Percentage –Tips and Tricks Concept

 

🧮 1️⃣ Percentage – Concept & Tricks

🔹 Definition:

Percentage means “per hundred.”
It is used to express a number as a fraction of 100.

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

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🔹 Basic Conversions:

Fraction	Percentage
1/2	50%
1/3	33.33%
1/4	25%
1/5	20%
1/6	16.66%
1/8	12.5%
1/9	11.11%
3/4	75%
2/5	40%
4/5	80%

💡 Tip: Memorize this table — it saves precious time in exam calculations!

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🔹 Increase or Decrease in Percentage

If a value increases by R%,

$$\text{New Value} = \text{Original Value} × \left(1 + \frac{R}{100}\right)$$

If a value decreases by R%,

$$\text{New Value} = \text{Original Value} × \left(1 - \frac{R}{100}\right)$$

Example:
Salary = ₹10,000, increased by 20% → ₹10,000 × 1.2 = ₹12,000
Later decreased by 10% → ₹12,000 × 0.9 = ₹10,800

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🔹 Successive Percentage Change

If a value changes by A% and then by B%,

$$\text{Net Change} = A + B + \frac{A×B}{100}$$

Example:
Price increases by 20% and then decreases by 10%.
→ Net Change = 20 – 10 – (20×10)/100 = +8%

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🔹 Percentage Comparison Shortcut

If A’s value is x% more than B’s value,
then B’s value is $\frac{x}{100+x} × 100 \%$ less than A’s.

Example:
If A = 20% more than B → B = (20/120)×100 = 16.67% less than A.

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💸 2️⃣ Profit & Loss – Complete Notes

🔹 Basic Terms

Term	Meaning
Cost Price (C.P.)	Price at which article is bought
Selling Price (S.P.)	Price at which article is sold
Profit	When S.P. > C.P.
Loss	When C.P. > S.P.

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🔹 Formulas

$$\text{Profit} = S.P. - C.P.$$ $$\text{Loss} = C.P. - S.P.$$ $$\text{Profit \%} = \frac{\text{Profit}}{\text{C.P.}} × 100$$ $$\text{Loss \%} = \frac{\text{Loss}}{\text{C.P.}} × 100$$

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💹 Selling Price & Cost Price Formula

$$S.P. = \text{C.P.} × \left(1 + \frac{\text{Profit\%}}{100}\right)$$ $$C.P. = \text{S.P.} × \frac{100}{(100 + \text{Profit\%})}$$ $$S.P. = \text{C.P.} × \left(1 - \frac{\text{Loss\%}}{100}\right)$$ $$C.P. = \text{S.P.} × \frac{100}{(100 - \text{Loss\%})}$$

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🔹 Shortcut Examples

Example 1:
A shopkeeper buys an item for ₹200 and sells it for ₹250.
Profit% = ((250–200)/200)×100 = 25%

Example 2:
An article is sold at a 10% loss for ₹450. Find cost price.
C.P. = (450×100)/(100–10) = ₹500

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🔹 Discount Formula

$$\text{Discount} = \text{Marked Price} - \text{Selling Price}$$ $$\text{Discount \%} = \frac{\text{Discount}}{\text{Marked Price}} × 100$$

Example:
Marked Price = ₹1000, Discount = 20%
→ Selling Price = 1000 – (20% of 1000) = ₹800

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🔹 Successive Discount Formula

If two successive discounts of A% and B% are given:

$$\text{Net Discount} = A + B - \frac{A×B}{100}$$

Example:
Discounts 20% and 10% → Net Discount = 20 + 10 – 2 = 28%

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💡 Trick: Double Profit or Loss

If profit = loss%,
then overall loss = $\left(\frac{x}{10}\right)^2 \%$

Example:
Gain 10% on one article and lose 10% on another.
→ Overall loss = (10/10)² = 1% loss

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📊 3️⃣ Quick Practice Table

Topic	Formula	Example
Profit %	(P/C.P.)×100	C.P.=100, S.P.=120 → 20%
Loss %	(L/C.P.)×100	C.P.=100, S.P.=90 → 10%
S.P. for given Profit%	C.P.×(100+P%)/100	200×(120/100)=240
C.P. for given Profit%	S.P.×100/(100+P%)	240×100/120=200
Net Change (Succession)	A+B+(AB/100)	20, -10 → 8%
Discount%	(D/M.P.)×100	(200/1000)×100=20%

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🧠 4️⃣ Real Exam Tips

✨ Convert percentages into fractions — saves time!
✨ Remember: Gain on Cost Price, Loss on Cost Price!
✨ Always use successive formula for double changes.
✨ Practice at least 20 questions daily from past year papers.

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📘 5️⃣ Bonus: Percentage & Profit-Loss in Exams

Exam	No. of Questions	Difficulty	Weightage
SSC CGL / CHSL	2–3	Easy–Moderate	High
Bank PO / Clerk	2–4	Moderate	High
Railway (RRB NTPC)	1–2	Easy	Medium
State Exams	3–5	Moderate	High

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🧾 6️⃣ Practice Set Ideas

✅ 100% – 120% type increment-decrement
✅ Double successive discount problems
✅ Cost price/Selling price reverse calculation
✅ Marked price-based tricky questions

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🏆 JobVaale Expert Tips

💡 Revise formulas every morning.
💡 Practice mental calculation daily.
💡 Attempt JobVaale.com’s free online quizzes for instant feedback.
💡 Maintain your personal Maths Trick Notebook.

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🌟 Final Thoughts

Mastering Percentage and Profit-Loss is all about understanding relationships and patterns — not memorizing formulas blindly.
Practice daily, use shortcuts, and apply logic — success will follow! 💪

✨ Stay smart, stay confident, and keep learning with JobVaale.com —
“Find all jobs at one place.” 💼