✅ Pehle Yeh Aata Hai?
Yeh post shuru karne se pehle, in teen sawaalon ko 1 minute mein khud try kijiye:
- 12 : 18 ko simplest form mein likho.
- 3/4 aur 9/12 barabar hain ya nahi?
- 5 pen ₹40 ke hain. 1 pen kitne ka?
Answers dekho
- 12 : 18 = 2 : 3 (dono ko 6 se divide)
- Haan, 9/12 ko 3 se divide karo to 3/4 aata hai
- ₹40 ÷ 5 = ₹8
Teeno sahi? Badhiya, aage chaliye! Koi galat hua? Koi baat nahi, Book 1 ka Chapter 7 (Proportional Reasoning-1) ek baar dekh lijiye (Class 8 Maths TOC), phir yahan wapas aaiye.
— 📌 charumam.com
🎬 Kahani: Pinky Ki Chai Party
Sunday ki shaam, Pinky ki mummy 4 logon ke liye adrak wali chai banati hain: 2 cup paani, 2 cup doodh, 4 chammach chai patti aur 2 chammach cheeni.
Achanak 6 mehmaan aur aa gaye, ab kul 10 log! Mummy ne Pinky se kaha, “Beta, chai ka saamaan badha do.”
Pinky ne turant socha, “6 log zyada aaye, to har cheez mein 6 jod deti hoon!” 8 cup paani, 8 cup doodh, 10 chammach patti, 8 chammach cheeni.
Chai bani… aur sabne muh banaya. “Itni meethi aur itni phiki ek saath kaise?” 🤔
Galti kahan hui? Aaj hum ratio aur proportion ko dobara yaad karenge, jo Book 1 mein seekha tha, aur Pinky ki chai bhi theek karenge. 😉
— 📌 charumam.com
📖 Concept: Ratio Aur Proportion Ki Yaad
Step 1: Ratio matlab guna-bhaag wali tulna
Do quantities ki tulna divide karke karte hain to use ratio kehte hain. Patti : paani = 4 : 2, padhte hain “4 is to 2”.
Ratio ko simplest form mein laane ke liye dono terms ko same number se divide karo: 4 : 2 = 2 : 1.
WHY? Ratio batata hai “ek ke mukable doosra kitne guna”. 4 : 2 aur 2 : 1 dono kehte hain ki patti, paani se double hai. Dono terms ko same number se guna ya divide karne pe yeh “kitne guna” nahi badalta. Aise ratios ko equivalent ratios kehte hain.
Step 2: Proportion matlab do barabar ratios
Jab do ratios barabar hon, to hum kehte hain ki woh proportion mein hain:
$a : b :: c : d$
Jaise 2 : 4 :: 5 : 10, kyunki 2/4 = 1/2 aur 5/10 = 1/2.
WHY yeh zaroori hai? Recipe badi karni ho, keemat nikaalni ho, ya map padhna ho, har jagah humein ek naya ratio chahiye jo purane ke barabar ho. Yahi proportion hai.
Step 3: Cross-check: a × d = b × c
Proportion check karne ka pakka tareeka: bahar wale terms ka guna = andar wale terms ka guna.
$a : b :: c : d \iff a \times d = b \times c$
2 : 4 :: 5 : 10 → 2 × 10 = 20 aur 4 × 5 = 20 ✅
WHY? a/b = c/d ke dono taraf b × d se guna karo: (a/b) × b × d = a × d, aur (c/d) × b × d = b × c. Barabar cheezon ko same number se guna karne pe woh barabar hi rehti hain.
Step 4: Rule of Three (Trairashika): chautha term nikaalo
Agar teen terms pata hain aur chautha nahi, to cross-check se hi nikaal lo:
$a : b :: c : d \Rightarrow d = \dfrac{b \times c}{a}$
Example: 6 kg aaloo ₹150 ke. 10 kg kitne ke? 6 : 150 :: 10 : d → d = (150 × 10) ÷ 6 = 1500 ÷ 6 = ₹250.
Unitary method se check: 1 kg = 150 ÷ 6 = ₹25, to 10 kg = 25 × 10 = ₹250 ✅
WHY? a × d = b × c se dono taraf a se divide karo, d akela bach jaata hai. Teen raashiyon (quantities) se chauthi nikaalne ki is vidhi ko bhaarat mein Trairashika kehte the.
