✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 3 : 5 :: 12 : x. x nikaalo.
- 1 m mein kitne cm hote hain? 1 km mein kitne m?
- 2 cm : 1 m ko simplest form mein likho.
Answers dekho
- x = (5 × 12) ÷ 3 = 20
- 1 m = 100 cm, 1 km = 1,000 m
- 1 m = 100 cm, to 2 : 100 = 1 : 50
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 1 — Proportion Ka Recap ek baar dekh lijiye, phir yahan wapas aaiye.
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🎬 Kahani: Rohan Ka Atlas vs Papa Ka Phone
Rohan ki family Lucknow se Kanpur jaane ki planning kar rahi thi. Rohan ne apna school atlas khola aur ruler se naapa: dono shehron ke beech 1.5 cm.
Map ke neeche kone mein chhota sa likha tha: RF 1 : 50,00,000.
Rohan bola, “Papa, sirf 1.5 cm hai, paidal chal lete hain!” 😄 Papa hase, “Beta, yeh 1.5 cm kaagaz pe hai. Zameen pe kitna hai, woh yeh chhota sa ratio batayega.”
Phir Papa ne phone pe dekha, road se doori lagbhag 90 km aa rahi thi. Rohan ne atlas se hisaab lagaya to kuch aur aaya. “To atlas galat hai ya phone?” 🤔
Aaj hum seekhenge ki map ka scale (RF) kya hota hai, aur Rohan ka confusion bhi door karenge. 😉
— 📌 charumam.com
📖 Concept: Kaagaz Ke Centimetre, Zameen Ke Kilometre
Step 1: RF matlab map doori : asli doori
Representative Fraction (RF) ek ratio hai jo batata hai ki map ki doori, zameen ki asli doori ka kitna hissa hai:
$\text{RF} = \text{Map par doori} : \text{Zameen par asli doori}$
RF 1 : 50,00,000 ka matlab: map ka 1 cm = zameen ka 50,00,000 cm.
WHY? Pura desh kaagaz pe nahi aa sakta, to har doori ko ek hi factor se chhota kar diya jaata hai. Har doori same factor se chhoti hui, yaani map aur zameen proportion mein hain (Post 1 wali baat!).
Step 2: Units badlo: cm se km
50,00,000 cm sunke kuch samajh nahi aata. Isliye km mein badlo:
- 1 m = 100 cm
- 1 km = 1,000 m = 1,000 × 100 = 1,00,000 cm
50,00,000 cm ÷ 1,00,000 = 50 km. To map ka 1 cm = zameen ke 50 km.
Trick: cm se km banana ho to 5 zero hatao (÷ 1,00,000). 50,00,000 → 50.
WHY 5 zero? 1 km mein 1,00,000 cm hain, aur 1,00,000 mein 5 zero hain. 1,00,000 se divide = 5 zero kam.
Step 3: Map se asli doori nikaalo
$\text{Asli doori} = \text{Map doori} \times \text{RF ka bada number}$
Rohan: 1.5 cm × 50,00,000 = 75,00,000 cm = 75 km.
Ya seedha: 1 cm = 50 km, to 1.5 cm = 1.5 × 50 = 75 km.
WHY guna? Har 1 cm ke peeche 50 km chhupe hain. 1.5 cm mein 1.5 baar 50 km.
Step 4: Asli doori se map doori nikaalo
Ulta sawaal: 200 km ki doori is map pe kitni lambi dikhegi?
1 cm = 50 km, to 200 km = 200 ÷ 50 = 4 cm.
WHY divide? Poochh rahe hain “200 km mein 50 km wale kitne tukde hain?” Har tukda map pe 1 cm hai.
Step 5: Khud RF banao
Kisi naksha pe likha ho “2 cm = 10 km”, to RF kya hoga?
- Same unit: 10 km = 10 × 1,00,000 = 10,00,000 cm
- Ratio: 2 : 10,00,000
- Pehla term 1 banao (dono ÷ 2): 1 : 5,00,000
WHY same unit? RF mein dono terms same unit mein hon tabhi units cancel hoti hain. Isliye RF ki koi unit nahi hoti, aur woh cm, inch, kisi bhi ruler se kaam karta hai.
