✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 3/8 ko percentage mein likho.
- 360 ka 1/4 kitna hai?
- ₹1,200 ko 1 : 2 : 3 mein baanto.
Answers dekho
- 3/8 × 100 = 37.5%
- 360 ÷ 4 = 90
- Kul 6 hisse, 1 hissa = 200: ₹200, ₹400, ₹600
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 4 — Ratio Mein Baantna aur Fraction ↔ Decimal ↔ Percentage ek baar dekh lijiye, phir yahan wapas aaiye.
— 📌 charumam.com
🎬 Kahani: Assembly Ka Gol Chart
Monday ki assembly mein Principal Ma’am ne ek bada sa chart dikhaya. Usmein ek gola tha, rang-birange tukdon mein bata hua, aur upar likha tha: “Class 8B ke 40 bachchon ka pasandeeda khel”.
Sabne turant bola, “Cricket sabse popular hai!” Par phir Ma’am ne poochha, “Achha, to batao, kitne bachchon ko kabaddi pasand hai?”
Chart pe koi ginti likhi hi nahi thi, sirf angles! Sab chup. 🤔 Aaj seekhenge ki is gol chart, yaani pie chart, ko kaise padhte hain, aur Ma’am ke sawaal ka jawab bhi denge. 😉
— 📌 charumam.com
📖 Concept: Ek Gola, Kai Tukde
Step 1: Poora gola = poori cheez = 360° = 100%
Pie chart ek gola (circle) hai jo poori cheez ko dikhata hai. Gole ke centre pe poora angle 360° hota hai.
$\text{Poora gola} = 360^\circ = 100\% = 1$
WHY gola? Roti ya pizza ki tarah socho. Jitna bada hissa, utna bada tukda. Saare tukde milke hamesha poori roti banate hain, isliye pie chart sirf poore ke hisson ke liye hota hai.
Step 2: Tukde ka angle, hisse ke proportion mein
Har tukde ka angle uske hisse ke proportion mein hota hai:
$\dfrac{\text{Tukde ka angle}}{360^\circ} = \dfrac{\text{Uski ginti}}{\text{Kul ginti}}$
WHY? Yeh wahi proportion hai jo Post 1 mein seekha: angle : 360 :: ginti : kul. Agar kisi cheez ki ginti double ho, to uska angle bhi double hoga.
Step 3: Angle se fraction aur percentage
Fraction = angle ÷ 360. Percentage = fraction × 100.
| Angle | Fraction | Percentage |
|---|---|---|
| 180° | 1/2 | 50% |
| 120° | 1/3 | 33 1/3 % |
| 90° | 1/4 | 25% |
| 72° | 1/5 | 20% |
| 60° | 1/6 | 16 2/3 % |
| 45° | 1/8 | 12.5% |
| 36° | 1/10 | 10% |
Yaad rakhne layak: 100% = 360°, to 1% = 3.6° aur 10% = 36°.
WHY? 360 ÷ 100 = 3.6. Percentage aur angle dono same poori cheez ko alag “tape” se naapte hain: ek 100 ke tape se, doosra 360 ke tape se.
Step 4: Angle se asli ginti nikaalo
$\text{Ginti} = \dfrac{\text{Angle}}{360^\circ} \times \text{Kul ginti}$
Ma’am ka sawaal: Kabaddi = 90°. 90/360 = 1/4. To kabaddi wale = 1/4 × 40 = 10 bachche.
Isi tarah: Cricket = 135/360 × 40 = 15, Football = 72/360 × 40 = 8, Kho-kho = 63/360 × 40 = 7. Check: 15 + 10 + 8 + 7 = 40 ✅
WHY? Angle batata hai poore ka kitna hissa (fraction). Kisi cheez ka fraction nikaalne ke liye us fraction se guna karte hain (Ch 1 wali Kisi Cheez Ka Percentage soch).
Step 5: Bina number ke bhi padho
- Sabse bada tukda = sabse zyada, sabse chhota = sabse kam.
- Tukda aadhe gole (seedhi line) jitna = 50%.
- Tukde ka kona right angle (L shape) = 25%.
- Do tukde barabar dikhein = dono ki ginti barabar.
WHY yeh kaam ka hai? Pie chart ki asli taakat yahi hai: ek nazar mein samajh aa jaata hai ki kaun bada hai aur poore ka kitna hissa hai.
