✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 1 m mein kitne cm?
- 18 aur 12 ka HCF?
- 30 ko 3 se bhaag do.
Answers dekho
- 100 cm
- 6
- 10
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 1 — Proportional Badlaav Kya Hai? ek baar padh lijiye, phir yahan aaiye.
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🎬 Kahani: Kirti Ki Class Ka Hisaab
Kirti ki class mein 18 ladkiyan aur 12 ladke hain. Sports teacher ne teams banaate hue kaha, “Har team mein 3 ladkiyan aur 2 ladke rakho, tabhi poori class jaisi lagegi.”
Kirti ne socha, “18 aur 12 ka 3 aur 2 se kya lena-dena?” 🤔
Teacher muskuraayin: “18 : 12 aur 3 : 2, dono ek hi rishta batate hain. Har 3 ladkiyon pe 2 ladke!”
Yeh “:” wala rishta hi hai ratio. Aaj seekhenge ise padhna, likhna aur sahi use karna. 😉
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📖 Concept: a : b Ka Asli Matlab
Step 1: Ratio padhna aur samajhna
a : b ko padhte hain “a is to b” ya “a ratio b”. Matlab: har a pehli cheez ke liye, b doosri cheez.
Kirti ki class: ladkiyan : ladke = 18 : 12. Matlab “har 18 ladkiyon pe 12 ladke”, ya chhote mein “har 3 pe 2”.
WHY ratio? Ratio ek line mein do cheezon ka rishta bata deta hai, chahe numbers chhote hon ya bade.
Step 2: Terms kya hain?
18 : 12 mein 18 pehla term aur 12 doosra term hai. Dono milke ratio ke “terms” kehlaate hain.
WHY naam yaad rakhein? Aage “dono terms ko same number se guna karo” jaise niyam aayenge.
Step 3: Order bahut zaroori hai
- Ladkiyan : ladke = 18 : 12
- Ladke : ladkiyan = 12 : 18
Dono alag baatein hain! Pehla kehta hai ladkiyan zyada, doosra ladke kam.
WHY? Ratio mein jo cheez pehle bolte ho, uska number pehle aata hai. Order ulta = matlab ulta.
Step 4: Units same hone chahiye
Ek rassi 50 cm, doosri 2 m. Ratio = 50 : 2? Nahi!
Pehle same unit: 2 m = 200 cm. Ratio = 50 : 200.
WHY? 50 aur 2 alag “size ke dabbe” hain (cm aur m). Same unit mein badle bina tulna galat hogi. Aur jab units same hon, to ratio ki apni koi unit nahi hoti.
Step 5: Hissa : hissa aur hissa : poora
Class mein kul 30 bachche.
- Ladkiyan : ladke = 18 : 12 (hissa : hissa)
- Ladkiyan : kul = 18 : 30 (hissa : poora)
WHY dhyaan? Sawaal mein “kul” ya “poori class” likha ho to doosra term poora hoga. Yahi aage fraction aur percentage se judta hai.
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🔐 Deep Concept: Ratio Aur Rate Mein Kya Farak Hai?
Ab tak dono cheezein ek hi type ki thin (ladke-ladkiyan, cm-cm). Par kabhi alag type ki cheezein bhi jodte hain:
- Bus 180 km, 3 ghante mein: 180 km : 3 h → har ghante 60 km. Ise rate kehte hain: 60 km/h.
- ₹120 mein 4 kg aaloo → ₹30 per kg.
Antar: Ratio mein units same hoti hain aur hat jaati hain. Rate mein units alag hoti hain, isliye jawab ke saath unit likhte hain (km/h, ₹/kg).
Gehri baat: Ratio sirf “kitna zyada” nahi batata, “kitne guna” batata hai. 18 aur 12 ka farak 6 hai, par ratio batata hai ladkiyan ladkon ki 1.5 guna hain. Farak se shakal ya swaad samajh nahi aata, ratio se aata hai (Post 1 — Proportional Badlaav Kya Hai? yaad hai?).
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✏️ Solved Examples
Example 1 (Easy): Ek tokri mein 7 aam aur 5 kele hain. (a) aam : kele (b) kele : aam (c) aam : kul phal
(a) 7 : 5 (b) 5 : 7 (c) kul = 12, to 7 : 12
WHY sahi hai? Jo pehle bola, uska number pehle ✅
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Example 2 (Medium): 75 paise aur ₹3 ka ratio likho.
₹3 = 300 paise. Ratio = 75 : 300.