Step 6: Geographical doori vs road doori
Map pe ruler hamesha seedhi line naapta hai. Isse jo doori milti hai use geographical (seedhi) doori kehte hain, jaise chidiya udke jaaye.
Sadak ghoomti hai, mod leti hai, isliye road doori aksar zyada hoti hai. Rohan ke 75 km aur phone ke lagbhag 90 km dono sahi hain, bas alag cheezein naap rahe hain!
WHY yeh farak yaad rakhna? Exam mein map se nikli doori ko geographical doori hi likho, road doori nahi.
— 📌 charumam.com
🔐 Deep Concept: Bada Number Matlab Chhota Map
Ek hi 300 km ki doori teen alag maps pe dekho:
| RF | 1 cm = ? | 300 km map pe | Map doori × scale |
|---|---|---|---|
| 1 : 10,00,000 | 10 km | 30 cm | 30 × 10 = 300 km |
| 1 : 50,00,000 | 50 km | 6 cm | 6 × 50 = 300 km |
| 1 : 1,00,00,000 | 100 km | 3 cm | 3 × 100 = 300 km |
RF ka bada number badhta hai to map pe wahi doori chhoti hoti jaati hai. Bada number = zyada area ek kaagaz pe, par kam detail. Chhota number (jaise ghar ka naksha 1 : 100) = kam area, zyada detail.
Gehri baat: Last column dekho. Map doori × (1 cm ki km) hamesha 300 km aata hai, kyunki zameen ki doori fixed hai. Ek badha to doosra utne hi guna ghata. Is “ulte rishte” ka naam hum Post 7 mein seekhenge: inverse proportion! 😉
sirf charumam.com readers ke liye 🔐
✏️ Solved Examples
Example 1 (Easy): Ek map ka RF 1 : 1,00,000 hai. Do gaon map pe 4.5 cm door hain. Asli doori?
1,00,000 cm = 1 km, to 1 cm = 1 km.
Asli doori = 4.5 × 1 = 4.5 km.
WHY sahi hai? 4.5 × 1,00,000 = 4,50,000 cm, aur 4,50,000 ÷ 1,00,000 = 4.5 km ✅
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Example 2 (Medium): RF 1 : 25,00,000 wale map pe 340 km door do shehar kitne cm door dikhenge?
25,00,000 cm = 25 km, to 1 cm = 25 km.
Map doori = 340 ÷ 25 = 13.6 cm.
WHY sahi hai? Ulta check: 13.6 × 25 = 340 km ✅
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Example 3 (NCERT style): School ke naksha mein likha hai “1 cm = 5 m”. RF kya hai? Agar playground asal mein 60 m lamba hai, to naksha pe kitna lamba hoga?
5 m = 500 cm, to RF = 1 : 500.
Playground: 60 m = 6,000 cm. Map pe = 6,000 ÷ 500 = 12 cm. (Ya seedha 60 ÷ 5 = 12 cm.)
WHY sahi hai? 12 cm × 5 m = 60 m ✅
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Ab Rohan bhi expert: Ruler se naapo, RF se guna karo, aur cm ko km banana mat bhoolo! 🎉
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🏠 Real Life Mein Map Scale
- 📘 School atlas: Bharat ke map pe aksar 1 : 40,00,000 ya 1 : 60,00,000 jaisa scale hota hai.
- 🏠 Ghar ka naksha: Architect 1 : 100 use karte hain, yaani naksha ka 1 cm = asli 1 m.
- 🚗 Toy cars: Bahut si model cars 1 : 64 scale pe bani hoti hain. Asli car ka har 64 cm, model ka 1 cm.
- 📱 Phone ka map: Kone mein ek chhoti line (scale bar) pe “500 m” ya “2 km” likha hota hai, jo zoom karne pe badalta hai.
