✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 2 : 3 : 5 mein kul kitne hisse hain?
- ₹350 ka 1/7 kitna hai?
- A : B = 2 : 3 aur B : C = 6 : 5. A : B : C?
Answers dekho
- 2 + 3 + 5 = 10 hisse
- 350 ÷ 7 = ₹50
- B ko 6 banao: A : B = 4 : 6, to A : B : C = 4 : 6 : 5
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Post 3 — Do Se Zyada Terms Wala Ratio ek baar dekh lijiye, phir yahan wapas aaiye.
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🎬 Kahani: Diwali Ke Diyon Ki Kamaai
Diwali se pehle Chintu, Mintu aur Pinky ne milkar mitti ke diye bechne ka chhota sa kaam shuru kiya. Saamaan khareedne mein Chintu ne ₹400, Mintu ne ₹200 aur Pinky ne ₹100 lagaaye.
Saare diye bik gaye aur kul ₹1,400 aaye! 🪔
Mintu bola, “Teen log hain, to sabko ₹1,400 ÷ 3 de do.” Chintu ne turant kaha, “Par maine sabse zyada paisa lagaya tha, mera hissa bhi zyada hona chahiye!”
Dono ki baat mein dum hai. To fair tareeka kya hai? 🤔 Aaj seekhenge kisi poori cheez ko diye gaye ratio mein baantna. 😉
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📖 Concept: Poori Cheez, Ratio Ke Hisse
Step 1: Ratio dhoondo aur kul hisse jodo
Paisa 400 : 200 : 100 mein laga, yaani 100 se divide karke 4 : 2 : 1.
Kul hisse = 4 + 2 + 1 = 7.
WHY jodna? Ratio kehta hai Chintu ke 4 hisse, Mintu ke 2, Pinky ka 1. Poori kamaai in sab hisson se milkar bani hai, yaani 7 barabar hisse.
Step 2: Ek hisse ki value nikaalo
1 hissa = ₹1,400 ÷ 7 = ₹200.
WHY divide? Poori cheez ko 7 barabar tukdon mein toda, to har tukda poore ka 1/7 hai.
Step 3: Har ek ka hissa = uske terms × 1 hissa
- Chintu = 4 × 200 = ₹800
- Mintu = 2 × 200 = ₹400
- Pinky = 1 × 200 = ₹200
$\text{Hissa} = \dfrac{\text{apna term}}{\text{sab terms ka jod}} \times \text{Poori cheez}$
Chintu = 4/7 × 1,400 = ₹800. Dono tareekon se ek hi jawab.
WHY fraction wala tareeka bhi sahi? 7 mein se 4 hisse Chintu ke, to woh poore ka 4/7 hai. Post 3 ke HOTS mein bhi yahi dekha tha.
Step 4: Check karo: jod = poori cheez
800 + 400 + 200 = ₹1,400 ✅ aur 800 : 400 : 200 = 4 : 2 : 1 ✅
WHY do check? Pehla batata hai koi paisa chhoota ya zyada nahi baanta. Doosra batata hai ratio sahi laga.
Step 5: Ulte sawaal: ek ka hissa ya farak diya ho
(a) Ek ka hissa diya hai: Agar Pinky (1 hissa) ko ₹200 mile, to poori kamaai = 7 × 200 = ₹1,400.
(b) Farak diya hai: Agar Chintu ko Mintu se ₹400 zyada mile, to farak = 4 − 2 = 2 hisse = ₹400 → 1 hissa = ₹200.
WHY yeh chalta hai? Jo bhi diya ho, use “kitne hisse” mein badlo. Phir 1 hisse ki value nikaalo aur baaki sab usi se.
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🔐 Deep Concept: Barabar Baantna Hamesha Fair Nahi Hota
Mintu ka tareeka (÷ 3) aur ratio wala tareeka compare karo:
| Lagaaya | Barabar (÷ 3) | Ratio 4 : 2 : 1 | |
|---|---|---|---|
| Chintu | ₹400 | ≈ ₹466.67 | ₹800 |
| Mintu | ₹200 | ≈ ₹466.67 | ₹400 |
| Pinky | ₹100 | ≈ ₹466.67 | ₹200 |
Ratio wale tareeke mein har ek ka paisa exactly double hua (400 → 800, 200 → 400, 100 → 200). Sabko apne lagaaye paise pe same 100% kamaai. Yahi fairness hai: hissa, yogdaan ke proportion mein.
