Lesson 2 — Intermediate

Percentages & Ratio-Proportion

Percentages MNC aptitude ka sabse frequent topic hai. Har exam mein 5-8 questions aate hain. Agar percentages ke shortcuts aa gaye, toh 50% paper easy ho jaayega. Chalo fraction method seekhte hain.

⏱ 25 min• Intermediate• Basic arithmetic

Percentage basics

WHAT

Percentage ka matlab hai "per hundred". 25% ka matlab hai 25 out of 100. Formula: (Part/Whole) — 100. But exam mein formula lagana slow hai — shortcuts use karo.

WHEN

Discount, profit-loss, interest, population growth, election results — har jagah percentage use hota hai. MNC exams mein ye sabse zyada aata hai.

WHERE

Percentages se ratio, proportion, aur fraction sab related hai. Agar percentage strong hai, toh profit-loss, time-work, aur DI bhi easy ho jaayega.

Shortcut King: Har percentage ko fraction mein convert karo. 20% = 1/5, 25% = 1/4, 33.33% = 1/3. Isse calculation 3x fast hoti hai. Ye fractions yaad karo — exam game badal jaayega.

Percentage to Fraction table

Ye table ratta maar lo — exam mein 30% time bachega:

Percentage — Fraction — Use Case
-------------------------------------
10% — 1/10 — 10% of 500 = 500/10 = 50
12.5% — 1/8 — 12.5% of 240 = 240/8 = 30
16.67% — 1/6 — Quick division
20% — 1/5 — 20% of 350 = 350/5 = 70
25% — 1/4 — 25% of 480 = 480/4 = 120
30% — 3/10 — 30% of 700 = 210
33.33% — 1/3 — 33.33% of 900 = 300
37.5% — 3/8 — 37.5% of 800 = 300
40% — 2/5 — 40% of 250 = 100
50% — 1/2 — 50% of 600 = 300
60% — 3/5 — 60% of 500 = 300
62.5% — 5/8 — 62.5% of 320 = 200
66.67% — 2/3 — 66.67% of 900 = 600
70% — 7/10 — 70% of 800 = 560
75% — 3/4 — 75% of 400 = 300
80% — 4/5 — 80% of 250 = 200
83.33% — 5/6 — 83.33% of 600 = 500
87.5% — 7/8 — 87.5% of 240 = 210
90% — 9/10 — 90% of 500 = 450

Successive Percentage Change

Jab do percentages ek ke baad apply ho — jaise pehle 10% badha phir 20% ghata — toh net change sirf addition nahi hota. Shortcut formula use karo:

# Successive change formula:
# Net% = a + b + (a?b)/100

# Example: Pehle 10% badha, phir 20% ghata
# Net = 10 + (-20) + (10?(-20))/100
# Net = 10 - 20 - 2 = -12%
# MATLAB 12% overall decrease

# Example: Pehle 20% badha, phir 30% badha
# Net = 20 + 30 + (20?30)/100
# Net = 50 + 6 = 56% overall increase

# Shortcut for a + b + ab/100:
# Jab dono same sign ho — add karo
# Jab opposite sign ho — subtract karo, sign bado wale ka

Pro Tip: Agar a aur b ke values chhoti hain (like 5% and 10%), toh (a×b)/100 bahut chhota hoga. Exam mein approximately a+b le sakte ho. But exact answer chahiye toh formula use karo.

Ratio & Proportion shortcuts

Ratio percentage ka doosra roop hai. Agar A:B = 2:3 hai, toh A total ka 2/5 aur B total ka 3/5 hai. Simple hai but exam mein fast kaise karein?

# Ratio to Fraction:
# A:B = 2:3 — A = 2/5, B = 3/5
# A:B:C = 1:2:3 — A = 1/6, B = 2/6, C = 3/6

# Example: A aur B ka total ?900 hai. A:B = 2:7.
# A = 2/(2+7) — 900 = 2/9 — 900 = ?200
# B = 7/9 — 900 = ?700

# Componendo & Dividendo:
# If a/b = c/d, then (a+b)/(a-b) = (c+d)/(c-d)
# Useful for comparing ratios quickly

# Example: If A gets 40% and B gets 60%
# A:B = 40:60 = 2:3
# A gets 2/5 and B gets 3/5 of total

Population & Depreciation

Population growth aur depreciation (value girta hai) mein percentage same formula use hota hai, bas sign badal jaata hai:

# Population formula:
# Future = Present — (1 + R/100)^n
# R = growth rate, n = years

# Depreciation formula:
# Future = Present — (1 - R/100)^n
# R = depreciation rate, n = years

# Example: Population 10000 hai, 10% annual growth, 2 years baad?
# Future = 10000 — (1 + 10/100)^2
# = 10000 — (1.1)^2
# = 10000 — 1.21 = 12100

# Shortcut: 10% growth 2 years = 21% net (not 20%)
# Because: 10 + 10 + (10?10)/100 = 21%

Exercise

Question: 280 mein se 25% kaat do. Kitna bachega? Sirf number daalo.

Question: Kisi cheez ka pehle 20% badha phir 10% ghata. Net change kitna hai? (Positive ya negative mein percentage daalo, bina % sign ke. Example: -12 ya 14)

Question: A:B = 3:5 hai. Agar total 400 hai, toh A ki value kitni hai? Sirf number daalo.

Question: Population 6000 hai, 10% annual growth hai, 3 years baad population kitni hogi? (Approximate, round to nearest 100. (1.1)^3 = 1.331)

Common mistakes

Successive change mein direct add karna: 10% + 20% = 30% nahi hota. Formula use karo: a + b + ab/100.
Fraction table yaad nahi hona: Exam mein har baar calculate karna padega. Table yaad karo — 5 seconds mein answer aa jaayega.
"Of" ka matlab samajhna: "25% of 480" ka matlab hai 25/100 — 480. "Of" hamesha multiplication hai.
Negative percentage mein sign bhool jaana: "Decrease by 15%" ka matlab hai multiply by 0.85, nahi ki 1.15.

Desi example: Jio recharge + UPI cashback

239 wale recharge pe 10% cashback = kitna effective? Aur Diwali sale me 40% off ke baad GST?

Cashback: 239 x 0.10 = 23.9, effective = 215.1
Sale: 1000 x 0.60 = 600, +18% GST = 708
Trick: denominator (1 +/- %/100) hamesha likho.

Exam mapping (SSC / CAT / TCS)

SSC me 3-4Q, CAT me 5-6Q — percentage + ratio combo.
Trap: 20% badha phir 20% ghata = wapas same nahi, 4% kam.

Lesson complete?

Percentages aur ratio-proportion samajh aa gaya? Ab Profit, Loss & Discount seekhte hain — ye percentages pe based hai.