Post 16.1 mein ÷ 5 seekha: double, phir 10 se divide. Aaj uski badi bahan: ÷ 25. Number ka double, phir ek baar aur double (yaani × 4), phir 100 se divide (do 0 remove karo, ya point do jagah left). 175 ÷ 25 = 7, teen second mein! Kyun? Kyunki ₹100 mein chaar ₹25 hote hain. Yeh Chapter 5 ke × 25 ka bilkul reverse hai.
⏱ Before Timer: Pehle Purane Method Se
Pehle “25 add karte jao” method (ek doosre number pe, taaki timer wale sawaal ka jawab pehle na dikhe). 150 ÷ 25: 150 tak 25-25 ke kitne group?
- 25, 50, 75, 100, 125, 150: har baar 25 add karo aur ungli pe count karo.
- 6 ungliyaan: to 150 ÷ 25 = 6 (check: 25 × 6 = 150).
Bade number pe (jaise 1000 ÷ 25) yeh bahut long ho jaata hai. Ab timer wala sawaal isi tarah kijiye.
Ab phone ya clock mein stopwatch (time measure karne wali clock) chalu kijiye. Neeche wala sawaal isi “25 add karte jao” method se (ya long division se) kijiye, copy-pencil ke saath. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
175 ÷ 25 = 7, kyunki 25 × 7 = 175
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki compare karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Chahiye: Post 16.1 ka ÷, quotient, remainder aur point; Chapter 5 ka × 25 (36 × 25 = 900). Yaad ke liye boxes neeche. Naye word:
📖 Word jo is post mein aayenge
- Double ka double: do baar double = × 4. 175 → 350 → 700.
- 100 se divide: peeche ke do 0 remove karo (700 → 7), ya point do jagah left (520 → 5.2).
- Hundredth part: ek ke 100 equal pieces mein se ek: 0.01. Jaise ₹1 ka 1 money.
- Quarter (÷ 4): 4 equal parts karke ek: half ka half. 20 ka quarter 5 (20 → 10 → 5).
- Packet: yahan ₹25 ka ek packet. ₹100 = 4 packet.
📏 Bade numbers padhna aur round number mein add karna
Har digit ki ek jagah (place) hoti hai. Right se count karo: pehli jagah Units (ones, 1 wale), uske left mein Tens (10 wale), phir Hundred (100 wale), phir Thousand (1000 wale).
10 ka bundle: 10 units = 1 ten (10). 10 tens = 1 hundred (100). 10 hundreds = 1 thousand (1000). Har jagah apne right wali jagah se 10 times badi hai.
| Number | Kaise padhein | Kis cheez se bana |
|---|---|---|
| 98 | attaanve | 9 tens (90) + 8 units |
| 165 | ek sau painsath | 1 hundred (100) + 6 tens (60) + 5 units |
| 999 | nau sau ninyaanve | 9 hundreds (900) + 9 tens (90) + 9 units |
| 1011 | ek hazaar gyaarah | 1 thousand (1000) + 0 hundred + 1 ten (10) + 1 unit |
Round number mein chhota number add karna (place box rule): chhote number ko right se likho, yaani units ke neeche units, tens ke neeche tens. Phir har box mein jo hai, woh jawab mein utaar do. Ek digit wala number sirf units ka zero badalta hai, do digit wala units aur tens dono.
- 100 + 65: 65 mein do digit, to 6 tens mein aur 5 units mein: 1|6|5 = 165.
- 100 + 2: 2 sirf units mein, tens ka 0 waise hi rehta hai: 1|0|2 = 102 (12 nahi, 120 nahi!).
- 200 + 6: 6 sirf units mein: 2|0|6 = 206.
- 1000 + 11: 11 mein do digit, to 1 tens mein aur 1 units mein: 1|0|1|1 = 1011.
➗ Division kya hai? ÷, quotient aur remainder
Chapter 5 mein dekha tha: ÷ (divide ka sign) matlab equal parts mein divide karna. “12 ÷ 4” padho “12 divided by 4” ya “12 ko 4 se divide”: 12 laddoo 4 students mein equal divide karo, har ek ko 3. Ise aise bhi soch sakte ho: 12 mein 4-4 ke kitne group bante hain? 3 group. Dono ka jawab ek hi: 12 ÷ 4 = 3, kyunki 4 × 3 = 12.
