Speed Maths Tricks to Solve Simplification Questions Mentally

Simplification Questions are asked significantly in the RRB Clerk exam every year. Solving this type of question in exam requires quick calculation. Most of the questions from this topic can be solved using speed math tricks. Some speed math or mental math tricks make the calculation simpler and quicker. These tricks and techniques help in answering such questions within seconds. Mental math is not only used in simplification but in every numerical that you solve. When these shortcut tricks are learnt and practiced well, these play a huge role in improving your score. Therefore, in this blog, we are providing most used speed math tricks to solve simplification questions mentally. 

Why Simplification Matters in Bank Exams?

Simplification questions are the bread and butter of the Quantitative Aptitude section in banking exams like IBPS RRB Clerk. If you master speed maths tricks, you can solve these questions mentally, saving precious time and boosting your score. This blog will walk you through the most effective techniques, examples, and tips to crack simplification questions like a pro.

• Weightage: 10–15 questions in the Quant section
• Time-saving: Quick mental calculations = more time for DI and word problems
• Scoring: High accuracy if you know the tricks

Common Types of Simplification Questions

• BODMAS-based expressions
• Fractions and decimals
• Surds and indices
• Percentages
• Approximation
• Square roots and cube roots

Speed Maths Tricks You Must Know

Below we have listed 7 must know speed maths tricks to solve simplification question quickly 

1. BODMAS Rule – The Foundation

Always follow the order: Brackets → Orders or of (powers, roots) → Division → Multiplication → Addition → Subtraction

Example:
Solve: 12 + 6 × (3² – 1) ÷ 2
Step-by-step:
→ 3² = 9
→ (9 – 1) = 8
→ 6 × 8 = 48
→ 48 ÷ 2 = 24
→ 12 + 24 = 36

2. Multiplication Shortcuts

a. Multiplying by 5

Just halve the number and add a zero.
Example: 86 × 5 → 86 ÷ 2 = 43 → 430

b. Multiplying by 11

Add adjacent digits and place them in between.
Example: 52 × 11 → 5 (5+2) 2 → 572

3. Squaring Numbers Ending in 5

Use the formula:
If the number is x5, then
x × (x + 1) followed by 25

Example: 35² → 3 × 4 = 12 → 1225

4. Quick Percentage Calculations

Use fractions for common percentages:

• 10% = ÷10
• 25% = ÷4
• 50% = ÷2
• 75% = ×¾

Example: 75% of 240 → 240 × ¾ = 180

5. Approximations for Faster Elimination

Round off numbers smartly:

• 198 ≈ 200
• 49.8 ≈ 50
  Use this in options-based questions to eliminate wrong choices quickly.

6. Surds and Indices Simplification

Know basic conversions:

• √4 = 2
• √9 = 3
• 2³ = 8
• 5² = 25
  Use these to simplify expressions like:
  Example: √25 + 2³ = 5 + 8 = 13

7. Digit Sum Trick for Quick Checks

Use digit sum to verify options: 

Example:
Check which of the following is divisible by 9:

1. 243 → 2+4+3 = 9 
2. 234 → 2+3+4 = 9 
3. 225 → 2+2+5 = 9
   All are divisible!

Practice Set for Mental Simplification

Try solving these mentally:

1. 48 × 5 = ?
2. √144 + 25% of 80 = ?
3. 11 × 67 = ?
4. 35² = ?
5. 2³ + √49 = ?

Answers:

1. 240
2. 12 + 20 = 32
3. 737
4. 1225
5. 8 + 7 = 15

Solutions:

1. 48 × 5 = ?

Answer: 240
Explanation: Use the shortcut for multiplying by 5: halve the number and add a zero.
→ 48 ÷ 2 = 24 → Add a zero → 240

2. √144 + 25% of 80 = ?

Answer: 32
Explanation:

• √144 = 12
• 25% of 80 = 80 ÷ 4 = 20
  → 12 + 20 = 32

3. 11 × 67 = ?

Answer: 737
Explanation: Use the shortcut for multiplying by 11:
→ 6 (6+7) 7 → 6 + 7 = 13 → Carry over 1
→ Final result = 737

4. 35² = ?

Answer: 1225
Explanation: Use the squaring trick for numbers ending in 5:
→ 3 × 4 = 12 → Add 25 → 1225

5. 2³ + √49 = ?

Answer: 15
Explanation:

• 2³ = 8
• √49 = 7
  → 8 + 7 = 15

Advanced Speed Maths Tricks for Mental Simplification

These tricks go beyond the basics and help you tackle tougher simplification questions with ease.