Step 5: Direct proportion: dono same factor se, same disha mein
Jab ek quantity jitne guna hoti hai, doosri bhi utne hi guna hoti hai, to dono direct proportion mein hain. Inka ratio (y/x) hamesha same rehta hai.
| Aaloo (kg) | 1 | 2 | 4 | 10 |
|---|---|---|---|---|
| Daam (₹) | 25 | 50 | 100 | 250 |
| Daam ÷ kg | 25 | 25 | 25 | 25 |
$\dfrac{y}{x} = k \ (\text{constant})$
WHY? Har kg ka daam fixed (₹25) hai. Kg double, to utne hi ₹25 aur jud jaate hain, daam bhi double. Isi chapter mein aage (Post 7) hum ek ulti kism ka proportion dekhenge, jahan ek badhta hai to doosra ghatta hai.
— 📌 charumam.com
🔐 Deep Concept: Proportion Mein Jodna Nahi, Guna Hota Hai
Pinky ki chai ka hisaab dekho. Patti : paani asli recipe mein 4 : 2 = 2 : 1 tha.
| Paani (cup) | Patti (chammach) | Patti : Paani | |
|---|---|---|---|
| Asli (4 log) | 2 | 4 | 2 : 1 |
| Pinky (+6 jodkar) ❌ | 8 | 10 | 5 : 4 |
| Sahi (× 2.5) ✅ | 5 | 10 | 2 : 1 |
Log 4 se 10 hue, yaani 10 ÷ 4 = 2.5 guna. To har cheez 2.5 guna honi chahiye: 5 cup paani, 5 cup doodh, 10 chammach patti, 5 chammach cheeni.
Gehri baat: Jodne se chhoti cheez ka hissa zyada badh jaata hai. Cheeni 2 se 8 hui, yaani 4 guna, par paani 2 se 8 bhi 4 guna, aur patti 4 se 10 sirf 2.5 guna. Har cheez alag guna badhi, isliye taste bigad gaya. Proportion ka matlab hai sab ek hi factor se badhein.
Golden rule: Pehle poochho, “kitne guna hua?” Phir har quantity ko usi factor se guna karo.
sirf charumam.com readers ke liye 🔐
✏️ Solved Examples
Example 1 (Easy): 15 : 25 aur 6 : 10 proportion mein hain kya?
15 : 25 → 5 se divide → 3 : 5. 6 : 10 → 2 se divide → 3 : 5.
Dono simplest form mein same, to haan, proportion mein hain.
WHY sahi hai? Cross-check: 15 × 10 = 150 aur 25 × 6 = 150 ✅
📌 charumam.com
Example 2 (Medium): Ammi 12 logon ki idli ke liye 6 cup chawal aur 2 cup urad dal bhigoti hain. 18 logon ke liye kitna chahiye?
Factor = 18 ÷ 12 = 1.5.
Chawal = 6 × 1.5 = 9 cup, Urad dal = 2 × 1.5 = 3 cup.
WHY sahi hai? Ratio check: asli 6 : 2 = 3 : 1, naya 9 : 3 = 3 : 1 ✅. Dono ek hi factor se badhe, isliye batter ka swaad wahi rahega.
📌 charumam.com
Example 3 (NCERT style): Ek car 3 litre petrol mein 54 km chalti hai. Usi tarah chalaane pe 8 litre mein kitni doori tay karegi?
Petrol aur doori direct proportion mein hain (same road, same speed maan ke).
3 : 54 :: 8 : d → d = (54 × 8) ÷ 3 = 432 ÷ 3 = 144 km.
WHY sahi hai? Unitary check: 1 litre = 54 ÷ 3 = 18 km, 8 litre = 18 × 8 = 144 km ✅
📌 charumam.com
Ab Pinky bhi expert: Proportion mein guna hota hai, jodna nahi! 🎉
— 📌 charumam.com
🏠 Real Life Mein Proportion
- 🍛 Recipe: 4 logon ki biryani mein 500 g chawal, to 10 logon ke liye 500 × 10 ÷ 4 = 1,250 g.
- ⛽ Petrol pump: ₹100 prati litre pe 5 litre = ₹500. Litre double, daam double.
- 🧱 Mistri ka masala: Cement : ret = 1 : 4. 3 bori cement ho to 12 bori ret.