Quotient = division ka jawab: har ek ko kitna mila, ya kitne poore group bane. Remainder = jo aakhir mein bach gaya, jisse ek aur poora group nahi ban sakta. 47 laddoo, 5-5 ke boxes: 9 boxes bharte hain (5 × 9 = 45), aur 2 laddoo bach jaate hain. To quotient 9 (9 poore boxes) aur remainder 2 (2 bache laddoo). Hum likhenge: 47 ÷ 5 → quotient 9, remainder 2. (Remainder hamesha divide karne wale number se chhota hota hai: 5 se divide mein remainder 0, 1, 2, 3 ya 4.)
Check ka rule: divide karne wala × quotient + remainder = asli number. Is line mein pehle multiply, phir add: 47 = 5 × 9 + 2, kyunki 5 × 9 = 45 aur 45 + 2 = 47 ✅. (Agar pehle 9 + 2 = 11 add karte aur phir 5 × 11 = 55 karte, to galat hota.)
Poora divide: jab remainder 0 ho, to kehte hain number “poora divide” ho gaya: 45 ÷ 5 = 9, kuch nahi bacha.
🔸 10 aur 100 se divide, aur point (decimal)
10 se divide, jab peeche 0 ho: peeche ka ek 0 remove kar do. 170 ÷ 10 = 17 (170 = 17 tens, to 10-10 ke 17 group). 100 se divide: peeche ke do 0 remove karo: 700 ÷ 100 = 7.
Peeche 0 na ho to? Tab point (.) lagate hain, jise decimal point kehte hain (Post 14.3). Point ke left wala part poore number, right wala part “ek ke pieces”. 94 ÷ 10: har digit ek jagah right khisakta hai, yaani point ek jagah left: 9.4. Padho “nau point chaar”: 9 poore aur 4 tenth parts (ek ke 10 equal pieces mein se 4). Money mein: ₹94 ko 10 logon mein divide karo, har ek ko ₹9.40, yaani 9 rupees 40 money.
100 se divide: point do jagah left. 520 ÷ 100 = 5.20. Point ke baad aakhir ka 0 kuch nahi badalta (₹5.20 aur ₹5.2 ek hi: 5 rupees 20 money), to 5.2 likh sakte ho. 36 ÷ 100 = 0.36 (poore 0, aur 36 hundredths; jaise 36 money = ₹0.36).
Point wale jawab ka check: 47 ÷ 5 = 9.4? 9.4 × 5: 9 × 5 = 45, aur 0.4 × 5 = 2 (4 tenths, 5 baar = 20 tenth = 2 poore). 45 + 2 = 47 ✅.
🔁 Chapter 5 yaad karo: × 5 aur × 25
Chapter 5: × 5 = pehle × 10 (peeche 0), phir half: 46 × 5: 460 ka half, yaani 230. Kyunki 5, 10 ka half hai. Aur × 25 = pehle × 100, phir half ka half: 36 × 25: 3600 → 1800 → 900. Kyunki 25, 100 ka quarter hai.
Aaj hum reverse chalenge: multiply ki jagah division. Jo Chapter 5 mein “half” tha, woh aaj “double” banega; aur jo “× 10” tha, woh “÷ 10”.
🔁 Chhota sa warm-up
- 175 + 175 = ?
- 700 ÷ 100 = ?
- 20 ka quarter?
Answers dekho
- 350
- 7 (do 0 remove karo)
- 5 (20 → 10 → 5, half ka half)
Teeno mila do: 175 ÷ 25 = 7, aur remainder ke liye quarter. Aaj ka poora game!
— 📌 charumam.com
🎬 Story: Canteen Ke Coupon
School canteen mein ek coupon ₹25 ka tha. Class monitor Aisha ke paas class ke ₹475 add the. Teacher ne poocha: “Kitne coupon aayenge?”
Aisha ne socha: “₹100 mein chaar coupon. To 475 ka double 950, phir double 1900. 100 se divide: do 0 remove karo: 19 coupon!”