WHY sahi hai? Dono paise mein, ab tulna sahi ✅ (Isse chhota kaise karein, agle post mein.)
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Example 3 (NCERT style): Ek mala mein har 3 safed motiyon ke baad 2 laal moti hain. 40 motiyon ki mala mein kitne safed, kitne laal? Safed : laal aur laal : kul ratio likho.
Ek group = 3 + 2 = 5 moti. 40 ÷ 5 = 8 group.
Safed = 8 × 3 = 24, laal = 8 × 2 = 16.
Safed : laal = 24 : 16 (yaani 3 : 2). Laal : kul = 16 : 40 (yaani 2 : 5).
WHY sahi hai? 24 + 16 = 40 ✅
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Kirti ab pro: “Ratio = har itne pe utne. Order dhyaan se, units same!” 🎉
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🏠 Real Life Mein Ratio
- ☕ Chai: Paani : doodh = 1 : 1, ya ghar ka apna ratio.
- 🧱 Construction: Cement : ret = 1 : 4, mistri bhaiya ka roz ka ratio.
- 🏫 School: Teacher : student ratio, jaise 1 : 30.
- 📱 Screen: 16 : 9 matlab har 16 chaudaai pe 9 oonchaai.
- 🍚 Khichdi: Chawal : daal = 2 : 1, aur paani alag se!
Jahan bhi “har itne pe utna” sunai de, wahan ratio chhupa hai.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| Do same type ki cheezon ka rishta | ✅ Ratio a : b, units same karke | Units hat jaati hain |
| Alag type (km aur ghanta) | ✅ Rate likho, unit ke saath | Jaise 60 km/h |
| Order ulta likh diya | ❌ Matlab badal jaayega | a : b ≠ b : a |
| Units alag (cm aur m) | ❌ Seedha mat likho, pehle convert | Galat tulna |
| Sawaal mein “kul” poocha | ✅ Hissa : poora likho | Doosra term total hai |
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❌→✅ Worked Mistake
Sawaal: Riya ne 30 minute padhaai ki aur 2 ghante TV dekha. Padhaai : TV ka ratio?
❌ Galat: “30 : 2.”
Galti kya hai? 30 minute mein hai, 2 ghante mein. Is hisaab se lagta hai padhaai 15 guna zyada! Jabki asal mein TV zyada tha ❌
✅ Sahi:
- 2 ghante = 120 minute
- Ratio = 30 : 120 (yaani 1 : 4). TV padhaai ka 4 guna! 😬
Yaad rakho: Ratio likhne se pehle units same karo.
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📝 10 MCQs
Q1. 5 : 8 mein pehla term kaunsa hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 8 doosra term hai.
- (b) sahi: Jo pehle likha, woh pehla term ✅
- (c) galat: 13 to jod hai.
- (d) galat: 3 farak hai.
Q2. 12 ladke aur 15 ladkiyan. Ladkiyan : ladke?
Solution dekho
Sahi jawab: (b)
- (a) galat: Order ulta: yeh ladke : ladkiyan hai.
- (b) sahi: Ladkiyan pehle boli gayi, to 15 pehle ✅
- (c) galat: Yeh ladkiyan : kul (27) hai.
- (d) galat: 27 kul hai, ladke nahi.
Q3. 40 cm aur 1 m ka ratio?
Solution dekho
Sahi jawab: (b)
- (a) galat: Units alag rakh di (cm aur m).
- (b) sahi: 1 m = 100 cm, to 40 : 100 ✅
- (c) galat: 4 : 1 matlab 40 cm, 10 cm ka 4 guna; yahan 40 cm chhota hai.
- (d) galat: Ulta, aur units bhi alag.
Q4. “Har 2 cup chawal pe 1 cup daal” ka ratio?
Solution dekho
Sahi jawab: (b)
- (a) galat: Order ulta: daal : chawal ho gaya.
- (b) sahi: Chawal : daal = 2 : 1 ✅
- (c) galat: Yeh chawal : kul (3) hai.
- (d) galat: 3 kahin se nahi aaya.
Q5. Jab dono cheezein same unit mein hon, to ratio ki unit kya hoti hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: Units cancel ho jaati hain.
- (b) sahi: Ratio bina unit ka hota hai ✅
- (c) galat: Doosri ki unit bhi cancel ho jaati hai.
- (d) galat: Dono units cancel, koi nahi bachti.
Q6. 9 laal aur 6 neeli gend. Neeli : kul?
Solution dekho
Sahi jawab: (b)
- (a) galat: Yeh neeli : laal hai.