- 📷 Photo resize: Lambai aur chaudai dono ko same factor se badhao, warna chehra khinch jaata hai.
- 📱 Mobile data: Roz 1.5 GB, to 30 din mein 1.5 × 30 = 45 GB.
Har jagah ek hi sawaal: ek cheez kitne guna hui, to doosri bhi utne guna.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Kya karein | Kyun |
|---|---|---|
| Dono quantities saath badhein aur ratio same rahe | ✅ Proportion / rule of three | Dono same factor se badhti hain |
| Recipe, keemat, petrol-doori (same rate) | ✅ Direct proportion | Ek double to doosri double |
| Umar aur lambai | ❌ Proportion mat lagao | 10 saal ka bachcha 5 saal wale se double lamba nahi hota |
| Ek badhe, doosri ghate (mazdoor aur din) | ❌ Direct nahi, inverse (Post 7) | Badlaav ulti disha mein hai |
| Har cheez mein same number jodna | ❌ Kabhi nahi | Ratio guna se bachta hai, jodne se nahi |
— 📌 charumam.com
❌→✅ Worked Mistake
Sawaal: 5 kg chawal ₹300 ke hain. 8 kg chawal kitne ke honge?
❌ Galat: “5 : 300 :: 8 : d → d = (300 × 5) ÷ 8 = ₹187.50.”
Galti kya hai? Formula mein terms ki jagah badal di. d = (b × c) ÷ a hota hai, yaani (300 × 8) ÷ 5. Sense check bhi fail: zyada chawal ka daam kam kaise?
✅ Sahi:
- d = (300 × 8) ÷ 5 = 2400 ÷ 5 = ₹480
- Unitary check: 1 kg = 300 ÷ 5 = ₹60, 8 kg = 60 × 8 = ₹480 ✅
Yaad rakho: Jawab nikaalne ke baad poochho, “kya yeh sense banata hai?” Zyada cheez → zyada daam (direct proportion).
sirf charumam.com pe milenge!
📝 10 MCQs
Q1. 18 : 24 ka simplest form kya hai?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 6 se divide karo: 18 ÷ 6 = 3, 24 ÷ 6 = 4.
- (b) galat: 6 : 8 ko abhi 2 se aur divide kar sakte ho.
- (c) galat: 9 : 12 ko abhi 3 se aur divide kar sakte ho.
- (d) galat: Order ulta ho gaya. Ratio mein order matter karta hai.
Q2. Kaunsa pair proportion mein hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 2 × 9 = 18 aur 3 × 4 = 12, barabar nahi.
- (b) sahi: 3 × 15 = 45 aur 5 × 9 = 45, barabar ✅
- (c) galat: 4 × 4 = 16 aur 7 × 7 = 49, order ulta hai.
- (d) galat: 1 × 3 = 3 aur 2 × 2 = 4, barabar nahi.
Q3. 4 : 6 :: 10 : x ho, to x = ?
Solution dekho
Sahi jawab: (b)
- (a) galat: 4 se 6 mein 2 jude, to 10 + 2 = 12. Yeh Pinky wali jodne ki galti hai.
- (b) sahi: x = (6 × 10) ÷ 4 = 15. Check: 4 × 15 = 60 = 6 × 10 ✅
- (c) galat: 4 × 6 = 24 ka koi matlab nahi, formula galat laga.
- (d) galat: (10 × 4) ÷ 6 ≈ 6.67, terms ulte rakh diye.
Q4. 6 notebook ₹180 ki hain. 10 notebook kitne ki?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 1 notebook = 180 ÷ 6 = ₹30, to 10 = ₹300.
- (b) galat: 6 se 10 mein 4 jude, to 180 + 4 = 184. Jodna galat hai.
- (c) galat: (180 × 6) ÷ 10 = 108, ulta hisaab. Zyada notebook ka daam kam nahi ho sakta.
- (d) galat: 180 × 10 kar diya, 6 se divide karna bhool gaye.
Q5. Direct proportion mein kya same rehta hai?
Solution dekho
Sahi jawab: (c)
- (a) galat: 1 kg aur ₹25 ka jod 26, 2 kg aur ₹50 ka jod 52. Badal gaya.
- (b) galat: Farak bhi 24 se 48 ho gaya.