Canteen wale bhaiya ne 19 coupon diye aur ek rupaya bhi nahi bacha. 🪙 Aaj yahi trick!
— 📌 charumam.com
🪄 Trick Step by Step: Double Ka Double, Phir 100 Se Divide
💡 Is post ki ek badi baat: Kisi number ÷ 25 = us number ka double, phir double (× 4), phir 100 se divide. 100 se divide: peeche do 0 hon to remove karo, nahi to point do jagah left. Kyunki har 100 mein chaar 25 hote hain. Remainder chahiye to: × 4 wale number ke last do digit remove karo (= quotient), un do digit ka quarter = remainder.
Step 1: Pehla double
175 ÷ 25. Double: 175 + 175 = 350.
Step 2: Doosra double (ab × 4 ho gaya)
350 + 350 = 700. Do baar double = 4 times (175 × 4 = 700).
Step 3: 100 se divide
700 ke peeche do 0: remove karo → 7. To 175 ÷ 25 = 7.
Step 4: Peeche 00 nahi? Point do jagah left
130 ÷ 25: 130 → 260 → 520. Peeche do 0 nahi, to point do jagah left: 5.20, yaani 5.2 (aakhir ka 0 point ke baad kuch nahi badalta).
Step 5: Remainder wala jawab aur check
130 ÷ 25: 520 ke last do digit 20 remove karo → quotient 5. 20 ka quarter: 20 → 10 → 5 → remainder 5. Check: 25 × 5 = 125 (Chapter 5: 500 ka half ka half), aur 125 + 5 = 130 ✅.
Aur examples, ek ke baad ek
625 ÷ 25: double: 625 + 625 = 1250. Phir double: 1250 + 1250 = 2500 (yaani × 4). 100 se divide: peeche ke do 0 remove karo → 25.
1000 ÷ 25: double: 1000 + 1000 = 2000. Phir double: 2000 + 2000 = 4000 (yaani × 4). 100 se divide: peeche ke do 0 remove karo → 40.
90 ÷ 25: double: 90 + 90 = 180. Phir double: 180 + 180 = 360 (yaani × 4). 100 se divide: point do jagah left → 3.6. Remainder wala jawab: 360 ke last do digit 60 remove karo → quotient 3; hataye do digit ÷ 4: 60 ÷ 4 = 15 → remainder 15. Check: 25 × 3 = 75, 75 + 15 = 90 ✅
30 ÷ 25: double: 30 + 30 = 60. Phir double: 60 + 60 = 120 (yaani × 4). 100 se divide: point do jagah left → 1.2.
Dhyaan: chhote number (jaise 30) ka jawab 1 ke aas-paas: 30 mein 25 ek baar aur thoda sa (1.2). Jawab hamesha number se chhota aana chahiye.
🆘 Atak gaye? Aise socho
- Do baar double (× 4), ek baar nahi.
- 100 se divide: do 0 remove karo, ya point do jagah left.
- Remainder: × 4 wale number ke last do digit remove karo; unka quarter (half ka half) remainder.
- Remainder 25 se chhota hi hoga (0 se 24).
- Check: quotient × 25 (Chapter 5: × 100 phir half ka half) + remainder.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Har ₹100 mein chaar ₹25. 130 = 100 + 30. ₹100 ke 4 packet (₹25 ke). Bache ₹30 mein ek packet aur (25 + 5 = 30), aur ₹5 bache. Total 5 packet, remainder 5. Diagram dekho.
× 4 phir ÷ 100 kyun? Division mein dono number 4 multiply kar do, to jawab nahi badalta. 25 dost ₹130 divide karein, ya 100 dost ₹520 divide karein (4 times money, 4 times dost): har ek ko utna hi milta hai. Jaise 50 ÷ 25 = 2 aur 200 ÷ 100 = 2, dono same. To 130 ÷ 25 ki jagah 520 ÷ 100 karo: 100 se divide sabse aasaan, point do jagah left → 5.2. Jawab wahi.
Remainder ke liye “quarter” kyun?
