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Percentage

Lesson 70 of 113

1. Ye topic hai kya?

Percent = per hundred. 25% matlab 25 hisse har 100 mein — fraction 25/100 = 1/4. Paper teen sawal ghumata hai: (1) itna % of itna kitna, (2) ye number us number ka kitna %, (3) badha / ghata / do baar change ke baad net. Simplification ne of sikhaya; yahan pehle % ko fraction/decimal banao, phir of.

Paper yahan kya maangta

x% of y, “what percent”, fraction↔%, +r% / −r%, reverse (A B se 20% zyada ≠ B A se 20% kam), successive a+b+ab/100, pass-fail, population, expenditure = price × qty.

Yahan kya nahi

2+3×4, 36÷6 of 2, 15² — Simplification. Bells–tiles — HCF/LCM. CP SP discount — Profit/loss. PRT/100 — SI. Milk–water — Mixture. 3:5 — Ratio agla. Cricket “ab kitna chahiye” — Average.

Teen lines: x% of y = (x/100)×y. y is what % of x = (y/x)×100. % change = (new − old)/old × 100 — hamesha purana neeche.

2. Convert, of, table

% → fraction: 25% = 25/100 = 1/4. % → decimal: 25% = 0.25. Ulta: 0.45 = 45%, 3/8 = 37.5%. Simplification P10 yahi 25% of 80 bheja tha — of = ×, lekin 25 pehle /100.

100 dabbe. 25 bhare = 25% = 1/4. Isi 1/4 ko 80 pe lagaao: 25% of 80 = 20. Grid 100 hai, 80 nahi — of alag number pe chalta.

Paper ke shortcuts — 12.5% dekho to 1/8, 16⅔% to 1/6. Multiply lambi mat.

%Fraction%Fraction
50%1/212.5%1/8
25%1/46.25%1/16
75%3/416⅔%1/6
20%1/58⅓%1/12
40%2/533⅓%1/3
60%3/537.5%3/8
10%1/1062.5%5/8
x% of y = y% of x. 15% of 80 = 12, 80% of 15 = 12. Check ke liye useful, naya number nahi. 10% of 20% of 300 = 0.1×0.2×300 = 6 — pehle dono % decimal, phir ×. 2/3 of 3/4 of 96 Simplification pe (wahan % nahi tha).
Example

25% of 80 = ? (Simplification P10 yahi bheja.)

Solution

  1. /100 phir of

    25/100 × 80 = 1/4 × 80 = 20. 25×80=2000 mat chhodna — /100 zaroori.

Answer20
Example

40 is what percent of 160?

Solution

  1. (part/whole)×100

    40/160 × 100 = 25%. Whole 160 neeche. 160 of 40 nahi.

Answer25%
Example

3/8 = kitna %?

Solution

  1. ×100

    (3/8)×100 = 300/8 = 37.5%. Table 3/8. 3/5=60% mix mat.

Answer37.5%
Example

30% of a number = 150. Number?

Solution

  1. Reverse

    n × 30/100 = 150 → n = 150 × 100/30 = 500. 30% = 150, 10% = 50, 100% = 500.

Answer500

3. Increase, decrease, reverse

r% badhaana = × (100+r)/100. r% ghatana = × (100−r)/100. Dono mein r% usi original ka hissa. 400 ka 25% = 100 — plus 500, minus 300. 500 se wapas 400 aane ke liye 20% ghatana padta (100/500), 25% nahi. Base badal gaya.

A, B se r% zyada: A = B(100+r)/100. Ulta poochhe “B, A se kitna % kam?”: farq / A × 100 = r/(100+r)×100.
A, B se r% kam: ulte B, A se r/(100−r)×100 zyada.
B = 100 A = 120 (+20% of B)

A, B se 20 zyada — 20, B=100 ka 20%. Wahi 20 ab A=120 ka hissa: 20/120 = 1/6 ≈ 16⅔%. Isliye B, A se 16⅔% kam — 20% kam nahi.

% change ka denominator hamesha jis se compare (reference). “Kam than A” → A neeche. Exam mein option 20% trap. Profit% CP pe lagta — woh agla chapter, yahan salary/height/marks.
Example

400 ko 25% badhao. 400 ko 25% ghatao.

Solution

  1. Same 100

    25% of 400 = 100. 400+100=500. 400−100=300. 500 se 25% cut = 375, 400 nahi.

Answer500 and 300
Example

A ki salary B se 20% zyada. B, A se kitna % kam?

Solution

  1. B=100

    A=120. Farq 20. 20/120 × 100 = 50/3 = 16⅔%.

Answer16⅔%
Example

A, B se 25% kam. B, A se kitna % zyada?

Solution

  1. B=100

    A=75. Farq 25. 25/75 × 100 = 33⅓%. Formula 25/(100−25)×100 = 25/75.

Answer33⅓%

4. Successive, exam, population

Do changes ek ke baad: pehle wale ke result pe doosra. Net single %:

net = a + b + (a×b)/100
Decrease ke liye woh % negative. +20% phir −20%: 20+(−20)+(20)(−20)/100 = −4. Matlab 4% net kam. 0 nahi — kyunki doosra 20% badi base pe kata.
100 +20% 120 −20% 96

100 → 120 → 96. Net −4%. Same |%| ulta direction mein cancel nahi. CI ka year-year yahan nahi — woh Compound interest. Yahan do % changes, time nahi.

Price +10%, consumption −10% → expenditure = 1.10×0.90 = 0.99 → net −1%. (Quantity × price, CP–SP nahi.)