- (c) sahi: 25 ÷ 1 = 50 ÷ 2 = 25, ratio same ✅
- (d) galat: Guna (product) same rehna inverse proportion ki pehchaan hai (Post 7).
Q6. Chai mein 2 cup paani ke saath 1 chammach patti padti hai. 7 cup paani ke liye kitni patti?
Solution dekho
Sahi jawab: (a)
- (a) sahi: Factor = 7 ÷ 2 = 3.5, to patti = 1 × 3.5 = 3.5 chammach.
- (b) galat: Paani mein 5 jude, patti mein bhi 5 jod diye. Jodne ki galti.
- (c) galat: 7 × 2 = 14, ratio ulta laga diya.
- (d) galat: 7 − 2 = 5, ghataane ka koi matlab nahi.
Q7. Inmein se kaunsa direct proportion NAHI hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 2 guna kapda, 2 guna daam. Direct hai.
- (b) sahi: Umar double hone pe lambai double nahi hoti. Proportion nahi ✅
- (c) galat: Same mileage pe double petrol, double doori. Direct hai.
- (d) galat: Double notebook, double daam. Direct hai.
Q8. Agar a : b :: c : d ho, to kaunsa hamesha sahi hai?
Solution dekho
Sahi jawab: (b)
- (a) galat: 2 : 4 :: 5 : 10 lo. 2 × 5 = 10, 4 × 10 = 40. Barabar nahi.
- (b) sahi: 2 × 10 = 20 = 4 × 5 ✅ Bahar ka guna = andar ka guna.
- (c) galat: 2 + 10 = 12, 4 + 5 = 9. Barabar nahi.
- (d) galat: 2 ÷ 5 = 0.4, 10 ÷ 4 = 2.5. Barabar nahi.
Q9. Ek bike 3 litre petrol mein 45 km jaati hai. 60 km ke liye kitna petrol?
Solution dekho
Sahi jawab: (a)
- (a) sahi: 1 litre = 45 ÷ 3 = 15 km. 60 ÷ 15 = 4 litre.
- (b) galat: 45 se 60 mein 15 jude, to 3 + 15 = 18. Jodne ki galti.
- (c) galat: 5 litre mein to 5 × 15 = 75 km jaayegi, 60 nahi.
- (d) galat: 45 × 60 ÷ 3 = 900, quantities aapas mein mila di.
Q10. Ek recipe mein 4 logon ke liye 300 g paneer lagta hai. 6 logon ke liye?
Solution dekho
Sahi jawab: (b)
- (a) galat: 4 se 6 mein 2 jude, to 300 + 2. Jodne ki galti.
- (b) sahi: Factor = 6 ÷ 4 = 1.5, paneer = 300 × 1.5 = 450 g ✅
- (c) galat: (300 × 4) ÷ 6 = 200, ulta. Zyada logon ko kam paneer?
- (d) galat: 300 × 6 = 1,800, 4 se divide karna bhool gaye.
— 📌 charumam.com
❓ FAQs (Bachchon Ke Asli Sawaal)
1. Ratio aur fraction mein kya farak hai?
2 : 3 ko 2/3 likh sakte ho, value wahi hai. Par dhyaan do: agar doodh : paani = 2 : 3 hai, to doodh poore mixture ka 2/3 nahi, balki 2/(2 + 3) = 2/5 hai. Ratio do hisson ki aapas mein tulna hai, fraction poore ka hissa batata hai. Yahi baat Post 4 mein bahut kaam aayegi.
2. Ratio mein units ka kya karein?
Dono terms same unit mein honi chahiye. 50 cm : 2 m ko 50 : 2 mat likho. Pehle 2 m = 200 cm, phir 50 : 200 = 1 : 4. Units same hone pe cancel ho jaati hain, isliye ratio ki koi unit nahi hoti.
3. Cross multiplication kyun kaam karta hai?
a/b = c/d ke dono taraf b × d se guna karo. Left side: a × d, right side: c × b. Barabar cheezon ko same number se guna karne pe barabari bani rehti hai. Isliye a × d = b × c.
4. Rule of three ko Trairashika kyun kehte hain?
“Trai” = teen, “raashi” = quantity. Teen quantities di hoti hain aur chauthi nikaalni hoti hai. Aryabhata (lagbhag 499 CE) ne apne granth Aryabhatiya mein is vidhi ka zikr kiya hai, aur baad mein yeh vidhi Arab aur Europe tak pahunchi.