Humne number ko 4 se multiply kiya tha. To jo part bacha (520 ke last do digit, 20), woh bhi 4 times hai. Asli remainder paane ke liye usko waapas 4 se divide: 20 ÷ 4 = 5. Post 16.1 mein 2 se multiply kiya tha, isliye wahan half liya tha. Jitne se multiply, utne se divide.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Method Se Check)
Example 1: 625 ÷ 25 = ?
625 ÷ 25: double: 625 + 625 = 1250. Phir double: 1250 + 1250 = 2500 (yaani × 4). 100 se divide: peeche ke do 0 remove karo → 25.
✔️ Normal method se check: 25 × 25 = 625 (Chapter 6: 2 × 3 = 6, peeche 25) ✅
Example 2: 90 ÷ 25 = ? (point wala aur remainder wala)
90 ÷ 25: double: 90 + 90 = 180. Phir double: 180 + 180 = 360 (yaani × 4). 100 se divide: point do jagah left → 3.6. Remainder wala jawab: 360 ke last do digit 60 remove karo → quotient 3; hataye do digit ÷ 4: 60 ÷ 4 = 15 → remainder 15. Check: 25 × 3 = 75, 75 + 15 = 90 ✅
✔️ Normal method se check: 3.6 × 25: 3 × 25 = 75 aur 0.6 × 25 = 15 (6 tenth × 25 = 150 tenth = 15); 75 + 15 = 90 ✅
Example 3: 1000 ÷ 25 = ?
1000 ÷ 25: double: 1000 + 1000 = 2000. Phir double: 2000 + 2000 = 4000 (yaani × 4). 100 se divide: peeche ke do 0 remove karo → 40.
✔️ Normal method se check: 40 × 25: 4000 ka half ka half: 4000 → 2000 → 1000 ✅
Example 4: Ek pen ₹25 ka. ₹475 mein kitne pen?
475 ÷ 25: double: 475 + 475 = 950. Phir double: 950 + 950 = 1900 (yaani × 4). 100 se divide: peeche ke do 0 remove karo → 19.
19 pen.
✔️ Normal method se check: 19 × 25: 1900 → 950 → 475 (Chapter 5: × 100 phir half ka half) ✅
— 📌 charumam.com
💡 CharuMam Ki Smart Trick
Wahi CharuMam soch: mushkil number ki jagah aasaan relative. 25 ka relative 100 (25 = 100 ka quarter). 100 se divide sabse aasaan, to cost bas do double. Isi tarah 125 ka relative 1000 hai (125 = 1000 ka aathvaan part): ÷ 125 = × 8, phir 1000 se divide (Challenge dekho).
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Koi bhi number ÷ 25 (175, 1000) | ✅ Haan | Double, double, 100 se divide. |
| Remainder poocha (90 ÷ 25) | ✅ Haan | Last do digit ka quarter. |
| Money, ₹25 ke coupon/pen | ✅ Haan | Seedha × 4, phir ÷ 100. |
| 25 mein se marks ko 100 mein change karna | ✅ Bahan | × 4 (Challenge dekho). |
| ÷ 24, ÷ 26 jaise | ❌ Nahi | Yeh trick sirf 25 (aur 250, 2500) ke liye. |
— 📌 charumam.com
❌→✅ Common Mistakes
Mistake 1: Sirf ek baar double
Sawaal: 175 ÷ 25
❌ Galat: “175 → 350 → 100 se divide → 3.5.”
✅ Sahi: do baar double: 350 → 700, phir 100 se divide → 7.
Mistake 2: 100 ki jagah 10 se divide
Sawaal: 175 ÷ 25
❌ Galat: “700 → ek 0 hataya → 70.”
✅ Sahi: 100 se divide: do 0 remove karo → 7. Socho: 175 mein 25 sirf 7 baar.
Mistake 3: Double ki jagah half
Sawaal: 300 ÷ 25
❌ Galat: “Chapter 5 jaisa half ka half: 75.”
✅ Sahi: division mein reverse: double ka double 1200 → 100 se divide → 12.
Mistake 4: Remainder mein quarter bhool gaye
Sawaal: 90 ÷ 25 ka remainder
❌ Galat: “360 ke last do digit 60, to remainder 60.”
✅ Sahi: 60 ka quarter: 60 → 30 → 15. (Remainder 25 se chhota hona chahiye; 60 to bada hai!)