— 📌 charumam.com
🔐 Deep Concept: Angle Ko Percentage Mat Samjho
Sabse common bhool: “Football ka angle 72° hai, to 72% bachchon ko football pasand hai.” ❌
Socho, agar angle hi percentage hota, to 4 tukdon ka jod 360% ho jaata! Par poori cheez to 100% hai.
| Khel | Angle | Angle ÷ 360 | Percentage |
|---|---|---|---|
| Cricket | 135° | 3/8 | 37.5% |
| Kabaddi | 90° | 1/4 | 25% |
| Football | 72° | 1/5 | 20% |
| Kho-kho | 63° | 7/40 | 17.5% |
| Kul | 360° | 1 | 100% |
Golden rule: Angle ko percentage banane ke liye 3.6 se divide karo (kyunki 1% = 3.6°). 72 ÷ 3.6 = 20%. Aur percentage ko angle banane ke liye 3.6 se guna.
Ek aur baat: Tukde ka area bhi angle ke proportion mein hota hai. 90° wala tukda poore gole ke area ka bhi 1/4 hota hai. Isliye aankh se dekhke bhi sahi andaaza lagta hai.
sirf charumam.com readers ke liye 🔐
✏️ Solved Examples
Example 1 (Easy): Pie chart ka ek tukda 90° ka hai. Woh poori cheez ka kitna fraction aur kitne percent hai?
Fraction = 90/360 = 1/4. Percentage = 1/4 × 100 = 25%.
WHY sahi hai? Shortcut: 90 ÷ 3.6 = 25% ✅
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Example 2 (Medium): 480 bachchon ke survey mein aane ke saadhan: Bus 120°, Cycle 60°, Paidal 90°, Auto 45°, Car 45°. Har saadhan se kitne bachche aate hain?
Bus = 120/360 × 480 = 1/3 × 480 = 160
Cycle = 60/360 × 480 = 1/6 × 480 = 80
Paidal = 90/360 × 480 = 1/4 × 480 = 120
Auto = Car = 45/360 × 480 = 1/8 × 480 = 60 each
WHY sahi hai? 160 + 80 + 120 + 60 + 60 = 480 ✅ aur angles ka jod 360° ✅
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Example 3 (NCERT style): Ek parivaar ki mahine ki kamaai ₹40,000 hai. Kharche ka pie chart neeche hai. Har cheez pe kitna kharch hua, aur kitne percent?
Khaana = 144/360 = 0.4 = 40% → 0.4 × 40,000 = ₹16,000
Kiraya = 108/360 = 0.3 = 30% → ₹12,000
Padhaai = 54/360 = 0.15 = 15% → ₹6,000
Bachat = 36/360 = 0.1 = 10% → ₹4,000
Baaki = 18/360 = 0.05 = 5% → ₹2,000
WHY sahi hai? 16,000 + 12,000 + 6,000 + 4,000 + 2,000 = 40,000 ✅ aur 40 + 30 + 15 + 10 + 5 = 100% ✅
📌 charumam.com
Ab poori assembly expert: Kabaddi wale 10 bachche, aur angle ÷ 360 hi hai asli chaabi! 🎉
— 📌 charumam.com
🏠 Real Life Mein Pie Chart
- 🗳️ Chunav results: TV pe har party ke vote share ka gol chart.
- 📱 Phone storage: Settings mein Photos, Apps, System ka hissa aksar gol ya patti wale chart mein dikhta hai.
- 🏛️ Sarkari budget: “Rupaya kahan se aata hai, kahan jaata hai” wala gol chart har saal akhbaar mein chhapta hai.
- 🍽️ Thaali ka balance: Diet chart mein sabzi, anaaj, dal, phal ka hissa pie ki tarah dikhaya jaata hai.
- 📝 Exam paper: Kis chapter se kitne marks aayenge, uska weightage chart.
Har jagah ek hi sawaal: poore ka kitna hissa? Jawab: angle ÷ 360.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| Poori cheez ke hisse dikhaane hain (kharcha, vote, survey) | ✅ Pie chart | Saare tukde milke 100% bante hain |
| Samay ke saath badlaav (har mahine ka taapmaan) | ❌ Pie nahi, line graph (Ch 5) | Yeh hisse nahi, alag-alag samay ki values hain |
| Ek insaan kai options chun sake (multiple choice survey) | ❌ Pie nahi | Jod 100% se zyada ho jaata hai |
| Bahut saare chhote-chhote hisse | ❌ Mushkil, “Baaki” mein milao ya bar graph lo | Patle tukde padhe nahi jaate |
| Angle se ginti chahiye | ✅ (angle ÷ 360) × kul | Angle poore ka fraction batata hai |
— 📌 charumam.com
❌→✅ Worked Mistake
Sawaal: 40 bachchon ke pie chart mein football ka tukda 72° hai. Kitne percent bachchon ko football pasand hai, aur kitne bachche?