- 🌍 Globe: Poori dharti ka chhota model, har doori ek hi factor se chhoti ki gayi.
Har jagah ek hi soch: asli = model × scale, aur model = asli ÷ scale.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| Map doori aur RF diye hain | ✅ Map doori × bada number, phir cm → km | Har 1 cm ke peeche utni zameen |
| Asli doori di hai, map doori chahiye | ✅ Asli doori ÷ (1 cm ki asli doori) | Kitne “1 cm wale tukde” aayenge |
| “x cm = y km” diya hai, RF chahiye | ✅ Same unit (cm) karo, phir 1 : __ banao | RF mein units cancel hoti hain |
| Road ya safar ki doori poochhi ho | ❌ Map ki seedhi doori ko road doori mat maano | Sadak ghoomti hai, zyada lambi hoti hai |
| Map photocopy mein bada/chhota hua | ❌ Purana RF number mat lagao | Scale bar sahi rehta hai, RF number nahi |
— 📌 charumam.com
❌→✅ Worked Mistake
Sawaal: Ek map ka RF 1 : 20,00,000 hai. Do shehar map pe 3 cm door hain. Asli doori kitni hai?
❌ Galat: “3 × 20,00,000 = 60,00,000 km.”
Galti kya hai? 20,00,000 cm mein hai, km mein nahi! 60 lakh km to dharti se chaand ki doori (lagbhag 3.84 lakh km) se bhi 15 guna se zyada hai. 😄
✅ Sahi:
- 3 × 20,00,000 = 60,00,000 cm
- 60,00,000 ÷ 1,00,000 = 60 km
Yaad rakho: RF ke dono terms same unit mein hote hain. Map cm mein naapa, to bada number bhi cm hi hai. Phir 5 zero hatao, km mil jaayega.
sirf charumam.com pe milenge!
📝 10 MCQs
Q1. RF 1 : 50,000 ka matlab kya hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: RF mein dono terms same unit mein hote hain. cm aur km mix nahi hote.
- (b) sahi: Dono same unit mein: 1 cm map = 50,000 cm zameen ✅ (yaani 500 m).
- (c) galat: Ulta ho gaya. Map hamesha chhota hota hai, zameen badi.
- (d) galat: Map pe 50,000 cm (500 m) ka kaagaz nahi hota!
Q2. 1 km mein kitne cm hote hain?
Solution dekho
Sahi jawab: (c)
- (a) galat: 1,000 to 1 km mein metre hain.
- (b) galat: 10,000 cm = 100 m hi hai.
- (c) sahi: 1 km = 1,000 m = 1,000 × 100 cm = 1,00,000 cm ✅
- (d) galat: 10,00,000 cm = 10 km hai.
Q3. RF 1 : 30,00,000 wale map pe 1 cm kitne km ke barabar hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 30,00,000 ÷ 1,00,000 = 30, 3 nahi. Ek zero zyada hata diya.
- (b) sahi: 30,00,000 cm ÷ 1,00,000 = 30 km ✅
- (c) galat: Zero kam hataaye.
- (d) galat: Yeh sirf 2 zero hatane jaisa hai, cm se km ke liye 5 zero hatate hain.
Q4. RF 1 : 20,00,000 wale map pe do jagah 4 cm door hain. Asli doori?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 1 cm = 20 km, to 4 cm = 80 km ✅
- (b) galat: Zero ki galti: 4 × 2 = 8.
- (c) galat: Ek zero zyada laga diya.
- (d) galat: 20 ÷ 4 = 5, divide kar diya, guna karna tha.
Q5. RF 1 : 10,00,000 wale map pe 75 km ki doori kitni lambi dikhegi?
Solution dekho
Sahi jawab: (b)
- (a) galat: 75 km ko seedha cm likh diya.
- (b) sahi: 1 cm = 10 km, to 75 ÷ 10 = 7.5 cm ✅
- (c) galat: Ek decimal zyada khisak gaya.
- (d) galat: Guna kar diya, divide karna tha.