Ek aur gehri baat: Agar cheez tod nahi sakte (log, kursiyan, toffee), to kul cheezein, kul hisson se poori divide honi chahiye. 22 toffee ko 1 : 2 mein baantna ho to 22 ÷ 3 poora nahi bantta, isliye exact baantwaara mumkin nahi.
sirf charumam.com readers ke liye 🔐
✏️ Solved Examples
Example 1 (Easy): ₹600 ko 1 : 2 mein baanto.
Kul hisse = 3. 1 hissa = 600 ÷ 3 = ₹200.
Hisse = ₹200 aur ₹400.
WHY sahi hai? 200 + 400 = 600 ✅ aur 200 : 400 = 1 : 2 ✅
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Example 2 (Medium): 90 minute ki practice ko warm-up : drill : match = 1 : 3 : 2 mein baanto.
Kul hisse = 1 + 3 + 2 = 6. 1 hissa = 90 ÷ 6 = 15 minute.
Warm-up = 15 min, drill = 45 min, match = 30 min.
WHY sahi hai? 15 + 45 + 30 = 90 ✅
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Example 3 (NCERT style): School library mein Hindi : English : Sanskrit kitaabein 5 : 3 : 2 mein hain. English ki 360 kitaabein hain. Kul kitaabein aur baaki kitni?
English = 3 hisse = 360 → 1 hissa = 120.
Hindi = 5 × 120 = 600, Sanskrit = 2 × 120 = 240, Kul = 10 × 120 = 1,200.
WHY sahi hai? 600 + 360 + 240 = 1,200 ✅
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Ab teeno bachche khush: Chintu ₹800, Mintu ₹400, Pinky ₹200, sabka paisa double! 🎉
— 📌 charumam.com
🏠 Real Life Mein Ratio Mein Baantna
- 🤝 Business partnership: Jisne zyada paisa lagaaya, use munaafe mein zyada hissa, lagaaye paise ke ratio mein.
- 🏡 Zameen ka batwara: Khet ko parivaar mein tay ratio (jaise 2 : 1 : 1) mein baantna.
- ⏰ Time table: 3 ghante ko Maths : Science : English = 3 : 2 : 1 mein, yaani 90, 60, 30 minute.
- 🥤 Sharbat: 1.5 litre jug mein syrup : paani = 1 : 4, yaani 300 ml syrup aur 1,200 ml paani.
- 🏫 School fund: ₹50,000 ko library : khel : lab = 2 : 2 : 1 mein, yaani ₹20,000, ₹20,000, ₹10,000.
Har jagah wahi teen kadam: hisse jodo → 1 hissa nikaalo → guna karo.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| Poori rakam aur ratio diye hain | ✅ Kul hisse jodo, 1 hissa nikaalo | Poori cheez = sab hisson ka jod |
| Ek ka hissa diya hai | ✅ Use uske terms se divide karke 1 hissa nikaalo | Ek hisse se sab nikal aata hai |
| Do hisson ka farak diya hai | ✅ Terms ka farak = utne hisse | Farak bhi hisson mein hota hai |
| Logon ki ginti se seedha divide (÷ 3) | ❌ Jab yogdaan alag ho tab nahi | Ratio wala baantwaara hi fair hai |
| Toote na jaane wali cheezein, kul hisson se divide na hon | ❌ Exact baantwaara mumkin nahi | Aadha bachcha ya aadhi kursi nahi hoti |
— 📌 charumam.com
❌→✅ Worked Mistake
Sawaal: ₹1,400 ko 4 : 2 : 1 mein baanto.
❌ Galat: “3 log hain, to 1 hissa = 1,400 ÷ 3 ≈ 466.67. Chintu = 4 × 466.67 ≈ ₹1,866.67…”
Galti kya hai? Logon ki ginti (3) se divide kiya, hisson ki ginti (7) se nahi. Check fail: akele Chintu ko hi ₹1,400 se zyada mil gaye! 😮
✅ Sahi:
- Kul hisse = 4 + 2 + 1 = 7
- 1 hissa = 1,400 ÷ 7 = ₹200
- Chintu ₹800, Mintu ₹400, Pinky ₹200 (jod = ₹1,400 ✅)
Yaad rakho: Divide ratio ke terms ke jod se karo, logon ki ginti se nahi.
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📝 10 MCQs
Q1. ₹500 ko 2 : 3 mein baanto.
Solution dekho
Sahi jawab: (a)
- (a) sahi: Kul hisse 5, 1 hissa = 100. 200 aur 300 ✅
- (b) galat: Yeh barabar baantwaara hai, ratio 1 : 1.
- (c) galat: 100 : 400 = 1 : 4 hai.
- (d) galat: Jod 450 hai, 500 nahi.