1. Squaring Numbers Quickly

There are two shortcuts for squaring a number quickly. One is for the number ending in 5 and the other is the Near base method.

a. Numbers ending in 5

Use: ( x5^2 = x \times (x+1) ) followed by 25
Example: 85² → 8 × 9 = 72 → 7225

b. Near Base Method

Use for numbers close to 100, 50, etc.
Example: 103²
→ Base = 100, Difference = +3
→ 103² = 100² + 2×100×3 + 3² = 10000 + 600 + 9 = 10609

2. Cubing Numbers Mentally

Use identity:
[ (a + b)^{3 =} a^3+ 3ba^{2 +} 3ab^2 + b^3 ]

Example: 12³
→ a = 10, b = 2
→ 1000 + 3×100×2 + 3×10×4 + 8 = 1000 + 600 + 120 + 8 = 1728

3. Square Root Tricks

There are two types of square root tricks. One is perfect square calculation and the other is estimation method.

a. Perfect Squares Recognition

Memorize squares up to 30 for instant recall.
Example: √625 = 25

b. Estimation Method

For non-perfect squares, estimate between known roots.
Example: √50 → between √49 (7) and √64 (8) → approx 7.1

4. Cube Root Tricks

Memorize cubes up to 20:

• 2³ = 8
• 3³ = 27
• 4³ = 64
• 5³ = 125
  Example: ∛216 = 6

Find ∛17576

• Last 3 digits: 576 → ends in 6 → unit digit is 6 (because 6³ = 216)
• Remaining part: 17 → closest cube less than 17 is 8³ = 512 → root is 2
• Final answer: 26

6. Alligation Rule (for Averages)

Used to find the ratio of mixing two items at different prices to get a mean price.

Example:
Tea at ₹60/kg and ₹90/kg mixed to get ₹75/kg
→ Difference:

• 90 – 75 = 15
• 75 – 60 = 15
  → Ratio = 1:1

7. Unit Digit Trick for Powers

Helps in finding the last digit of large powers.

Example:
Find unit digit of ( 7^{103} )
→ Cycle of 7: 7, 9, 3, 1 (repeats every 4)
→ 103 mod 4 = 3 → 3rd digit = 3

8. Divisibility Rules

Quick checks for options:

• By 2: Last digit even
• By 3: Sum of digits divisible by 3
• By 4: Last two digits divisible by 4
• By 5: Ends in 0 or 5
• By 9: Sum of digits divisible by 9
• By 11: Alternating sum of digits is either 0 or 11

Example: Is 121 divisible by 11?
→ 1 – 2 + 1 = 0 → Yes 

9. Vedic Maths Sutras (Optional)

If your students are familiar with Vedic Maths, you can introduce:

• Nikhilam Sutra: For subtraction from base
• Urdhva Tiryagbhyam: For vertical and crosswise multiplication
• Anurupyena: For proportional calculations

These are optional but powerful for advanced learners.

Practice Set – Advanced Simplification

Try solving mentally:

1. 95² = ?
2. ∛512 = ?
3. √225 + 5² = ?
4. 13³ = ?
5. Use Componendo-Dividendo: If a/b = 4/3, find (a + b)/(a – b)

Answers:

1. 9025
2. 8
3. 15 + 25 = 40
4. 2197
5. (4 + 3)/(4 – 3) = 7/1 = 7

Solution:

1. 999 × 36 = ?

Answer: 35964
Explanation: Use the shortcut:
→ 999 × 36 = (1000 × 36) – 36 = 36000 – 36 = 35964

2. 48 × 25 = ?

Answer: 1200
Explanation: Use doubling and halving:
→ 48 × 25 = 24 × 50 = 12 × 100 = 1200

3. 102² – 98² = ?

Answer: 800
Explanation: Use identity:
→ a² – b² = (a + b)(a – b)
→ (102 + 98)(102 – 98) = 200 × 4 = 800

4. 23 × 12 = ?

Answer: 276
Explanation: Use split and merge:
→ (20 × 12) + (3 × 12) = 240 + 36 = 276

5. Simplify: (a + b)² when a = 5, b = 3

Answer: 64
Explanation:
→ (5 + 3)² = 8² = 64
Or use identity:
→ a² + 2ab + b² = 25 + 30 + 9 = 64

More Speed Maths Tricks for Mental Simplification

Here’s a fresh batch of tricks that go beyond the usual shortcuts which is ideal for aspirants aiming to master mental calculations.