Q6. Kisi map pe 2 cm = 5 km hai. RF kya hai?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 5 km = 5,00,000 cm. 2 : 5,00,000 = 1 : 2,50,000 ✅
- (b) galat: Units alag hain (cm aur km), seedha 2 : 5 nahi likh sakte.
- (c) galat: Unit change bhool gaye, sirf 5 ÷ 2 kiya.
- (d) galat: 5,00,000 × 2 kar diya, divide karna tha.
Q7. Kaunsa map ek gali ko sabse zyada detail mein dikhayega?
Solution dekho
Sahi jawab: (a)
- (a) sahi: Sabse chhota number: 1 cm = sirf 100 m. Zyada detail ✅
- (b) galat: 1 cm = 1 km, detail kam.
- (c) galat: 1 cm = 10 km, gali dikhegi hi nahi.
- (d) galat: 1 cm = 100 km, yeh to poore desh ka map hoga.
Q8. Map se do shehron ki doori 120 km aayi. Sadak se jaane pe doori kya hogi?
Solution dekho
Sahi jawab: (b)
- (a) galat: Theek 120 tabhi jab sadak bilkul seedhi ho, jo bahut kam hota hai.
- (b) sahi: Map seedhi doori deta hai, sadak mod leti hai, isliye aksar zyada ✅
- (c) galat: Seedhi line sabse chhota raasta hai, sadak usse chhoti nahi ho sakti.
- (d) galat: Itna pakka bata sakte hain ki sadak seedhi doori se kam nahi hogi.
Q9. RF ki unit kya hoti hai?
Solution dekho
Sahi jawab: (c)
- (a) galat: RF mein cm ÷ cm hota hai, unit cancel ho jaati hai.
- (b) galat: km bhi cancel ho jaata hai jab dono terms same unit mein hon.
- (c) sahi: Same unit ÷ same unit = koi unit nahi ✅ Isliye RF kisi bhi ruler se chalta hai.
- (d) galat: RF mein dono terms same unit mein likhe jaate hain, mixed nahi.
Q10. Ghar ka naksha 1 : 50 pe hai. Naksha pe kamra 8 cm lamba hai. Asli lambai?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 8 × 50 = 400 cm = 4 m ✅
- (b) galat: 400 cm ko 40 m samajh liya. 100 cm = 1 m.
- (c) galat: Decimal galat jagah.
- (d) galat: 400 cm ko seedha m likh diya.
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. RF mein pehla number hamesha 1 kyun hota hai?
Taaki padhna aasaan ho: “map ka 1 unit = zameen ke itne units”. 2 : 10,00,000 bhi sahi hai, par 1 : 5,00,000 se turant samajh aata hai ki 1 cm = 5 km.
2. 60,00,000 ko kaise padhein? Kuch maps pe 6,000,000 likha hota hai.
60,00,000 = 60 lakh (Indian system). 6,000,000 = 6 million (international system). Dono ek hi number hain! Comma ki jagah alag hai, value nahi. Detail ke liye Lakh vs Million dekho.
3. Atlas aur phone ki doori alag kyun aati hai?
Atlas pe ruler seedhi line naapta hai (geographical doori). Phone aksar road doori batata hai, jo ghoomti sadak ki lambai hai. Isliye Rohan ke 75 km aur phone ke lagbhag 90 km dono sahi hain.
4. Scale bar aur RF mein kya farak hai?
RF ek number hai (1 : 50,00,000). Scale bar map pe bani ek line hai jispe likha hota hai “0 — 50 km”. Agar map ki photocopy badi ya chhoti karo, to scale bar bhi saath mein bada-chhota ho jaata hai aur sahi rehta hai, par RF ka likha number ab galat ho jaata hai.
5. Kya RF mein pehla number bada ho sakta hai, jaise 10 : 1?
Haan! Jab kisi chhoti cheez ko bada karke banaate hain, jaise science book mein machhar ya cell ka diagram, tab scale 10 : 1 ya 100 : 1 ho sakta hai. Matlab drawing asli se badi hai.