5. Kaise pehchaanein ki sawaal direct proportion ka hai?
Ek chhota test: “Agar ek quantity double kar doon, to doosri ka kya hoga?” Doosri bhi double → direct proportion. Doosri aadhi → inverse proportion (Post 7). Na double, na aadhi → proportion lagao hi mat.
6. Kya ratio mein decimal ya fraction aa sakte hain?
Haan. Unhe whole numbers mein badal lo. 1.5 : 2 → dono ko 2 se guna → 3 : 4. 1/2 : 1/3 → dono ko 6 se guna → 3 : 2. Same number se guna karne pe ratio nahi badalta.
— 📌 charumam.com
🏋️ Practice Zone (12 Sawaal)
Q1. Easy 20 : 35 ko simplest form mein likho.
Solution dekho
Dono ko 5 se divide: 4 : 7.
Q2. Easy 6 : 9 aur 10 : 15 proportion mein hain kya?
Solution dekho
6 × 15 = 90, 9 × 10 = 90. Barabar, to haan. (Dono ka simplest form 2 : 3 hai.)
Q3. Easy 3 : 5 :: 12 : x. x nikaalo.
Solution dekho
x = (5 × 12) ÷ 3 = 60 ÷ 3 = 20. Check: 3 × 20 = 60 = 5 × 12 ✅
Q4. Easy 1 kg seb ₹120 ka hai. 2.5 kg kitne ka?
Solution dekho
120 × 2.5 = ₹300.
Q5. Medium 8 pen ₹96 ke hain. 15 pen kitne ke?
Solution dekho
1 pen = 96 ÷ 8 = ₹12. 15 pen = 12 × 15 = ₹180.
Q6. Medium 45 cm : 1.5 m ko simplest form mein likho.
Solution dekho
1.5 m = 150 cm. 45 : 150 → 15 se divide → 3 : 10.
Q7. Medium Nimbu-paani ke ek 250 ml glass mein 2 chammach cheeni padti hai. 2 litre ke jug mein kitni?
Solution dekho
2 litre = 2000 ml. Glass = 2000 ÷ 250 = 8. Cheeni = 8 × 2 = 16 chammach.
Q8. Medium x : 12 :: 15 : 20. x nikaalo.
Solution dekho
x × 20 = 12 × 15 = 180 → x = 180 ÷ 20 = 9. Check: 9 : 12 = 3 : 4 aur 15 : 20 = 3 : 4 ✅
Q9. NCERT style Ek machine 5 minute mein 120 bottle bharti hai. Usi raftaar se 1 ghante mein kitni?
Solution dekho
1 ghanta = 60 minute = 12 × 5 minute. Bottle = 120 × 12 = 1,440.
Q10. NCERT style 12 m kapda ₹1,080 ka hai. 7 m kitne ka?
Solution dekho
1 m = 1080 ÷ 12 = ₹90. 7 m = 90 × 7 = ₹630.
Q11. NCERT style Ek printer 3 minute mein 45 page chhaapta hai. 210 page kitne minute mein?
Solution dekho
1 minute = 45 ÷ 3 = 15 page. Samay = 210 ÷ 15 = 14 minute.
Q12. NCERT style x aur y direct proportion mein hain. Table poori karo: x = 4, 6, __, 15 aur y = 10, __, 25, __.
Solution dekho
k = y ÷ x = 10 ÷ 4 = 2.5.
x = 6 → y = 6 × 2.5 = 15. y = 25 → x = 25 ÷ 2.5 = 10. x = 15 → y = 15 × 2.5 = 37.5.
Answer Key — charumam.com exclusive
🧠 HOTS (Sochne Wale Sawaal)
Q1. Riya kehti hai, “2 : 3 ke dono terms mein 1 jod doon to 3 : 4 milega, yeh bhi wahi ratio hai.” Kya Riya sahi hai?
Solution dekho
Nahi. 2 × 4 = 8 aur 3 × 3 = 9, barabar nahi. 2/3 ≈ 0.67 jabki 3/4 = 0.75.
WHY: Ratio guna-bhaag se bachta hai. Jodne se ratio tabhi same rehta hai jab dono terms pehle se barabar hon (1 : 1 → 2 : 2).
Q2. Ek bachcha 5 saal ki umar mein 110 cm lamba hai. Kya 10 saal mein woh 220 cm ka hoga?
