find final price.
Ans: 10% of 15,000 = 1500 → 15,000 – 1500 = ₹13,500
2. A shirt is ₹1200. GST = 5%. Find total price.
Ans: 5% of 1200 = 60 → 1200 + 60 = ₹1260
3. 3 kg apples cost ₹240. What is cost of 7 kg?
Ans: 240 ÷ 3 = 80 per kg → 80 × 7 = ₹560
Bank & Interest
4. Deposit = ₹10,000 at 6% simple interest for 2 years. Find SI.
Ans: (10000 × 6 × 2)/100 = ₹1200
5. ₹5000 at 10% compound interest for 2 years.
Ans: A = 5000(1.1)² = 5000 × 1.21 = 6050 → CI = 6050 – 5000 = ₹1050
Speed, Distance & Time
6. A train travels 300 km in 5 hrs. Speed?
Ans: 300 ÷ 5 = 60 km/h
7. Speed = 50 km/h, Time = 6 hrs. Distance?
Ans: 50 × 6 = 300 km
8. Distance = 180 km, Speed = 60 km/h. Time?
Ans: 180 ÷ 60 = 3 hrs
Work & Ratio
9. A does a job in 15 days, B in 30 days. Together?
Ans: 1/15 + 1/30 = 3/30 = 1/10 → 10 days
10. Divide ₹1200 between A:B = 2:3.
Ans: Total = 5 parts → A = 480, B = 720
11. In a recipe, flour: sugar = 4:1. If sugar = 200 g, how much flour?
Ans: Flour = 4 × 200 = 800 g
Geometry in Life
12. Square garden side = 20 m. Area?
Ans: 20 × 20 = 400 m²
13. Circular park radius = 7 m. Area? (π = 22/7)
Ans: 22/7 × 7 × 7 = 154 m²
14. Rectangle floor = 12 m × 8 m. Tiles area = 1 m². How many tiles?
Ans: 12 × 8 = 96 tiles
Daily Calculations
15. A fan costs ₹2400. EMI = 12 months, no interest. Monthly payment?
Ans: 2400 ÷ 12 = ₹200
16. A student scored 360 out of 500. Find percentage.
Ans: (360/500) × 100 = 72%
17. A shopkeeper buys at ₹500, sells at ₹650. Profit%?
Ans: Profit = 650 – 500 = 150 → (150/500) × 100 = 30%
18. Electricity bill: 250 units @ ₹6 per unit. Find cost.
Ans: 250 × 6 = ₹1500
19. Petrol = ₹105 per litre. Cost of 12 litres?
Ans: 105 × 12 = ₹1260
20. A TV price = ₹20,000. After 1 year value drops 15%. Find resale value.
Ans: 15% of 20000 = 3000 → 20000 – 3000 = ₹17,000
Shopping / Discounts
1. A bag costs ₹2400. Festival discount = 15%. What is the new price?
Ans: 15% of 2400 = 360 → 2400 – 360 = ₹2040
2. A shopkeeper marks an item ₹500, gives 10% discount. What is selling price?
Ans: 10% of 500 = 50 → 500 – 50 = ₹450
Money & Banking
3. ₹8000 at 7% simple interest for 4 years. Find SI.
Ans: (8000 × 7 × 4)/100 = ₹2240
4. ₹4000 at 5% compound interest for 3 years. Find CI.
Ans: A = 4000(1.05)³ = 4000 × 1.157625 = 4630.5
CI = 4630.5 – 4000 = ₹630.5
Profit & Loss
5. A cycle bought for ₹2000, sold for ₹2500. Profit%?
Ans: Profit = 500 → (500/2000)×100 = 25%
6. A watch costs ₹1500, sold at ₹1200. Find loss%.
Ans: Loss = 300 → (300/1500)×100 = 20%
Time & Work
7. A can finish work in 20 days, B in 30 days. Together?
Ans: 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12
Time = 12 days
8. If 10 workers finish a job in 8 days, how long for 5 workers?
Ans: Work = 10×8 = 80 worker-days.