❌ Galat: “Angle 72° hai, to 72%. Yaani 40 ka 72% = 28.8 bachche.”
Galti kya hai? Angle ko seedha percentage maan liya. Aur 28.8 bachche? Aadha bachcha nahi hota! Yeh khud signal hai ki kuch gadbad hai. 😄
✅ Sahi:
- Fraction = 72/360 = 1/5
- Percentage = 1/5 × 100 = 20% (ya 72 ÷ 3.6 = 20)
- Bachche = 1/5 × 40 = 8
Yaad rakho: Pie chart mein poora = 360°, 100 nahi. Pehle 360 se divide karo.
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📝 10 MCQs
Q1. Poore pie chart ke centre pe kul angle kitna hota hai?
Solution dekho
Sahi jawab: (c)
- (a) galat: 100 percentage ka “poora” hai, angle ka nahi.
- (b) galat: 180° sirf aadha gola hai.
- (c) sahi: Poora gola = 360° ✅
- (d) galat: 90° sirf ek chauthai hai.
Q2. 180° ka tukda poori cheez ka kitne percent hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: Angle ko 10 se divide kar diya, galat.
- (b) sahi: 180/360 = 1/2 = 50% ✅
- (c) galat: Angle ko seedha % maan liya.
- (d) galat: 25% to 90° hota hai.
Q3. 90° ka tukda poori cheez ka kaunsa fraction hai?
Solution dekho
Sahi jawab: (c)
- (a) galat: 1/2 = 180°.
- (b) galat: 1/3 = 120°.
- (c) sahi: 90/360 = 1/4 ✅
- (d) galat: 90 ko 10 samjha, 1/9 nahi.
Q4. 25% hissa dikhaane ke liye kitne degree ka tukda chahiye?
Solution dekho
Sahi jawab: (b)
- (a) galat: % ko seedha degree maan liya.
- (b) sahi: 25 × 3.6 = 90° ✅
- (c) galat: 100° ka koi aadhaar nahi.
- (d) galat: 45° = 12.5% hai.
Q5. 10% ke liye angle kitna?
Solution dekho
Sahi jawab: (b)
- (a) galat: % ko seedha degree maan liya.
- (b) sahi: 10 × 3.6 = 36° ✅
- (c) galat: 3.6° to 1% hai.
- (d) galat: 100° ≈ 27.8% hoga.
Q6. Kul 60 cheezon ke pie chart mein ek tukda 120° ka hai. Us tukde mein kitni cheezein?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 120/360 = 1/3, 1/3 × 60 = 20 ✅
- (b) galat: 1 − 1/3 = 2/3 wala hissa nikaal diya.
- (c) galat: 120 ÷ 10 = 12, galat.
- (d) galat: 30 to aadha hai, 180° wala.
Q7. 200 logon ke survey mein ek tukda 54° ka hai. Us tukde mein kitne log?
Solution dekho
Sahi jawab: (b)
- (a) galat: Angle ko seedha log maan liya.
- (b) sahi: 54/360 = 0.15, 0.15 × 200 = 30 ✅
- (c) galat: 54 × 2 = 108, galat soch.
- (d) galat: 54 ÷ 2 = 27, galat soch.
Q8. Kisi bhi pie chart ke saare tukdon ke angles ka jod kitna hota hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 100 percentages ka jod hai.
- (b) sahi: Hamesha 360° ✅ chahe kitne bhi tukde hon.
- (c) galat: Tukde kitne bhi hon, poora gola 360° hi rahega.
- (d) galat: 180° sirf aadha gola.
Q9. Kis data ke liye pie chart theek NAHI hai?
Solution dekho
Sahi jawab: (c)
- (a) galat: Kharche ke hisse poori kamaai banate hain, pie chalega.
- (b) galat: Har bachcha ek phal chunta hai, jod = poori class. Pie chalega.
- (c) sahi: Taapmaan hisse nahi hain, samay ke saath badlaav hai. Line graph lo ✅
- (d) galat: Vote share poore votes ke hisse hain, pie chalega.
Q10. Pie chart mein teen tukde hain: 100°, 140° aur x°. x = ?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 360 − 100 − 140 = 120° ✅
- (b) galat: 180 − 120, galat poora angle liya.
- (c) galat: 100 + 140 = 240, ghatana tha.
- (d) galat: Andaaze se barabar maan liya.
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Gola 360° ka hi kyun hota hai?
Yeh parampara purane Babylon se aayi hai. 360 ek bahut “friendly” number hai: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15… sabse poora divide hota hai. Isliye 1/3, 1/4, 1/5, 1/6 jaise hisse whole number degrees mein aa jaate hain.