🧠 Rule of thumb: ÷ 25 = double ka double, phir 100 se divide. Remainder = last do digit ka quarter.
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal. Target: 4 minute.
- 175 ÷ 25 = ?
- 625 ÷ 25 = ?
- 300 ÷ 25 = ?
- 1000 ÷ 25 = ?
- 130 ÷ 25 = ?
- 30 ÷ 25 = ?
- 90 ÷ 25 = ?
- 450 ÷ 25 = ?
- 2500 ÷ 25 = ?
- 10 ÷ 25 = ?
- 1250 ÷ 25 = ?
- 60 ÷ 25: quotient aur remainder?
- 110 ÷ 25: quotient aur remainder?
- 240 ÷ 25: quotient aur remainder?
- 775 ÷ 25 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 7
- 25
- 12
- 40
- 5.2
- 1.2
- 3.6
- 18
- 100
- 0.4
- 50
- 2, remainder 10
- 4, remainder 10
- 9, remainder 15
- 31
Kaise kiya (kuch): 10 ÷ 25: 10 → 20 → 40 → point do jagah left → 0.40, yaani 0.4. 240 ÷ 25: 960 → last 60 remove karo → quotient 9, 60 ka chautha 15 → remainder 15. 775 ÷ 25: 3100 → 31.
— 📌 charumam.com
⏰ One-Minute Challenge
Sirf 1 minute (60 second). Timer lagao, aur jitne ho sakein utne sawaal mann mein (bina copy ke) karo. Sirf jawab likhna hai.
- 50 ÷ 25 = ?
- 75 ÷ 25 = ?
- 200 ÷ 25 = ?
- 125 ÷ 25 = ?
- 400 ÷ 25 = ?
- 150 ÷ 25 = ?
- 5 ÷ 25 = ?
- 275 ÷ 25 = ?
- 20 ÷ 25 = ?
- 325 ÷ 25 = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya start! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 2
- 3
- 8
- 5
- 16
- 6
- 0.2
- 11
- 0.8
- 13
Dhyaan: 5 ÷ 25: 5 → 10 → 20 → 0.20, yaani 0.2. 20 ÷ 25: 80 → 0.80, yaani 0.8. 325 ÷ 25: 1300 → 13.
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har day thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Reason)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 175 ÷ 25 = ?
Jawab aur reason dekho
Sahi jawab: (b) 7
- (a) galat ❌: 70: 100 ki jagah 10 se divide kiya (ek hi 0 hataya).
- (b) sahi ✅: 175 → 350 → 700, do 0 remove karo → 7.
- (c) galat ❌: 700: × 4 kiya, par 100 se divide bhool gaye.
- (d) galat ❌: 3.5: sirf ek baar double kiya (350), phir 100 se divide.
Q2. 130 ÷ 25 = ?
Jawab aur reason dekho
Sahi jawab: (a) 5.2
- (a) sahi ✅: 130 → 260 → 520, point do jagah left → 5.2.
- (b) galat ❌: 52: point sirf ek jagah left shift kiya (10 se divide).
- (c) galat ❌: 0.52: point teen jagah left shift kiya (1000 se divide).
- (d) galat ❌: 2.6: sirf ek baar double kiya (260), phir 100 se divide.
Q3. 130 ÷ 25 → quotient 5. Remainder kitna?
Jawab aur reason dekho
Sahi jawab: (d) 5
- (a) galat ❌: 20: last do digit hi remainder maan liye; quarter lena tha.
- (b) galat ❌: 2: 5.2 ke point ke baad wala 2 hi remainder maan liya.
- (c) galat ❌: 30: 130 ke last do digit 30 remainder maan liye; par remainder 25 se chhota hota hai.
- (d) sahi ✅: 520 ke last do digit 20, quarter 5. Check: 125 + 5 = 130.
Q4. 1000 ÷ 25 = ?
Jawab aur reason dekho
Sahi jawab: (c) 40
- (a) galat ❌: 400: sirf ek 0 hataya (10 se divide).
- (b) galat ❌: 4: teen 0 hata diye (1000 se divide).
- (c) sahi ✅: 1000 → 2000 → 4000, do 0 remove karo → 40.