10. Addition & Subtraction Using Base Method

Use base numbers like 100, 1000, etc., to simplify mentally.

Example:
998 + 247
→ (1000 – 2) + 247 = 1247 – 2 = 1245

11. Split and Merge Method for Multiplication

Break numbers into parts to simplify.

Example:
23 × 12
→ (20 + 3) × 12 = (20 × 12) + (3 × 12) = 240 + 36 = 276

12. Doubling and Halving Method

If one number is even, halve it and double the other.

Example:
16 × 25 → 8 × 50 → 4 × 100 = 400

13. Cross Multiplication for Two-Digit Numbers

Use this for multiplying numbers like 23 × 31:

[ (2×3) | (2×1 + 3×3) | (3×1) = 6 | 11 | 3 → 713 ]

14. Multiplying Numbers Near 100

Use:
[ (x + a)(x + b) = x^2 + x(a + b) + ab ]

Example:
98 × 97
→ x = 100, a = –2, b = –3
→ 10000 – 500 + 6 = 9506

15. Quick Conversion of Fractions to Percentages

Memorize common percentage to fraction conversions:

16. Rule of 72 for Estimations

Used in finance to estimate doubling time:

Example:
At 6% interest, money doubles in ≈ 72 ÷ 6 = 12 years

17. Simplifying Ratios Mentally

Divide both terms by their HCF.

Example:
36:48 → HCF = 12 → 36 ÷ 12 : 48 ÷ 12 = 3:4

18. Using Complementary Numbers

For subtraction:
Instead of 1000 – 647, think of the complement of 647.

→ 1000 – 647 = 353

19. Multiplying by 9, 99, 999

Use:

• 9 × x = (x × 10) – x
• 99 × x = (x × 100) – x
• 999 × x = (x × 1000) – x

Example:
99 × 47 = 4700 – 47 = 4653

20. Using Algebraic Identities

These help simplify expressions quickly:

• (a + b)^{2 =} a^2 + 2ab + b^2
• (a – b)^{2 =} a^2 – 2ab + b^2
• a^{2 –}  b^2= ((a + b)(a – b))

Example:
( 102^{2 –} 98^2 = (102 + 98)(102 – 98) = 200 × 4 = 800 )

Bonus Practice Set – Apply These Tricks

Questions:

1. 999 × 36 = ?
2. 48 × 25 = ?
3. 102² – 98² = ?
4. 23 × 12 = ?
5. Simplify: (a + b)² when a = 5, b = 3

Answers:

1. 35964
2. 1200
3. 800
4. 276
5. 64

Solutions:

1. ∛32768 = ?

Answer: 32
Explanation:

• Last digit is 8 → unit digit is 2
• Remaining part: 32 → closest cube below is 27 (3³) → tens digit is 3
  → Final answer = 32

2. ∛13824 = ?

Answer: 24
Explanation:

• Last digit is 4 → unit digit is 4
• Remaining part: 13 → closest cube below is 8 (2³) → tens digit is 2
  → Final answer = 24

3. ∛74088 = ?

Answer: 42
Explanation:

• Last digit is 8 → unit digit is 2
• Remaining part: 74 → closest cube below is 64 (4³) → tens digit is 4
  → Final answer = 42

4. ∛91125 = ?

Answer: 45
Explanation:

• Last digit is 5 → unit digit is 5
• Remaining part: 91 → closest cube below is 64 (4³) → tens digit is 4
  → Final answer = 45

5. ∛512 = ?

Answer: 8
Explanation:
→ 512 is a known perfect cube → ∛512 = 8

Simplification Master Tips for Banking Exam Aspirants

4 most important tips to master simplification using shortcuts are given below.

1. Practice daily: 15–20 simplification questions
2. Use a timer: Build speed and accuracy
3. Revise tricks weekly: Keep them fresh
4. Mock tests: Apply tricks under exam pressure

Conclusion

Speed maths isn’t just about shortcuts, it’s about smart strategy. With consistent practice and these mental tricks, you’ll be able to solve simplification questions quickly in your exam. Bookmark this blog, share it with fellow aspirants, and start practicing today!

Disclaimer: The speed maths tricks, examples, and practice questions provided are compiled from expert analysis of exam trends and reliable sources. They are intended for practice and guidance only, not official banking exam content. Actual exam questions may differ. Candidates should always verify details through official IBPS/RRB notices.

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