Q2. 60 ko 1 : 2 : 3 mein baanto.
Solution dekho
Sahi jawab: (a)
- (a) sahi: Kul 6 hisse, 1 hissa = 10 ✅
- (b) galat: Yeh barabar baantwaara hai.
- (c) galat: Jod 36 hai, 60 nahi.
- (d) galat: 15 : 20 : 25 = 3 : 4 : 5 hai.
Q3. Ratio 3 : 5 mein kul kitne hisse hain?
Solution dekho
Sahi jawab: (b)
- (a) galat: 5 − 3 = 2 farak hai, kul nahi.
- (b) sahi: 3 + 5 = 8 ✅
- (c) galat: 3 × 5 = 15, guna nahi karna.
- (d) galat: 5 sirf doosra term hai.
Q4. ₹1,200 ko 1 : 2 : 3 mein baanto. Sabse bada hissa?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 1 hissa = 1,200 ÷ 6 = 200. Bada = 3 × 200 = ₹600 ✅
- (b) galat: ₹400 beech wala hissa hai.
- (c) galat: ₹200 sabse chhota hai.
- (d) galat: Kisi ek ko ₹1,000 mil hi nahi sakte is ratio mein.
Q5. Ratio 2 : 3 mein chhota hissa 40 hai. Poori cheez?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 2 hisse = 40 → 1 hissa = 20 → kul 5 × 20 = 100 ✅
- (b) galat: 60 to sirf bada hissa hai.
- (c) galat: 40 × 2 = 80, galat soch.
- (d) galat: 40 × 3 = 120, galat.
Q6. Ratio 3 : 5 mein dono hisson ka farak 30 hai. Poori cheez?
Solution dekho
Sahi jawab: (a)
- (a) sahi: Farak = 2 hisse = 30 → 1 hissa = 15 → kul 8 × 15 = 120 ✅
- (b) galat: 30 + 50 = 80, hisse galat pakde.
- (c) galat: 30 × 8 = 240, farak ko 1 hissa maan liya.
- (d) galat: 30 × 5 = 150, galat.
Q7. 5 : 3 mein baantne pe pehle vyakti ko poori cheez ka kitna hissa milta hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 5/3 to pehle aur doosre ki tulna hai.
- (b) sahi: 5 hisse, kul 8 mein se: 5/8 ✅
- (c) galat: 3/8 doosre ka hissa hai.
- (d) galat: 1/5 ka koi aadhaar nahi.
Q8. 50 students ko do teams mein 2 : 3 mein baanto.
Solution dekho
Sahi jawab: (a)
- (a) sahi: 1 hissa = 50 ÷ 5 = 10. 20 aur 30 ✅
- (b) galat: Barabar baanta, ratio 1 : 1.
- (c) galat: 10 : 40 = 1 : 4.
- (d) galat: 2 aur 3 sirf ratio hai, students ki ginti nahi.
Q9. Inmein se kaunsa baantwaara EXACT (bina todhe) nahi ho sakta?
Solution dekho
Sahi jawab: (b)
- (a) galat: 25 ÷ 5 = 5, ho sakta hai (10, 15).
- (b) sahi: 22 ÷ 3 poora nahi bantta, exact nahi ho sakta ✅
- (c) galat: 30 ÷ 3 = 10, ho sakta hai (10, 20).
- (d) galat: 28 ÷ 7 = 4, ho sakta hai (12, 16).
Q10. Triangle ke angles 2 : 3 : 4 mein hain. Angles kya hain?
Solution dekho
Sahi jawab: (a)
- (a) sahi: Angles ka jod 180°. 1 hissa = 180 ÷ 9 = 20°. 40°, 60°, 80° ✅
- (b) galat: Jod sirf 90° hai.
- (c) galat: Yeh barabar baantwaara hai.
- (d) galat: Jod 162° hai, 180° nahi.
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Barabar kyun nahi baant dete? Woh aasaan hai.
Aasaan hai, par hamesha fair nahi. Jab sabka yogdaan (paisa, mehnat, samay) alag ho, to hissa bhi usi proportion mein hona chahiye. Diyon wali kahani mein ratio se baantne pe sabka paisa barabar double hua.
2. Ratio ke terms jodte kyun hain?
Kyunki terms batate hain kiske kitne hisse hain. Sab hisse milkar hi poori cheez bante hain. 4 : 2 : 1 mein poori cheez = 7 hisse.