For 5 workers: 80/5 = 16 days
Speed, Distance, Time
9. A bike runs 180 km in 3 hours. Find speed.
Ans: 180 ÷ 3 = 60 km/h
10. Train speed = 90 km/h, time = 2 hrs 30 min. Distance?
Ans: 2.5 hrs × 90 = 225 km
Geometry / Measurement
11. A rectangular field 40 m × 25 m. Area?
Ans: 40 × 25 = 1000 m²
12. Circle radius = 14 cm. Find circumference (π=22/7).
Ans: 2πr = 2×22/7×14 = 88 cm
13. A room is 5 m × 4 m. How many 1 m² tiles needed?
Ans: 5 × 4 = 20 tiles
Daily Life Calculations
14. Petrol ₹105 per litre. Find cost of 20 litres.
Ans: 105 × 20 = ₹2100
15. A man earns ₹18,000 per month. Monthly expenses ₹14,500. Savings?
Ans: 18000 – 14500 = ₹3500
16. Student scored 425 marks out of 600. Find % score.
Ans: (425/600) × 100 = 70.8%
17. A bill = ₹950. GST = 12%. Find final price.
Ans: 12% of 950 = 114 → 950 + 114 = ₹1064
Conversions
18. Convert 2.5 kg into grams.
Ans: 2.5 × 1000 = 2500 g
19. Convert 5 km into meters.
Ans: 5 × 1000 = 5000 m
20. $1 = ₹83. What is $75?
Ans: 75 × 83 = 75 × (80 + 3) = 6000 + 225 = ₹6225
Tips to Solve Practical Maths Easily
1. Understand the Category First
Most daily-life maths problems fall into 5 main areas:
Shopping / Money → Discounts, Profit–Loss, GST, Currency
Banking / Interest → Simple Interest, Compound Interest, EMI
Speed / Distance / Time → Travel, Trains, Vehicles
Work & Ratio → Cooking, Sharing, Workers
Geometry / Measurement → Areas, Volumes, Tiles, Land
2. Learn Key Formulas by Heart
Some formulas are must-remember (don’t try to memorize too many):
Simple Interest: SI = (P × R × T) / 100
Compound Interest: A = P(1 + R/100)ⁿ
Profit %: Profit% = (Profit/Cost) × 100
Speed = Distance ÷ Time
Area of rectangle = L × B
Area of circle = πr²
3. Break Numbers for Fast Calculation
Example: 83 × 75 → (83 × 75 = 83 × (70 + 5))
= 83×70 + 83×5 = 5810 + 415 = 6225
This makes calculation simpler.
4. Estimate Before Final Answer
If a bill is ₹980 and GST is 5%, estimate quickly:
10% = 98 → half = ~49. So final bill ≈ 1030.
Helps to check mistakes.
5. Use Shortcuts for Squares & Percentages
Number ending in 5: 35² = (3×(3+1))25 = 1225
10% rule: Shift decimal → 450 → 45
5% rule: Half of 10% → 22.5
6. Practice Mental Maths Daily
While shopping, calculate discounts in your head.
While traveling, check time using Distance ÷ Speed.
Convert kg to g, litres to ml mentally.
This builds speed.
7. Solve Step by Step
Always:
1. Write formula (if any).
2. Substitute values.
3. Simplify carefully.
4. Write final answer with units (₹, %, km, m² etc).
8. Check Your Answer
If a discount is 50% on ₹200, the answer must be less than ₹200.
If speed is 60 km/h for 2 hrs, distance must be more than 100 km.
Quick logic check avoids silly mistakes.
9. Use Ratios to Save Time
Example: If 2 pens = ₹20, then 10 pens = ₹100.
Ratios are faster than repeating division.
10. Practice, Practice, Practice
The more you solve, the faster your brain will recognize patterns.
Start with 10 problems daily → after 1 month, you’ll be much quicker.