- (b) sahi: Kul = 15 ✅
- (c) galat: Yeh laal : kul hai.
- (d) galat: Ulta.
Q7. Kya 3 : 5 aur 5 : 3 ek hi baat hain?
Solution dekho
Sahi jawab: (b)
- (a) galat: Order badla to matlab badla.
- (b) sahi: 3 : 5 mein pehli cheez kam, 5 : 3 mein zyada ✅
- (c) galat: Kabhi nahi.
- (d) galat: Jod same hai par ratio alag.
Q8. 250 g aur 1 kg ka ratio?
Solution dekho
Sahi jawab: (b)
- (a) galat: Units alag (g aur kg).
- (b) sahi: 1 kg = 1000 g, to 250 : 1000 ✅
- (c) galat: Ulta, aur units bhi alag.
- (d) galat: 25 : 1 matlab 250 g, 10 g ka 25 guna; galat.
Q9. Bus 180 km, 3 ghante mein chali. Rate kya hai?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 180 ÷ 3 = 60, unit ke saath ✅
- (b) galat: Rate mein unit zaroori hai.
- (c) galat: Ulta bhaag.
- (d) galat: Guna kar diya.
Q10. Class mein ladke : ladkiyan = 4 : 5. Kul 36 bachche hon to ladke?
Solution dekho
Sahi jawab: (a)
- (a) sahi: Har 9 mein 4 ladke. 36 = 4 group, ladke = 16 ✅
- (b) galat: Yeh ladkiyan hain.
- (c) galat: 4 to ratio ka term hai.
- (d) galat: 9 to ek group hai.
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❓ FAQs (Bachchon Ke Asli Sawaal)
1. Ratio aur fraction mein kya farak hai?
Ratio do cheezon ka rishta hai (18 : 12). Fraction ek hisse ko poore ke roop mein batata hai (18/30). Hissa : poora wala ratio fraction jaisa hi hai.
2. Kya ratio mein 0 ho sakta hai?
Pehla term 0 ho sakta hai (0 ladke, matlab koi ladka nahi). Par doosra term 0 hone pe “har 0 pe kitne” ka koi matlab nahi banta, isliye use avoid karte hain.
3. Kya ratio ke terms decimal mein ho sakte hain?
Haan, jaise 1.5 : 2. Par aam taur pe use whole numbers mein badal dete hain (3 : 4). Yeh agle post mein seekhenge.
4. Ratio aur rate mein kya antar hai?
Ratio mein same type ki cheezein, unit nahi. Rate mein alag type ki cheezein, unit ke saath (60 km/h, ₹30/kg).
5. 3 : 2 ratio ka matlab hai 3 ladkiyan aur 2 ladke?
Zaroori nahi! 18 aur 12, ya 30 aur 20 bhi ho sakte hain. Ratio rishta batata hai, asli ginti nahi.
6. Teen cheezon ka ratio kaise likhein?
a : b : c, jaise chawal : daal : paani = 2 : 1 : 6. Iske baare mein Book 2 Ch 3 — Do Se Zyada Terms Wala Ratio mein detail se padh sakte ho.
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🏋️ Practice Zone (12 Sawaal)
Q1. Easy 9 pencil aur 4 pen. Pencil : pen?
Solution dekho
9 : 4.
Q2. Easy Upar wale sawaal mein pen : pencil?
Solution dekho
4 : 9.
Q3. Easy 2 m aur 70 cm ka ratio.
Solution dekho
200 : 70 = 20 : 7.
Q4. Easy 1 ghanta aur 15 minute ka ratio.
Solution dekho
60 : 15 = 4 : 1.
Q5. Medium Class mein 20 ladke aur 25 ladkiyan. Ladke : kul?
Solution dekho
Kul = 45. 20 : 45.
Q6. Medium Mala mein har 4 neele motiyon ke baad 1 peela. 60 moti mein kitne neele, kitne peele?
Solution dekho
Group = 5, 60 ÷ 5 = 12. Neele 48, peele 12.
Q7. Medium ₹2.50 aur 50 paise ka ratio.
Solution dekho
250 : 50 = 5 : 1.
Q8. Medium Ek dabbe mein har 5 toffee mein se 2 orange hain, baaki mango. Orange : mango?
Solution dekho
Mango = 3. Orange : mango = 2 : 3.
