35² ki trick ki ek bahan hai! Jab do numbers ki dahai same ho (jaise 43 aur 47 mein dono ki dahai 4) aur ikaiyon ka jod 10 ho (3 + 7 = 10), to guna do second mein: dahai × agla, aur uske peeche ikaiyon ka guna. Pehle shartein, phir trick, phir chitra se kyun.
⏱ Before Timer: Pehle Purane Tareeke Se
Pehle seedha tareeka. 43 × 47 matlab 43 ko 47 baar jodna. 47 = 40 + 7, to 43 ko 40 baar aur 43 ko 7 baar, phir jodo:
- 43 ko 10 baar = 430. 40 baar = 430 ko 4 baar: 430, 860, 1290, 1720.
- 43 ko 7 baar (column, GUNA box): ikai 7 × 3 = 21 → 1 likho, 2 carry. Dahai 7 × 4 = 28, usme 2 jodo: 30. Jawab 301.
- Dono jodo: 1720 + 301 = 2021.
Ab phone ya ghadi mein stopwatch (samay naapne wali ghadi) chalu kijiye. Neeche wala sawaal isi school wale tareeke (column method) se kijiye, copy-pencil ke saath. Column method na aata ho to ungliyon pe gin kar bhi kar sakte hain. Jaise hi jawab mil jaaye, stopwatch rok dijiye aur apna time likh lijiye.
Mera time: ______ second
Jawab dekho
43 × 47 = 2021
Abhi trick nahi dekhni! Post ke end mein After Timer mein yahi sawaal trick se karenge aur dono time ki tulna karenge. 😊
— 📌 charumam.com
✅ Pehle Yeh Aata Hai
Aaj ke liye: Post 6.1 ki trick (× agla, peeche kuch likhna), 1 se 9 ke guna (pahaada), aur place value (2021 = 20 saikde + 21). Neeche ke boxes dekh lo. Naye shabd:
📖 Shabd jo is post mein aayenge
- Dahai same: dono numbers ka left wala (dahai) digit ek jaisa. 43 aur 47: dono mein 4.
- Ikaiyon ka jod 10: dono numbers ke right wale (ikai) digit jodo to 10 aaye. 3 + 7 = 10, 2 + 8 = 10, 1 + 9 = 10, 5 + 5 = 10.
- Dahai × agla: dahai digit ko uske agle number se guna: 4 × 5 = 20.
- Ikaiyon ka guna: dono ikai digits ka guna: 3 × 7 = 21.
- Do digit mein likhna (09): ikaiyon ka guna agar ek digit ka aaye (jaise 1 × 9 = 9), to use 09 likho: 9 ikai mein, 0 dahai mein. Kyunki jawab ke aakhri do khaane (dahai aur ikai) iske hain.
- Bahan-trick: 35 × 35 bhi isi ka hissa hai: dahai same (3), ikaiyon ka jod 5 + 5 = 10, aur 5 × 5 = 25.
📏 Bade numbers padhna aur round number mein jodna
Har digit ki ek jagah (place) hoti hai. Right se gino: pehli jagah Ikai (ones, 1 wale), uske left mein Dahai (tens, 10 wale), phir Saikda (hundreds, 100 wale), phir Hazaar (thousands, 1000 wale).
10 ka bundle: 10 ikai = 1 dahai (10). 10 dahai = 1 saikda (100). 10 saikde = 1 hazaar (1000). Har jagah apne right wali jagah se 10 guna badi hai.
| Number | Kaise padhein | Kis cheez se bana |
|---|---|---|
| 98 | attaanve | 9 dahai (90) + 8 ikai |
| 165 | ek sau painsath | 1 saikda (100) + 6 dahai (60) + 5 ikai |
| 999 | nau sau ninyaanve | 9 saikde (900) + 9 dahai (90) + 9 ikai |
| 1011 | ek hazaar gyaarah | 1 hazaar (1000) + 0 saikda + 1 dahai (10) + 1 ikai |
Round number mein chhota number jodna (place box niyam): chhote number ko right se likho, yaani ikai ke neeche ikai, dahai ke neeche dahai. Phir har dabbe mein jo hai, woh jawab mein utaar do. Ek digit wala number sirf ikai ka zero badalta hai, do digit wala ikai aur dahai dono.