Solution dekho
Nahi. 220 cm to 7 feet se bhi zyada hai! Umar aur lambai direct proportion mein nahi hain. Bachpan mein lambai tezi se badhti hai, baad mein dheemi ho jaati hai, aur ek umar ke baad rukk jaati hai.
Seekh: Proportion lagaane se pehle check karo ki dono quantities sach mein same factor se badhti hain ya nahi.
Q3. a : b = 3 : 4 aur a + b = 63. a aur b nikaalo.
Solution dekho
Kul hisse = 3 + 4 = 7. Ek hissa = 63 ÷ 7 = 9.
a = 3 × 9 = 27, b = 4 × 9 = 36. Check: 27 + 36 = 63 aur 27 : 36 = 3 : 4 ✅
(Yahi “hisse” wali soch hum Post 4 mein detail mein seekhenge.)
Q4. 3 : x :: x : 12. x kya hai (x positive)?
Solution dekho
Cross-check: 3 × 12 = x × x → x × x = 36 → x = 6.
Check: 3 : 6 = 1 : 2 aur 6 : 12 = 1 : 2 ✅. Aise beech wale term ko “mean proportional” kehte hain.
sirf charumam.com pe milenge!
🏆 Olympiad Corner
Q1. a : b = 2 : 3 ho, to (3a + b) : (a + 2b) kya hoga?
Solution dekho
a = 2k, b = 3k lo. 3a + b = 6k + 3k = 9k. a + 2b = 2k + 6k = 8k.
Ratio = 9 : 8.
Q2. Do numbers ka ratio 5 : 7 hai. Dono mein 6 jodne pe ratio 7 : 9 ho jaata hai. Numbers kya hain?
Solution dekho
Numbers = 5k aur 7k. (5k + 6) : (7k + 6) = 7 : 9.
9(5k + 6) = 7(7k + 6) → 45k + 54 = 49k + 42 → 4k = 12 → k = 3.
Numbers = 15 aur 21. Check: 21 : 27 = 7 : 9 ✅
Q3. x : y = 3 : 5 ho, to (x + y) : (y − x) kya hoga?
Solution dekho
x = 3k, y = 5k. x + y = 8k, y − x = 2k.
Ratio = 8 : 2 = 4 : 1.
Q4. Ek recipe mein 6 logon ke liye 450 g atta aur 1.5 chammach namak lagta hai. 10 logon ke liye dono kitne?
Solution dekho
Factor = 10 ÷ 6 = 5/3.
Atta = 450 × 5/3 = 750 g. Namak = 1.5 × 5/3 = 2.5 chammach.
Check: 450 : 1.5 = 300 : 1 aur 750 : 2.5 = 300 : 1 ✅
sirf charumam.com readers ke liye 🔐
💗 CharuMam Motivation
Proportion ek bahut pyaari baat sikhaata hai: har cheez ko ek hi raftaar se badhao. Pinky ne ek din mein sab kuch jod diya, aur chai bigad gayi. 😅
Padhaai bhi aisi hi hai. Exam se ek raat pehle 10 ghante padhna “jodna” hai. Roz 1 ghanta padhna “proportion” hai: 7 din, 7 ghante, aur sab kuch santulit. Thoda focus, roz ki mehnat, aur sabr, result apne aap proportion mein badhega! 🌟
— 📌 charumam.com
🟢 Master Recap
- Ratio a : b = divide karke tulna. Dono terms same unit mein.
- Dono terms ko same number se guna/divide karo to equivalent ratio milta hai.
- Proportion a : b :: c : d matlab dono ratios barabar.
- Cross-check: a × d = b × c.
- Rule of three: d = (b × c) ÷ a. Unitary method se check karo.
- Direct proportion: ek k guna, to doosra bhi k guna. y ÷ x = constant.
- Proportion mein jodna nahi, guna hota hai (Pinky ki chai!).
- Hamesha sense check: zyada cheez → zyada daam.
— charumam.com 🎯
👉 Aage Kya?
Aapke school atlas ke kone mein kabhi 1 : 50,00,000 jaisa ratio dekha hai? Woh bhi ek proportion hai, jo kaagaz ke centimetre ko zameen ke kilometre se jodta hai. Agle post mein seekhenge map ka scale (RF) padhna! 🗺️
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