Arithmetic Shortcuts – Fast Calculation Tricks for Competitive Exams

🧮 Arithmetic Shortcuts – Fast Calculation Tricks for Competitive Exams

📅 Post Date: October 26, 2025 | ✍️ By: JobVaale.com | 📂 Category: Study Material / Exam Preparation

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💡 “Speed + Accuracy = Success!”

Arithmetic is one of the most scoring sections in any competitive exam — be it SSC, Banking, Railway, or Defence.
But solving every question in just 30–40 seconds requires smart calculation techniques and shortcut formulas.

Here’s your complete guide to Arithmetic Shortcuts that can help you solve faster, reduce errors, and boost your overall score! 🚀

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🔢 1️⃣ Percentage Shortcuts

✅ Basic Conversion Formula

$$\text{Percentage} = \frac{\text{Value}}{\text{Total Value}} \times 100$$

🧠 Common Fractions to Percentages:

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.66%
1/8	12.5%
3/4	75%

💡 Trick: Learn this table — it saves minutes in Profit & Loss, Discount, and Ratio questions!

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💰 2️⃣ Profit & Loss Shortcuts

💹 Formulas

• Profit % = (Profit / Cost Price) × 100

• Loss % = (Loss / Cost Price) × 100

• Selling Price = $\text{Cost Price} × \frac{(100 + Profit\%)}{100}$

• Cost Price = $\text{Selling Price} × \frac{100}{(100 + Profit\%)}$

💡 Shortcut Example

If cost price = ₹200 and profit = 25%
→ Selling Price = $200 × 1.25 = ₹250$

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⏳ 3️⃣ Simple Interest (SI) & Compound Interest (CI) Shortcuts

💰 Simple Interest:

$$SI = \frac{P × R × T}{100}$$

💰 Compound Interest (for 2 years):

$$CI = P \times \left(1 + \frac{R}{100}\right)^2 - P$$

⚡ Shortcut:

If rate (R) and time (T) are same:

$$Difference (CI - SI) = P \times \left(\frac{R}{100}\right)^2$$

Example:
P = 10,000, R = 10%, T = 2 years
Difference = 10,000 × (10/100)² = 100

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📊 4️⃣ Ratio & Proportion Tricks

⚙️ Shortcut Formula:

If $a:b = 2:3$ and $b:c = 4:5$,
Then make the middle term equal:
$a:b = 8:12$, $b:c = 12:15$
So, $a:b:c = 8:12:15$

💡 Use this in mixture, partnership & comparison questions.

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🧮 5️⃣ Average Shortcut Formula

$$\text{Average} = \frac{\text{Sum of All Items}}{\text{Number of Items}}$$

⚡ Quick Trick:

If one item is replaced:

$$\text{New Average} = \text{Old Average} + \frac{\text{Change}}{\text{Total Items}}$$

Example:
Average of 5 numbers is 30. One number 25 is replaced by 45.
→ New Average = 30 + (20 ÷ 5) = 34

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📈 6️⃣ Time, Speed & Distance

🕒 Basic Formula:

$$Speed = \frac{Distance}{Time}$$ $$Distance = Speed × Time$$

💡 Shortcut:

If same distance is covered at two speeds S₁ & S₂:

$$\text{Average Speed} = \frac{2 × S₁ × S₂}{S₁ + S₂}$$

Example:
Speed 60 km/h & 40 km/h
→ Avg Speed = $\frac{2×60×40}{60+40} = 48 \text{ km/h}$

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🧠 7️⃣ Time & Work Shortcuts

⚙️ Formula:

$$\text{Work Done} = \text{Time} × \text{Efficiency}$$

If A can do a work in 10 days, B in 20 days:
→ A:B = 1/10 : 1/20 = 2:1
→ Together they complete work in $\frac{1}{(1/10 + 1/20)} = 6.67 \text{ days}$

🪄 Shortcut:

If A is “x” times as good as B,
then A will take $\frac{1}{x}$ of B’s time.

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🧾 8️⃣ Partnership Trick

If A invests ₹x for t months, and B invests ₹y for s months:

$$\text{Profit Ratio} = (x × t) : (y × s)$$

Example:
A invests ₹2000 for 6 months, B ₹4000 for 3 months
→ Ratio = (2000×6):(4000×3) = 12,000:12,000 = 1:1

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📦 9️⃣ Mixture & Alligation Shortcut

When two quantities are mixed:

$$\text{Cheaper Quantity : Dearer Quantity} = (D - M) : (M - C)$$

where D = Dearer price, C = Cheaper price, M = Mean price

Example:
Tea ₹20/kg mixed with ₹30/kg to make ₹26/kg mixture
→ Ratio = (30-26):(26-20) = 4:6 = 2:3

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📘 🔟 Important Arithmetic Square & Cube Shortcuts

Number	Square	Cube
11	121	1331
12	144	1728
13	169	2197
14	196	2744
15	225	3375
20	400	8000
25	625	15625

💡 Learn up to 25 squares & 15 cubes — this helps in fast calculation for every exam.

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🎯 Bonus Section: Arithmetic Topics to Master for SSC & Banking Exams

Topic	Weightage	Shortcut Type
Percentage	4–5 Qs	Fraction Conversion
Profit & Loss	3–4 Qs	Ratio Tricks
Time & Work	3–5 Qs	Efficiency Concept
Speed & Distance	2–3 Qs	Average Speed Formula
SI/CI	2–3 Qs	Difference Formula
Mixture & Alligation	1–2 Qs	Ratio Shortcut

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🏆 Pro Tips from JobVaale Experts

✨ Revise arithmetic formulas every morning.
✨ Attempt Daily Practice Quiz on JobVaale.com.
✨ Maintain a small notebook of your personal shortcut tricks.
✨ Focus more on accuracy than guessing in exams.

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🌟 Final Thoughts

Arithmetic is not just about numbers — it’s about smart thinking and pattern recognition!
With these shortcut tricks, you can solve complex problems in seconds, gain confidence, and score top marks in any competitive exam.

Stay consistent, practice daily, and let JobVaale.com be your guide to government job success! 🚀

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