2. Pie chart aur bar graph mein kya farak hai?
Pie chart dikhata hai poore ka kitna hissa. Bar graph dikhata hai kiski kitni ginti, aur cheezon ko aapas mein compare karna aasaan karta hai. Agar hisse poora nahi banate (jaise alag-alag shehron ki aabaadi), to bar graph lo.
3. Angle naapte kaise hain?
Protractor (chaanda) se, jo geometry box mein hota hai. Pie chart banana agle post (Post 6 — Pie Chart Kaise Banayein) mein step-by-step seekhenge.
4. Kya saare tukdon ke percentages ka jod 100 hi aana chahiye?
Haan, kyunki saare tukde milke poori cheez hain. Kabhi round off karne se 99% ya 101% aa sakta hai, woh chalta hai. Par 120% aaye to samjho kuch galat hai.
5. Donut chart kya hota hai?
Bilkul pie chart jaisa, bas beech mein ek gol chhed hota hai. Niyam wahi: har tukde ka angle uske hisse ke proportion mein.
6. 3D pie chart se dhokha kaise hota hai?
Tircha (3D) pie chart mein aage wale tukde zyada bade dikhte hain aur peeche wale chhote, chahe angle same ho. Isliye sahi padhne ke liye seedha (2D) pie chart behtar hai, aur angle ya % likha ho to usi pe bharosa karo.
— 📌 charumam.com
🏋️ Practice Zone (12 Sawaal)
Q1. Easy 120° ka tukda poori cheez ka kaunsa fraction hai?
Solution dekho
120/360 = 1/3.
Q2. Easy 45° ka tukda kitne percent hai?
Solution dekho
45 ÷ 3.6 = 12.5% (ya 45/360 = 1/8 = 12.5%).
Q3. Easy 20% hisse ke liye kitne degree ka tukda chahiye?
Solution dekho
20 × 3.6 = 72°.
Q4. Easy Kul 36 cheezon ke pie chart mein ek tukda 60° ka hai. Kitni cheezein?
Solution dekho
60/360 = 1/6. 1/6 × 36 = 6.
Q5. Medium Ek pie chart ke angles 150°, 90°, x° aur 60° hain. x nikaalo.
Solution dekho
x = 360 − (150 + 90 + 60) = 360 − 300 = 60°.
Q6. Medium 300 students ke survey mein ek tukda 72° ka hai. Us tukde mein kitne students?
Solution dekho
72/360 = 1/5. 1/5 × 300 = 60.
Q7. Medium Ek parivaar ki kamaai ₹24,000 hai. Bachat ka tukda 30° ka hai. Bachat kitni?
Solution dekho
30/360 = 1/12. 24,000 ÷ 12 = ₹2,000.
Q8. Medium Kahani wale pie chart (40 bachche: Cricket 135°, Kabaddi 90°, Football 72°, Kho-kho 63°) se har khel ke bachche nikaalo.
Solution dekho
Cricket 15, Kabaddi 10, Football 8, Kho-kho 7. Check: jod = 40 ✅
Q9. NCERT style 120 students ka pasandeeda subject: Hindi 108°, English 72°, Maths 126°, Science 54°. Har subject ke students?
Solution dekho
Hindi = 108/360 × 120 = 36. English = 72/360 × 120 = 24. Maths = 126/360 × 120 = 42. Science = 54/360 × 120 = 18.
Check: 36 + 24 + 42 + 18 = 120 ✅
Q10. NCERT style Ek pie chart mein 18 students = 54°. Survey mein kul kitne students the?
Solution dekho
54/360 = 0.15. 0.15 × kul = 18 → kul = 18 ÷ 0.15 = 120.
Q11. NCERT style Ek pie chart mein tukda A 90° aur tukda B 108° ka hai. B, A se poori cheez ke kitne percent zyada hai?
Solution dekho
Farak = 108 − 90 = 18°. 18 ÷ 3.6 = 5%.
Q12. NCERT style School aane ke saadhan ke pie chart mein cycle ka tukda 45° ka hai aur 20 bachche cycle se aate hain. Survey mein kitne bachche the?
Solution dekho
45/360 = 1/8. Kul = 20 × 8 = 160.
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. Class A ke pie chart mein cricket 90° aur Class B ke pie chart mein cricket 120° hai. Riya kehti hai, “Class B mein zyada bachchon ko cricket pasand hai.” Kya yeh pakka hai?
Solution dekho
Pakka nahi. Angle sirf hissa batata hai, ginti nahi. Agar Class A mein 60 bachche hon: 90/360 × 60 = 15. Class B mein 30 bachche hon: 120/360 × 30 = 10. Yahan Class A mein zyada!