6. Map pe ghoomti nadi ya sadak ki lambai kaise naapein?
Ek dhaaga lo, use nadi ke saath-saath rakho, phir dhaage ko seedha karke ruler se naapo. Ab RF se guna karo. Isse lagbhag asli lambai mil jaayegi.
— 📌 charumam.com
🏋️ Practice Zone (12 Sawaal)
Q1. Easy RF 1 : 1,00,000 wale map pe 1 cm kitne km ke barabar hai?
Solution dekho
1,00,000 cm = 1 km.
Q2. Easy 5 km ko cm mein badlo.
Solution dekho
5 × 1,00,000 = 5,00,000 cm.
Q3. Easy RF 1 : 40,00,000 wale map pe do shehar 2 cm door hain. Asli doori?
Solution dekho
1 cm = 40 km, to 2 cm = 80 km.
Q4. Easy Ek plan ka scale 1 : 500 hai. Plan pe 6 cm ki deewar asal mein kitni lambi hai?
Solution dekho
6 × 500 = 3,000 cm = 30 m.
Q5. Medium RF 1 : 25,00,000, map doori 6.4 cm. Asli doori?
Solution dekho
1 cm = 25 km. 6.4 × 25 = 160 km.
Q6. Medium RF 1 : 60,00,000 wale map pe 450 km kitne cm dikhega?
Solution dekho
1 cm = 60 km. 450 ÷ 60 = 7.5 cm.
Q7. Medium Ek naksha pe 3 cm = 12 km hai. RF nikaalo.
Solution dekho
12 km = 12,00,000 cm. 3 : 12,00,000 → 3 se divide → 1 : 4,00,000.
Q8. Medium 1 : 200 ke naksha pe ek kamra 2.5 cm × 2 cm hai. Asli lambai-chaudai aur area?
Solution dekho
2.5 × 200 = 500 cm = 5 m. 2 × 200 = 400 cm = 4 m.
Area = 5 × 4 = 20 m².
Q9. NCERT style RF 1 : 80,00,000 wale map pe A se B 3.5 cm aur B se C 2 cm hai. A se B hote hue C tak ki geographical doori?
Solution dekho
1 cm = 80 km. A–B = 3.5 × 80 = 280 km, B–C = 2 × 80 = 160 km.
Kul = 440 km.
Q10. NCERT style 100 km ki doori (i) 1 : 20,00,000 aur (ii) 1 : 50,00,000 wale maps pe kitni lambi dikhegi?
Solution dekho
(i) 1 cm = 20 km → 100 ÷ 20 = 5 cm. (ii) 1 cm = 50 km → 100 ÷ 50 = 2 cm.
Bada RF number → chhoti map doori.
Q11. NCERT style Ek toy car 1 : 64 scale pe bani hai aur 7 cm lambi hai. Asli car kitni lambi hai?
Solution dekho
7 × 64 = 448 cm = 4.48 m.
Q12. NCERT style RF 1 : 40,00,000 wale map pe shehar P aur Q 6.5 cm door hain. Unke beech road doori 310 km hai. Road doori, geographical doori se kitni zyada hai?
Solution dekho
Geographical = 6.5 × 40 = 260 km.
Farak = 310 − 260 = 50 km.
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. Ek map pe RF 1 : 10,00,000 chhapa hai. Rohan ne uski photocopy 2 guna badi (har lambai double) kar li. Ab photocopy ka sahi RF kya hai?
Solution dekho
Pehle 1 cm = 10 km tha. Ab wahi 10 km photocopy pe 2 cm ho gaye. To 1 cm = 5 km.
Naya RF = 1 : 5,00,000. Purana chhapa number ab galat hai, par scale bar (agar bana ho) saath mein bada hua aur sahi hai.
Q2. Map A (1 : 25,00,000) pe do shehar 4 cm door hain. Map B pe wahi shehar 10 cm door hain. Map B ka RF kya hai?
Solution dekho
Asli doori = 4 × 25 = 100 km. Map B pe 10 cm = 100 km, to 1 cm = 10 km = 10,00,000 cm.