3. Agar jawab decimal mein aaye to?
Paisa, litre, kg jaisi cheezon mein chalega (₹466.50 ho sakta hai). Par log, kursiyan, kitaabein jaisi cheezein toot nahi sakti, wahan exact baantwaara tabhi hoga jab kul cheezein, kul hisson se poori divide hon.
4. Kaise check karein ki baantwaara sahi hai?
Do check: (1) Sab hisson ka jod = poori cheez. (2) Hisson ka ratio = diya gaya ratio (simplify karke dekho).
5. Ratio mein baantne aur percentage ka kya rishta hai?
2 : 3 mein pehle ko 2/5 milta hai, yaani 2/5 × 100 = 40%, aur doosre ko 60%. Har ratio ko percentage mein badal sakte ho. Yaad nahi to Percentage Kya Hai? dekho. Agle post (pie chart) mein yeh bahut kaam aayega.
6. Agar ratio fractions mein diya ho, jaise 1/2 : 1/3?
Pehle whole numbers banao (Post 3): LCM 6 se guna → 3 : 2. Ab normal tareeke se baanto. Jaise ₹500 → 1 hissa = 100 → ₹300 aur ₹200.
— 📌 charumam.com
🏋️ Practice Zone (12 Sawaal)
Q1. Easy ₹800 ko 3 : 5 mein baanto.
Solution dekho
Kul 8 hisse, 1 hissa = 100. ₹300 aur ₹500.
Q2. Easy 42 ko 1 : 2 : 3 mein baanto.
Solution dekho
Kul 6 hisse, 1 hissa = 7. 7, 14, 21.
Q3. Easy 1 ghante ko 1 : 2 mein baanto.
Solution dekho
60 minute, kul 3 hisse, 1 hissa = 20. 20 min aur 40 min.
Q4. Easy Ratio 4 : 1 mein pehle ko poori cheez ka kitna hissa milta hai?
Solution dekho
Kul 5 hisse, pehle ke 4: 4/5 (yaani 80%).
Q5. Medium ₹2,700 ko 2 : 3 : 4 mein baanto.
Solution dekho
Kul 9 hisse, 1 hissa = 300. ₹600, ₹900, ₹1,200. Check: jod 2,700 ✅
Q6. Medium Ratio 5 : 7 mein bada hissa 84 hai. Chhota hissa aur poori cheez?
Solution dekho
7 hisse = 84 → 1 hissa = 12. Chhota = 5 × 12 = 60, kul = 12 × 12 = 144.
Q7. Medium Ratio 4 : 9 mein hisson ka farak 35 hai. Dono hisse?
Solution dekho
Farak = 5 hisse = 35 → 1 hissa = 7. Hisse = 28 aur 63.
Q8. Medium Triangle ke angles 1 : 2 : 3 mein hain. Angles nikaalo. Triangle kaisa hai?
Solution dekho
1 hissa = 180 ÷ 6 = 30°. Angles = 30°, 60°, 90°. Ek angle 90° hai, to yeh right-angled triangle hai.
Q9. NCERT style Ek gullak mein 60 sikke hain: ₹5 : ₹2 : ₹1 ke sikkon ki ginti 1 : 2 : 3 mein hai. Kul kitne rupaye hain?
Solution dekho
1 hissa = 60 ÷ 6 = 10. ₹5 ke 10, ₹2 ke 20, ₹1 ke 30 sikke.
Rakam = 50 + 40 + 30 = ₹120.
Q10. NCERT style 1,200 m² ke bageeche ko phool : sabzi : ghaas = 3 : 5 : 4 mein baanto.
Solution dekho
Kul 12 hisse, 1 hissa = 100 m². 300 m², 500 m², 400 m².
Q11. NCERT style A ne ₹30,000 aur B ne ₹45,000 lagaakar business kiya. ₹15,000 munaafa hua. Kisko kitna?
Solution dekho
30,000 : 45,000 = 2 : 3. 1 hissa = 15,000 ÷ 5 = 3,000.
A = ₹6,000, B = ₹9,000.
Q12. NCERT style 35 litre sharbat mein juice : paani = 2 : 5 hai. (i) Juice kitna hai? (ii) Kitna juice aur daalein ki ratio 1 : 1 ho jaaye?
Solution dekho
(i) 1 hissa = 35 ÷ 7 = 5 L. Juice = 10 L, paani = 25 L.
(ii) 1 : 1 ke liye juice = paani = 25 L. Aur daalna = 25 − 10 = 15 L.
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. Kuch rakam 2 : 3 : 5 mein baanti gayi. Sabse bade aur sabse chhote hisse ka farak ₹600 hai. Kul rakam?
