Viral Maths — Ch09: Percentage

📌 What This Chapter Covers

Percentage chapter ki foundation hai fraction-percent conversions — har % value ko uske fraction se jodo, phir multiplication/division fast ho jaata hai.
12 named types hain, sab isi core idea pe based: "% ko fraction mein convert karo, phir multiply karo."
Dal Badlu Approach ek special reversal trick hai jo tough-looking % questions ko simple bana deta hai.

⚡ QUICK RECALL

Poori chapter ka core formula: a% of b = (fraction form of a%) × b. Fraction-Percent table (Tab 2) is chapter ki backbone hai — usse pehle cold yaad karo.

🗂️ Chapter Index

Tab	Content	Fractions Used
2	Fraction-Percent Reference Table	All key values
3	Type 1–2: 25%,50%,10%,20%	1/4, 1/2, 1/10, 1/5
4	Type 3–4: 40%,60%,75%,80%	2/5, 3/5, 3/4, 4/5
5	Type 5: 16.66%,33.33%	1/6, 1/3
6	Type 6–7: 6.66%,6.25%,12.5%,14.28%	1/15, 1/16, 1/8, 1/7
7	Type 8–9: 37.5%,7.14%,62.5%,9.09%	3/8, 1/14, 5/8, 1/11
8	Type 10,12: 11.11% & derived %s	1/9, multiples of known fractions
9	Type 11: Dal Badlu Approach	a% of b = b% of a
10	Master Table	All types summarized

🔢 Fraction ↔ Percent — Complete Reference Table

Fraction	%	Fraction	%	Fraction	%
1/2	50%	1/7	14.28%	3/8	37.5%
1/3	33.33%	2/7	28.57%	5/8	62.5%
2/3	66.67%	3/7	42.85%	7/8	87.5%
1/4	25%	4/7	57.14%	1/9	11.11%
3/4	75%	5/7	71.43%	2/9	22.22%
1/5	20%	6/7	85.71%	3/9	33.33%
2/5	40%	1/8	12.5%	4/9	44.44%
3/5	60%	1/6	16.67%	1/10	10%
4/5	80%	5/6	83.33%	1/11	9.09%
		1/12	8.33%	1/14	7.14%
		1/15	6.66%	1/16	6.25%

⚡ QUICK RECALL

Yeh table Ch05 (Division, Broken Heart Approach) aur Ch09 dono mein use hoti hai — cold yaad karna non-negotiable hai.

Type 1 — Finding 25% and 50% of Numbers

25% = 1/4, 50% = 1/2

25% of 48 = 1/4 × 48 = 12 50% of 642 = 1/2 × 642 = 321

Type 2 — Finding 10% and 20% of Numbers

10% = 1/10, 20% = 1/5

10% of 450 = 1/10 × 450 = 45 20% of 655 = 1/5 × 655 = 131

⚡ QUICK RECALL

10% = shift decimal 1 left. 20% = 10% doubled. 25% = ÷4. 50% = ÷2. Yeh sabse common exam percentages hain — instant honi chahiye.

Type 3 — Finding 40% and 60% of Numbers

40% = 2/5, 60% = 3/5

40% of 65 = 2/5 × 65 = 26 60% of 125 = 3/5 × 125 = 75

Type 4 — Finding 75% and 80% of Numbers

75% = 3/4, 80% = 4/5

75% of 48 = 3/4 × 48 = 36 80% of 225 = 4/5 × 225 = 180

⚡ QUICK RECALL

Sab "/5" family (20%,40%,60%,80%) → divide by 5, multiply by numerator. "/4" family (25%,75%) → divide by 4.

Type 5 — Finding 16.66% and 33.33% of Numbers

16.66% = 1/6, 33.33% = 1/3

16.66% of 246 = 1/6 × 246 = 41 33.33% of 810 = 1/3 × 810 = 270

⚠ EXAM TRAP

16.66% aur 33.33% dono "Point%" family hain — inka exact fraction repeating decimal se aata hai (1/6=0.1666..., 1/3=0.3333...). Exam mein rounded % dikhta hai, lekin fraction EXACT use karo.

Finding 6.66% and 6.25% of Numbers

6.66% = 1/15, 6.25% = 1/16

6.66% of 225 = 1/15 × 225 = 15 6.25% of 128 = 1/16 × 128 = 8

Finding 12.5% and 14.28% of Numbers

12.5% = 1/8, 14.28% = 1/7

12.5% of 488 = 1/8 × 488 = 61 14.28% of 154 = 1/7 × 154 = 22

⚡ QUICK RECALL

1/16=6.25% | 1/15=6.66% | 1/8=12.5% | 1/7=14.28% — inko ek dusre se confuse mat karo, denominators bahut close hain.

Finding 37.5% and 7.14% of Numbers

37.5% = 3/8, 7.14% = 1/14

37.5% of 64 = 3/8 × 64 = 24 7.14% of 350 = 1/14 × 350 = 25

Finding 62.5% and 9.09% of Numbers

62.5% = 5/8, 9.09% = 1/11

62.5% of 32 = 5/8 × 32 = 20 9.09% of 473 = 1/11 × 473 = 43

⚡ QUICK RECALL

7.14% = half of 14.28% (both from 1/7 family: 1/14 and 1/7). 9.09% comes from 1/11 — connects to Ch05 Division Type-7 (÷11 family).

Type 10 — Finding 11.11% of Numbers

11.11% = 1/9

11.11% of 819 = 1/9 × 819 = 91

Type 12 — Deriving New Percentages from Known Fractions

Multiply a known base fraction to get related percentages

Example: 22.22% (derived from 11.11%)

11.11% = 1/9 So 22.22% = 2 × (1/9) = 2/9

Example: 7.14% (derived from 14.28%)

14.28% = 1/7 So 7.14% (half of 14.28%) = 1/14

⚡ QUICK RECALL

Agar % ka double/half/multiple ek known fraction se related dikhe, to naya fraction bhi usi anupaat mein derive kar lo — nayi table yaad karne ki zaroorat nahi.

Type 11 — Dal Badlu Approach (Reversal Trick)

Rule: a% of b = b% of a — swap which number carries the % symbol

Example: 24% of 25

Rewrite as: 25% of 24 Step 1: 25% = 1/4 Step 2: 1/4 × 24 = 6

⚠ EXAM TRAP

"Dal Badlu" = swap kar do — jab % wala number "ugly" ho (jaise 24%) lekin doosra number "nice" fraction bana sake (jaise 25=1/4), to hamesha swap karo. Answer same rehta hai, calculation asaan ho jaata hai.

⚡ QUICK RECALL

112% of 12.5 = 12.5% of 112 = (1/8)×112 = 14 — is tarah bade-lagne-wale % questions turant simple ho jaate hain.

📋 Master Table — All Percentage Types

%	Fraction	%	Fraction
10%	1/10	37.5%	3/8
20%	1/5	62.5%	5/8
25%	1/4	87.5%	7/8
50%	1/2	11.11%	1/9
40%	2/5	22.22%	2/9
60%	3/5	9.09%	1/11
75%	3/4	8.33%	1/12
80%	4/5	7.14%	1/14
16.66%	1/6	6.66%	1/15
33.33%	1/3	6.25%	1/16
12.5%	1/8	14.28%	1/7

🔑 Special Techniques Recap

Dal Badlu Approach: a% of b = b% of a (swap when the other number gives a nicer fraction)
Derived %: multiples/halves of known fractions give new percentages instantly (e.g. 22.22% = 2×11.11%)