- (d) galat ❌: 4000: × 4 kiya, 100 se divide bhool gaye.
Q5. ÷ 25 ki trick kyun chalti hai?
Jawab aur reason dekho
Sahi jawab: (b) 100 mein chaar 25 hote hain
- (a) galat ❌: Mistake: last 5 se kuch tay nahi hota; asli baat 100 = 4 × 25.
- (b) sahi ✅: Isliye “kitne 100” × 4 = “kitne 25”.
- (c) galat ❌: Mistake: taaq hona yahan kaam nahi aata.
- (d) galat ❌: Mistake: 25 + 25 = 50 hota hai; 100 ke liye chaar 25 chahiye.
Q6. 30 ÷ 25 = ?
Jawab aur reason dekho
Sahi jawab: (a) 1.2
- (a) sahi ✅: 30 → 60 → 120, point do jagah left → 1.2.
- (b) galat ❌: 12: point sirf ek jagah left (10 se divide).
- (c) galat ❌: 0.12: point teen jagah left (1000 se divide).
- (d) galat ❌: 0.6: sirf ek baar double kiya (60), phir 100 se divide.
Q7. Ek pen ₹25 ka. ₹475 mein kitne pen?
Jawab aur reason dekho
Sahi jawab: (d) 19
- (a) galat ❌: 1900: 100 se divide bhool gaye.
- (b) galat ❌: 190: sirf ek 0 hataya (10 se divide).
- (c) galat ❌: 9.5: sirf ek baar double kiya (950), phir 100 se divide.
- (d) sahi ✅: 475 → 950 → 1900, do 0 remove karo → 19.
Q8. 90 ÷ 25 → quotient aur remainder?
Jawab aur reason dekho
Sahi jawab: (c) 3, remainder 15
- (a) galat ❌: 3.6, remainder 0: point wala jawab aur remainder mila diye.
- (b) galat ❌: 4, remainder 10: 90 ko upar 100 tak round kar diya (100 ÷ 25 = 4) aur upar ka difference 100 − 90 = 10 remainder likh diya. Par 25 × 4 = 100, jo 90 se bada hai; remainder bacha hua part hota hai.
- (c) sahi ✅: 360: last 60 remove karo → 3; 60 ka quarter 15. Check: 75 + 15 = 90.
- (d) galat ❌: 3, remainder 60: last do digit hi remainder maan liye; quarter lena tha.
Q9. 625 ÷ 25 = ?
Jawab aur reason dekho
Sahi jawab: (b) 25
- (a) galat ❌: 12.5: sirf ek baar double kiya (1250), phir 100 se divide.
- (b) sahi ✅: 625 → 1250 → 2500, do 0 remove karo → 25.
- (c) galat ❌: 2500: × 4 kiya, 100 se divide bhool gaye.
- (d) galat ❌: 250: sirf ek 0 hataya (10 se divide).
Q10. Kaunsa number 25 se poora divide hota hai (remainder 0)?
Jawab aur reason dekho
Sahi jawab: (a) 375
- (a) sahi ✅: Last do digit 75 (25 ke 3 packet): remainder 0.
- (b) galat ❌: Mistake: last do digit 85 = 75 + 10, remainder 10.
- (c) galat ❌: Mistake: last do digit 60 = 50 + 10, remainder 10.
- (d) galat ❌: Mistake: last do digit 10, remainder 10.
— 📌 charumam.com
🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda mind bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. 123456 ÷ 25 ka remainder kitna? (Bina poora divide kiye)
Solution dekho
123456 = 123400 + 56. 123400 ke peeche do 0, to woh 100-100 ke groups mein poora divide ho jaata hai, aur har 100 mein chaar 25: koi remainder nahi. Bache 56 = 50 + 6 → remainder 6. Matlab 25 se divide ka remainder sirf last do digit se.
Q2. □ ÷ 25 = 12. □ = ?
Solution dekho
Reverse: total = 12 × 25. Chapter 5: 1200 → 600 → 300 (× 100 phir half ka half).