Solution dekho
Farak = 5 − 2 = 3 hisse = 600 → 1 hissa = 200. Kul = 10 × 200 = ₹2,000.
Q2. Dadaji ne ₹7,000 aise baante ki Raj ko Sima ka double mile aur Sima ko Tina ka double. Kisko kitna mila?
Solution dekho
Tina = 1 hissa, Sima = 2, Raj = 4. Ratio 4 : 2 : 1, kul 7 hisse, 1 hissa = 1,000.
Raj ₹4,000, Sima ₹2,000, Tina ₹1,000.
Q3. A aur B ne kuch rakam 3 : 2 mein baanti. A kehta hai, “Mujhe poori rakam ka 3/2 mila.” Kya A sahi hai?
Solution dekho
Nahi. 3/2 to A aur B ki aapas mein tulna hai (A ko B ka 1.5 guna). Poori rakam ka A ko 3/(3 + 2) = 3/5 mila. 3/2 poore se bhi zyada hai, jo ho hi nahi sakta!
Q4. Kya 100 students ko do teams mein bilkul 3 : 4 ke ratio mein baant sakte hain?
Solution dekho
Kul hisse 7. 100 ÷ 7 = 14.28…, poora nahi bantta. Exact nahi ho sakta. Sabse kareeb: 43 aur 57 (43 : 57 ≈ 0.754, jabki 3 : 4 = 0.75).
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🏆 Olympiad Corner
Q1. ₹1,050 ko A, B, C mein baanto jahan A : B = 2 : 3 aur B : C = 4 : 5.
Solution dekho
A : B : C = 8 : 12 : 15 (Post 3). Kul 35 hisse, 1 hissa = 1,050 ÷ 35 = 30.
A = ₹240, B = ₹360, C = ₹450.
Q2. ₹1,800 ko A, B, C mein aise baanto ki A ko B ka 2/3 mile aur B ko C ka 3/4 mile.
Solution dekho
C = 4k lo → B = 3k → A = 2/3 × 3k = 2k. Ratio 2 : 3 : 4, kul 9 hisse, 1 hissa = 200.
A = ₹400, B = ₹600, C = ₹800.
Q3. Ek thaili mein ₹10, ₹5 aur ₹1 ke sikkon ki ginti 1 : 2 : 5 mein hai. Kul rakam ₹100 hai. Har tarah ke kitne sikke hain?
Solution dekho
Ek “set” = 1 sikka ₹10 + 2 sikke ₹5 + 5 sikke ₹1 = 10 + 10 + 5 = ₹25.
Sets = 100 ÷ 25 = 4. Sikke: ₹10 ke 4, ₹5 ke 8, ₹1 ke 20.
Q4. Ek rassi ko 2 : 3 : 7 mein teen tukdon mein kaata. Sabse lambe aur sabse chhote tukde ka farak 1.5 m hai. Rassi kitni lambi thi?
Solution dekho
Farak = 7 − 2 = 5 hisse = 1.5 m → 1 hissa = 0.3 m. Kul = 12 × 0.3 = 3.6 m.
sirf charumam.com readers ke liye 🔐
💗 CharuMam Motivation
Chintu, Mintu aur Pinky ki kahani ek sundar baat sikhaati hai: jitna yogdaan, utna hissa. 🪔 Zindagi mein bhi aisa hi hota hai. Aap jitni mehnat lagaate ho, result usi proportion mein aata hai.
Agar aaj aapka hissa chhota laga, to galat mat socho. Kal thoda zyada focus lagao, roz thoda badhao, aur sabr rakho. Hisse badalte der nahi lagti! 🌟
— 📌 charumam.com
🟢 Master Recap
- Kadam 1: Ratio ke saare terms jodo = kul hisse.
- Kadam 2: 1 hissa = poori cheez ÷ kul hisse.
- Kadam 3: Har ek ka hissa = uske terms × 1 hissa.
- Formula: hissa = (apna term ÷ terms ka jod) × poori cheez.
- Check: jod = poori cheez, aur hisson ka ratio = diya gaya ratio.
- Ek hissa ya farak diya ho to use hisson mein badlo, 1 hissa nikaalo.
- Divide hisson ki ginti se, logon ki ginti se nahi.
- Na tootne wali cheezon ke liye kul cheezein, kul hisson se poori divide honi chahiye.
— charumam.com 🎯
👉 Aage Kya?
Socho, agar class ke 40 bachchon ki pasandeeda game ek gol roti ki tarah dikhani ho, jismein har game ka tukda uske hisse ke proportion mein ho? Woh hai pie chart! Agle post mein seekhenge pie chart padhna. 🥧
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