Q9. NCERT style Bageeche mein 30 gulaab, 45 genda, 15 lily. (a) Gulaab : genda (b) Lily : kul
Solution dekho
(a) 30 : 45 (yaani 2 : 3) (b) kul = 90, 15 : 90 (yaani 1 : 6)
Q10. NCERT style Mistri “har 1 bori cement pe 4 bori ret” milaata hai. 5 bori cement ke liye kitni ret? Ratio?
Solution dekho
20 bori ret. Ratio cement : ret = 1 : 4.
Q11. NCERT style Car 150 km, 3 ghante mein chali. Iska rate kya hai? Ise ratio kyun nahi kehte?
Solution dekho
Rate = 50 km/h. Units (km aur ghanta) alag hain, isliye yeh rate hai.
Q12. NCERT style Ishaan kehta hai: “Ratio 3 : 4 ka matlab hai class mein 3 ladke aur 4 ladkiyan.” Sahi hai?
Solution dekho
Zaroori nahi. 30 aur 40, ya 15 aur 20 bhi ho sakte hain. Ratio sirf rishta batata hai.
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. Ladke : ladkiyan = 3 : 4 aur class mein 35 bachche hain. Kitne ladke, kitni ladkiyan?
Solution dekho
Group = 7, 35 ÷ 7 = 5. Ladke = 15, ladkiyan = 20. (Isse detail mein Post 7 — Barabar Nahi, Ratio Mein Hissa mein seekhenge.)
Q2. Class mein ladke : ladkiyan = 2 : 3 (10 aur 15). 4 naye ladke aaye. Ratio wahi rakhne ke liye kitni nayi ladkiyan aani chahiye?
Solution dekho
Ladke 14, ratio 2 : 3 rakhne ke liye ladkiyan = 14 × 3/2 = 21. Nayi = 6.
Q3. Mohan ne 2 kg aur 500 g ka ratio “2 : 500” likha. Kya galat hai, aur sahi kya hai?
Solution dekho
Units alag thin. 2 kg = 2,000 g. Sahi = 2000 : 500 = 4 : 1.
Q4. Agar a : b mein a, b se bada ho, to iska kya matlab hai? Example do.
Solution dekho
Pehli cheez zyada hai. Jaise ladkiyan : ladke = 18 : 12, ladkiyan zyada. Ratio 1.5 guna batata hai.
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🏆 Olympiad Corner
Q1. Ek bag mein laal : neeli gend = 5 : 3. Laal, neeli se 10 zyada hain. Har rang ki kitni?
Solution dekho
Farak = 5 − 3 = 2 hisse = 10, to 1 hissa = 5. Laal = 25, neeli = 15.
Q2. School mein teacher : student = 1 : 25 aur 450 student hain. 50 naye student aaye. Ratio wahi rakhne ke liye kitne naye teacher chahiye?
Solution dekho
Pehle teacher = 18. Ab 500 student → 20 teacher. Naye = 2.
Q3. Square A ki side 4 cm, square B ki 6 cm. Sides ka ratio aur area ka ratio?
Solution dekho
Sides 4 : 6 = 2 : 3. Area 16 : 36 = 4 : 9. (Area ratio = side ratio ka square!)
Q4. Gullak mein 50 paise aur ₹1 ke sikke 3 : 2 ke ratio mein hain. Kul ₹35 hain. Kitne sikke kis type ke?
Solution dekho
Ek group (3 × 50p + 2 × ₹1) = ₹3.50. 35 ÷ 3.5 = 10 group. 50p ke 30, ₹1 ke 20 sikke.
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💗 CharuMam Motivation
Kirti ko pehle “:” sirf ek nishaan lagta tha. Ab woh har jagah ratio dekhti hai: chai mein, cricket team mein, mala mein. ⚖️
Maths aise hi dheere-dheere khulta hai. Roz thoda focus, sawaal hal karne ki mehnat, aur khud pe sabr. Aapka rishta bhi maths se 1 : 1 pakka ho jaayega! 😊
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🟢 Master Recap
- a : b = har a pehli cheez pe b doosri.
- a aur b ratio ke terms hain.
- Order zaroori: a : b ≠ b : a.
- Ratio se pehle units same karo; ratio bina unit ka hota hai.
- Hissa : hissa aur hissa : poora alag hain.
- Alag units wali tulna = rate (km/h, ₹/kg).
- Ratio “kitne guna” batata hai, farak nahi.
— charumam.com 🎯
👉 Aage Kya?
18 : 12, 3 : 2, 30 : 20… sab ek hi rishta! To sabse chhota aur saaf roop kaunsa? Agle post mein seekhenge ratio ka simplest form, HCF ke jaadu se! ✂️
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