Check: 300 → 600 → 1200 → 12 ✅
Q3. 750 ÷ 125 = ? (Isi soch se)
Solution dekho
1000 mein aath 125 hote hain (125 + 125 = 250, 250 + 250 = 500, 500 + 500 = 1000: teen baar double = 8). To ÷ 125 = teen baar double (× 8), phir 1000 se divide. 750 → 1500 → 3000 → 6000, teen 0 remove karo → 6.
Check: 125 × 6 = 750 ✅
Q4. Riya ko test mein 25 mein se 18 marks mile. 100 mein se kitne hote? (Ise percent kehte hain: “hundred mein se kitna”.)
Solution dekho
Seedha socho: 25 ko 100 banane ke liye × 4 (25 × 4 = 100). To 18 ko bhi × 4: 18 × 4 = 72. Matlab 25 mein se 18 = 100 mein se 72, yaani 72 percent ✅.
Trick se bhi wahi: 18 ÷ 25 → 18 × 4 = 72 → point do jagah left → 0.72; ab 100 se multiply (point do jagah right) → 72.
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Division aur remainder, money ke word problem, marks ko percent mein change karna. |
| Maths Olympiad | Remainder ke pattern (last do digit), reverse sawaal. |
| NTSE / MAT | Tez Simplification. |
| SSC / Bank (aage) | Percentage: 25 mein se marks, ÷ 25 aur ÷ 125 daily aate hain. |
Shabdon ka matlab: Olympiad = school ke students ki maths competition. NTSE = Class 10 ke students ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ka exam (NTSE ka ek part). SSC / Bank exam = badon ke government job ke exam. Simplification = bade calculation ko chhota karke jawab nikaalna. Class 6–8 = school ki chhathi se aathvi class.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Mantra: “double, double, do zero.” Jab bhi 25 dikhe, ₹100 ke chaar coupon socho. Aur 25 mein se marks ko 100 mein change karna ho to bas × 4! Agle post mein ek naya game: ÷ 9, sirf digit add kar! 🪙
— 📌 charumam.com
⏱ After Timer: Ab Trick Se!
Wahi sawaal jo shuru mein kiya tha. Stopwatch phir chalu kijiye, aur is baar aaj ki trick se kijiye:
Trick se kaise karein (dekho)
Double: 175 + 175 = 350. Phir double: 350 + 350 = 700. 100 se divide: do 0 remove karo → 7 ✅
| Before time | After time | Kitna tez? |
|---|---|---|
| ____ second | ____ second | Before − After = ____ second bache! |
Pehli baar mein time zyada bhi lag sakta hai, ghabraiye nahi! Nayi trick ko 3 se 4 days ki practice chahiye. Phir yeh purane method se kaafi tez ho jaati hai. 🚀
— 📌 charumam.com
🤖 Aur Practice: AI Tutor Se Poochho
Neeche wali line copy kijiye aur CharuMam AI Tutor (tutor.charumam.com) mein paste kar dijiye. Tutor aapko naye sawaal dega aur mistake hone pe samjhayega:
— 📌 charumam.com
❓ FAQs (Students Ke Asli Sawaal)
1. Do baar double hi kyun?
Kyunki 100 mein chaar 25 hain, aur do baar double = × 4.
2. Point do jagah kyun?
100 se divide hai: har digit do jagah right khisakta hai, yaani point do jagah left.
3. Remainder ke liye quarter kyun?
× 4 kiya tha, to bacha part bhi 4 times hai; waapas 4 se divide.
4. 5.20 aur 5.2 ek hi hain?
Haan. Point ke baad aakhir ka 0 kuch nahi badalta (₹5.20 = 5 rupees 20 money).
5. Agle post mein kya hai?
Post 16.3: ÷ 9, digit add se quotient aur remainder: 43 ÷ 9 → 4, remainder 7.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- ÷ 25 = double ka double (× 4), phir 100 se divide: 175 → 700 → 7.
- Peeche 00 nahi to point do jagah left: 130 → 520 → 5.2.
- Remainder: last do digit ka quarter: 130 → 5, remainder 5.
- Kyun: har 100 mein chaar 25.
- Check: quotient × 25 (Chapter 5) + remainder.
- 25 mein se marks → 100 mein: × 4.
— charumam.com 🎯
👉 Aage Kya?