RF = 1 : 10,00,000.
Q3. School ka ground 120 m × 80 m hai. Use 1 : 1,000 scale pe A4 sheet (29.7 cm × 21 cm) pe banana hai. Kya fit hoga?
Solution dekho
120 m = 12,000 cm → 12,000 ÷ 1,000 = 12 cm. 80 m → 8 cm.
12 cm × 8 cm aaram se A4 pe aa jaayega, haan fit hoga. (1 : 500 pe bhi 24 cm × 16 cm aa jaata.)
Q4. Map ka RF 1 : 1,00,000 hai, yaani 1 cm = 1 km. Map pe ek park ka area 3 cm² hai. Kya asli area 3 km hai?
Solution dekho
Area ki unit km² hogi, km nahi. 1 cm × 1 cm ka chhota square asal mein 1 km × 1 km = 1 km² hai.
To 3 cm² → 3 km². (Dhyaan do: agar 1 cm = 2 km hota, to 1 cm² = 2 × 2 = 4 km² hota, 2 nahi!)
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🏆 Olympiad Corner
Q1. RF 1 : 2,50,000 wale map pe do jagah 8.4 cm door hain. Asli doori?
Solution dekho
2,50,000 cm = 2.5 km. 8.4 × 2.5 = 21 km.
Q2. Do shehar asal mein 90 km door hain aur map pe 4.5 cm. Map ka RF?
Solution dekho
90 km = 90,00,000 cm. 90,00,000 ÷ 4.5 = 20,00,000.
RF = 1 : 20,00,000.
Q3. RF 1 : 5,00,000 wale map pe do gaon 6 cm door hain. Ek cyclist 15 km/h ki raftaar se seedhe raaste pe jaaye to kitna samay lagega?
Solution dekho
1 cm = 5 km → 6 cm = 30 km. Samay = 30 ÷ 15 = 2 ghante.
(Asli sadak ghoomti ho to zyada samay lagega.)
Q4. RF 1 : 50,000 wale map pe ek jheel ka area 6 cm² hai. Asli area kitna hai?
Solution dekho
1 cm = 50,000 cm = 0.5 km. 1 cm² = 0.5 × 0.5 = 0.25 km².
6 cm² = 6 × 0.25 = 1.5 km².
sirf charumam.com readers ke liye 🔐
💗 CharuMam Motivation
Map ek chhota sa kaagaz hai, par poora desh dikha deta hai, bas ek ratio ki madad se. 🗺️ Aapka roz ka chhota kadam bhi aisa hi hai: aaj ki 1 page practice, kal ke ek bade chapter ka “scale model” hai.
Aur haan, Rohan ki tarah agar kabhi jawab 60 lakh km aa jaaye, to ghabraao mat, hanso aur units check karo! 😄 Galti pakadna bhi seekhna hai. Focus rakho, mehnat karo, sabr rakho, manzil zaroor aayegi. 🌟
— 📌 charumam.com
🟢 Master Recap
- RF = map doori : asli doori, dono same unit mein. RF ki koi unit nahi.
- 1 km = 1,00,000 cm. cm se km: 5 zero hatao.
- Asli doori = map doori × (1 cm ki asli doori).
- Map doori = asli doori ÷ (1 cm ki asli doori).
- “x cm = y km” se RF: y ko cm mein badlo, phir 1 : __ banao.
- Map se geographical (seedhi) doori milti hai, road doori aksar zyada hoti hai.
- RF ka bada number → chhota map, kam detail. Chhota number → zyada detail.
- Area ke liye scale ka square lagta hai (1 cm = 1 km → 1 cm² = 1 km²).
— charumam.com 🎯
👉 Aage Kya?
Ab tak humne do terms wale ratio dekhe (map : zameen). Par biryani mein chawal, paani aur masala teeno ka ratio hota hai! Agle post mein seekhenge do se zyada terms wala ratio, jaise 2 : 3 : 5. 🍛
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