Exam / population

  • Pass p%. Fail = 100−p. Pass count n ho to total = n × 100 / p.
  • Marks m, fail by k, pass p% → (m+k) = p% of total. Total = (m+k)×100/p.
  • Population P, +a% phir +b% → P(1+a/100)(1+b/100). HCF bells “saath” nahi.
Example

Number pe +20% phir −20%. Net?

Solution

  1. Formula

    20−20−400/100 = −4%. 100 se 96. Zero trap.

Answer4% decrease
Example

Pass 40%. Student 40 marks, 20 se fail. Total marks?

Solution

  1. Pass line

    40+20=60 = 40% of T. T=60×100/40=150. 40 hi 40% mat (woh pass hota).

Answer150
Example

35% fail. 455 pass. Total students?

Solution

  1. Pass 65%

    0.65 T = 455. T=455×100/65=700. Average “kitna chahiye” nahi.

Answer700
Example

8000, pehle 10% badha, phir 20%. Ab?

Solution

  1. Multiply

    8000×1.1×1.2=10560. Net 10+20+200/100=32% → 8000×1.32 same. 10+20=30% = 10400 trap.

Answer10560

5. Sawal — basic se pro

Q1 · Basic

25% of 80 = ?

  1. 20
  2. 25
  3. 2000
  4. 4

Solution

  1. 1/4 × 80

    20. C /100 bhool. Simplification of-only nahi.

Answer20
Q2 · Basic

40 is what % of 160?

  1. 25%
  2. 40%
  3. 400%
  4. 16%

Solution

  1. 40/160

    25%.

Answer25%
Q3 · Basic

3/8 = ? %

  1. 37.5%
  2. 38%
  3. 24%
  4. 3.8%

Solution

  1. ×100

    37.5%.

Answer37.5%
Q4 · Medium

30% of a number = 150. Number?

  1. 500
  2. 45
  3. 180
  4. 450

Solution

  1. ×100/30

    500.

Answer500
Q5 · Medium

400 ko 25% increase. Naya?

  1. 500
  2. 425
  3. 300
  4. 100

Solution

  1. +100

    500. C decrease. D sirf farq.

Answer500
Q6 · Medium

A, B se 20% zyada. B, A se kitna % kam?

  1. 16⅔%
  2. 20%
  3. 80%
  4. 25%

Solution

  1. 20/120

    16⅔%. B same-% trap.

Answer16⅔%
Q7 · Medium

+20% phir −20%. Net?

  1. 4% decrease
  2. 0
  3. 4% increase
  4. 40% decrease

Solution

  1. ab/100

    −4%. B cancel trap. CI nahi.

Answer4% decrease
Q8 · Pro

Pass 40%. 40 marks, fail by 20. Total?

  1. 150
  2. 100
  3. 60
  4. 200

Solution

  1. 60=40%

    150. B 40=40%.

Answer150
Q9 · Pro

10% of 20% of 300 = ?

  1. 6
  2. 60
  3. 30
  4. 9

Solution

  1. 0.1×0.2×300

    6. B ek /100 bhool.

Answer6
Q10 · Pro

2 + 3 × 4. Is chapter?

  1. Nahi — Simplification
  2. Haan, 20%
  3. of = 14%
  4. HCF 14

Solution

  1. BODMAS

    A. 14 wahan. Yahan /100.

AnswerA

Practice

Pehle khud, phir neeche kholo.

12345 678910

P1

400 ko 25% decrease. Naya?

  1. 300
  2. 375
  3. 500
  4. 100

Solution

  1. −100

    300. B 500 se 25% mix.

Answer300
P2

0.45 = ? %

  1. 45%
  2. 4.5%
  3. 0.45%
  4. 450%

Solution

  1. ×100

    45%.

Answer45%
P3

12.5% of 64 = ?

  1. 8
  2. 12.5
  3. 4
  4. 16

Solution

  1. 1/8 × 64

    8.

Answer8
P4

35% fail. 455 pass. Total?

  1. 700
  2. 455
  3. 1300
  4. 650

Solution

  1. 65% = 455

    700.

Answer700
P5

8000, +10% phir +20%. Ab?

  1. 10560
  2. 10400
  3. 11000
  4. 9600

Solution

  1. 1.32×

    10560. B 30% trap.

Answer10560
P6

A, B se 25% kam. B, A se kitna % zyada?

  1. 33⅓%
  2. 25%
  3. 75%
  4. 20%

Solution

  1. 25/75

    33⅓%.

Answer33⅓%
P7

15% of 80 vs 80% of 15.

  1. Dono 12
  2. Pehla 12, doosra 15
  3. Pehla 80
  4. Dono 15

Solution

  1. x% of y = y% of x

    12=12.

AnswerDono 12
P8

Price +10%, consumption −10%. Expenditure net?

  1. 1% decrease
  2. 0
  3. 1% increase
  4. 20% decrease

Solution

  1. 1.1×0.9

    0.99 → −1%. Profit% nahi — qty×price.

Answer1% decrease
P9

16⅔% of 72 = ?

  1. 12
  2. 16
  3. 18
  4. 8

Solution

  1. 1/6 × 72

    12. Bells 16-20-24 nahi.

Answer12
P10

CP 200, SP 250. Profit % — is chapter?

  1. Nahi — Profit / loss
  2. Haan, 25%
  3. HCF 50
  4. BODMAS 250

Solution

  1. CP base

    A. 50/200=25% formula wahan. Yahan general %.

AnswerA

← Index · Simplification · HCF / LCM

Agle topic: Ratio and proportion.