Ab Post 16.3: ÷ 9! Har 10 mein ek 9 aur 1 bacha, isliye digits add karo: 43 ÷ 9 → quotient 4, remainder 4 + 3 = 7. Check Chapter 10 ke × 9 se.
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
Har option pe tap karo, turant pata chalega sahi ya galat.
Q1. 225 ÷ 25 = ?
(a) 9
✅ Sahi! × 4: 225 × 4 = 900. 100 se divide: do 0 remove karo → 9. Check: 25 × 9 = 225.
(b) 900
❌ Galat: × 4 kiya par 100 se divide bhool gaye: 225 × 4 = 900.
(c) 90
❌ Galat: Sirf ek 0 hataya (10 se divide). 100 se divide mein do 0 hatate hain.
(d) 2.25
❌ Galat: × 4 bhool gaye, seedha 100 se divide kar diya. Pehle 225 × 4 = 900.
Q2. 340 ÷ 25 = ?
(a) 136
❌ Galat: Point sirf ek jagah left kiya. 100 se divide mein point do jagah left: 13.6.
(b) 3.4
❌ Galat: × 4 bhool gaye, seedha 100 se divide. Pehle 340 × 4 = 1360.
(c) 13.6
✅ Sahi! 340 × 4 = 1360. 100 se divide: point do jagah left → 13.6. Check: 13.6 × 25 = 340.
(d) 1.36
❌ Galat: Point teen jagah left kar diya. 100 mein do zero, to point do jagah: 13.6.
Q3. 110 ÷ 25 → quotient aur remainder?
(a) quotient 4, remainder 40
❌ Galat: Hataye do digit 40 hi remainder likh diye. Remainder = 40 ÷ 4 = 10.
(b) quotient 4, remainder 10
✅ Sahi! 110 × 4 = 440. Last do digit 40 remove karo → quotient 4. 40 ÷ 4 = 10 → remainder 10. Check: 25 × 4 + 10 = 110.
(c) quotient 4, remainder 20
❌ Galat: 40 ka sirf half liya (÷ 2). 25 wali trick mein hataye do digit ÷ 4 karte hain.
(d) quotient 44, remainder 0
❌ Galat: Sirf ek digit hataya. 25 wali trick mein last do digit hatate hain: 440 → 4.
Q4. Kitchen ke liye ek mug ₹25 ka hai. ₹350 mein kitne mug aayenge?
(a) 140
❌ Galat: Sirf ek 0 hataya. 100 se divide mein do 0 remove karo: 1400 → 14.
(b) 1400
❌ Galat: 350 × 4 = 1400 tak kiya, 100 se divide bhool gaye.
(c) 87.5
❌ Galat: × 4 ki jagah ÷ 4 kar diya. ÷ 25 = pehle × 4, phir ÷ 100.
(d) 14
✅ Sahi! 350 × 4 = 1400. Do 0 remove karo → 14 mug. Check: 25 × 14 = 350.
Q5. Kaunsa number 25 se divide karne par 16 deta hai?
(a) 400
✅ Sahi! 16 × 25 = 16 × 100 ÷ 4: 1600 ÷ 4 = 400. Check: 400 ÷ 25 = 16.
(b) 0.64
❌ Galat: Reverse sawaal mein multiply karna tha, par divide kar diya. Number = 16 × 25.
(c) 64
❌ Galat: Sirf × 4 kiya, × 100 bhool gaye. 16 × 25 = 1600 ÷ 4 = 400.
(d) 41
❌ Galat: 25 add kar diya. Number = 16 × 25.
💛 Post Achha Laga? Like, Share, Subscribe, Follow!
Agar aaj kuch naya samajh aaya, to post ko like kijiye, apne doston aur class ke group mein share kijiye, aur daily nayi trick ke liye humein subscribe aur follow kijiye! 🙏
- 🌐 Website: charumam.com
- 🤖 AI Tutor (doubt poochho, 24×7): tutor.charumam.com
- ▶️ YouTube (subscribe): @charumamofficial
- 📸 Instagram (follow): @charumamofficial
- ✈️ Telegram: t.me/charumam
- 💬 WhatsApp Channel: CharuMam WhatsApp Channel
— 📌 charumam.com