Do alag totals wale pie charts ki ginti compare karne ke liye totals pata hone chahiye (Ch 1 ka Percentage Se Tulna yaad karo).
Q2. Kya pie chart mein koi tukda 0° ka ho sakta hai? Aur 360° ka?
Solution dekho
0° ka matlab us category mein koi nahi, to aam taur pe use chart mein dikhaate hi nahi. 360° ka matlab sab ek hi category mein, tab pie chart mein sirf ek poora gola hoga, jo kuch compare nahi karta. Dono cases mein pie chart ka koi khaas fayda nahi.
Q3. Ek survey mein bachchon se poochha, “Kaunse phal pasand hain? (jitne chaaho chuno)”. Results: Aam 70%, Kela 50%, Seb 40%. Kya iska pie chart ban sakta hai?
Solution dekho
Nahi. 70 + 50 + 40 = 160%, jo 100% se zyada hai, kyunki ek bachche ne kai phal chune. Pie chart ke tukde milke 360° (100%) se zyada nahi ho sakte. Yahan bar graph sahi hai.
Q4. Ek pie chart mein teen cheezein 10, 10, 20 hain (angles 90°, 90°, 180°). Agar pehli cheez 10 se 20 ho jaaye aur baaki wahi rahein, to kya uska angle double (180°) ho jaayega?
Solution dekho
Nahi. Naya kul = 20 + 10 + 20 = 50. Pehli ka angle = 20/50 × 360 = 144°, 180° nahi.
WHY: Angle poore ka hissa hai. Ek cheez badhi to poora bhi badha, isliye doosron ke angle chhote ho gaye (72° aur 144°).
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🏆 Olympiad Corner
Q1. Ek pie chart ke chaar tukdon ke angles 2 : 3 : 4 : 6 ke ratio mein hain. Angles nikaalo.
Solution dekho
Kul 15 hisse, 1 hissa = 360 ÷ 15 = 24°.
Angles = 48°, 72°, 96°, 144°.
Q2. Ek pie chart mein tukda A, tukda B se 25% bada hai, aur teesra tukda C 90° ka hai. A aur B ke angles?
Solution dekho
A + B = 360 − 90 = 270. A = 1.25B → 2.25B = 270 → B = 120°, A = 150°.
Q3. 720 voters ke chunav mein Party X ko 35% vote mile, Party Y ka tukda 120° hai, baaki Party Z ko. Har party ke vote aur jeet kiski?
Solution dekho
X = 35% × 720 = 252. Y = 120/360 × 720 = 240. Z = 720 − 252 − 240 = 228.
Party X jeeti (252 vote).
Q4. Ravi ke din ke 24 ghante: neend 8, school 7, khel 2, padhaai 3, baaki 4 ghante. Pie chart mein har ek ka angle kya hoga? (Shortcut socho!)
Solution dekho
360 ÷ 24 = 15°, yaani 1 ghanta = 15°.
Neend 120°, school 105°, khel 30°, padhaai 45°, baaki 60°. Jod = 360° ✅
sirf charumam.com readers ke liye 🔐
💗 CharuMam Motivation
Pie chart dikhata hai ki poori cheez ke andar kaun kitni jagah leta hai. 🥧 Aapke din ka bhi ek pie chart hai: neend, school, khel, phone, padhaai.
Kabhi apna “din ka pie chart” banaake dekho. Agar phone ka tukda sabse bada nikle, to ghabraao mat, bas dheere-dheere padhaai ka tukda badhaao. Chhote badlaav, roz ka focus, thodi mehnat aur sabr, aur aapka pie chart khud badal jaayega! 🌟
— 📌 charumam.com
🟢 Master Recap
- Pie chart = gola jo poori cheez ke hisse dikhata hai.
- Poora gola = 360° = 100% = 1.
- Angle ÷ 360 = fraction. Fraction × 100 = percentage.
- 1% = 3.6°, 10% = 36°, 25% = 90°, 50% = 180°.
- Ginti = (angle ÷ 360) × kul ginti.
- Saare angles ka jod 360°, saare % ka jod 100%.
- Angle ko kabhi seedha % mat samjho.
- Samay ke saath badlaav ya multiple-choice data ke liye pie chart nahi.
— charumam.com 🎯
👉 Aage Kya?
Ab aap pie chart padh sakte ho. Par agar data diya ho aur chart khud banana ho? Angle kaise nikaalein, protractor kaise chalayein? Agle post mein seekhenge pie chart kaise banayein, step-by-step! 📐
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