- 100 + 65: 65 mein do digit, to 6 dahai mein aur 5 ikai mein: 1|6|5 = 165.
- 100 + 2: 2 sirf ikai mein, dahai ka 0 waise hi rehta hai: 1|0|2 = 102 (12 nahi, 120 nahi!).
- 200 + 6: 6 sirf ikai mein: 2|0|6 = 206.
- 1000 + 11: 11 mein do digit, to 1 dahai mein aur 1 ikai mein: 1|0|1|1 = 1011.
✖️ Guna kya hai? (Multiplication)
Guna (nishaan ×) matlab ek hi number ko baar-baar jodna. “6 × 4” ko bolte hain “6 guna 4”, matlab 4 ko 6 baar jodo:
6 × 4 = 4 + 4 + 4 + 4 + 4 + 4 = 24
Isi tarah 6 × 7 matlab 7 ko 6 baar jodo. Running total (har baar ka naya jod) dekho: 7, 14, 21, 28, 35, 42. To 6 × 7 = 42.
10 dahai = 1 saikda: 10 dande (har danda 10) milkar 100 bante hain, yaani 1 saikda. Isliye 24 dahai = 20 dahai + 4 dahai = 2 saikde + 4 dahai = 240. (Aur 10 saikde milkar 1 hazaar, yaani 1000, bante hain.)
Tukdon mein guna kyun kar sakte hain? 47 = 4 dande (40) + 7 cube (7). 47 ko 6 baar lena matlab neeche jaisi 6 line. Dande alag gin lo, cube alag gin lo, kul utna hi rahega:
6 × 47: 6 baar 40 = 240, 6 baar 7 = 42, kul 240 + 42 = 282
Guna mein carry 1 se bada ho sakta hai: jod mein carry aksar 1 hota hai, par guna mein bada bhi aa sakta hai. Column mein 6 × 7 = 42 aaya, yaani 4 dahai aur 2 ikai. To ikai mein 2 likho aur 4 dahai carry karo (aage le jao). Phir dahai mein 6 × 4 = 24, usme carry ke 4 jodo: 24 + 4 = 28. Jawab 282.
Guna mein jagah badlo, jawab wahi: 16 × 4 aur 4 × 16 ek hi cheez hain. Neeche dots dekho: 4 line, har line mein 16 dots. Line se gino to 4 baar 16; khade column se gino to 16 baar 4. Dots wahi hain, to jawab bhi wahi: 64. Isliye jo aasaan lage, us tarah jodo.
Copy pe column mein (28 + 15 jaisa):
- Ikai: 6 × 7 = 42. Neeche ikai mein 2 likho. 42 ke 4 dahai carry hain: chhota 4 dahai wale digit (4) ke upar likho.
- Dahai: 6 × 4 = 24, usme upar likha carry 4 jodo: 24 + 4 = 28. Neeche 28 likho (8 dahai mein, 2 saikde mein).
- Jawab: 282.
10 se guna: 3 × 10 matlab 10 ko 3 baar jodna: 10 + 10 + 10 = 30. Kisi number ko 10 se guna karo to woh har digit ek jagah left khisak jaata hai aur ikai mein 0 aa jaata hai: 3 → 30, 30 → 300.
💯 100 se guna = peeche do 0 lagao
100 = 10 × 10 (10 ko 10 baar jodo: 10, 20, 30, … 100). Isliye 100 se guna karna matlab do baar 10 se guna. Har baar 10 se guna pe peeche ek 0 lagta hai (upar wala box), to 100 se guna pe do 0:
36 → (× 10) 360 → (× 10) 3600
Place value se: 36 × 100 matlab 36 saikde (36 sau). 36 sau = 3600 (padho: teen hazaar chhe sau).
| Number | × 100 |
|---|---|
| 7 | 700 |
| 36 | 3600 |
| 37 | 3700 |
| 124 | 12400 (padho: barah hazaar chaar sau) |
Bade number padhna: 12400 mein right se paanchvi jagah Das hazaar (10000 wale) hai. 12400 = 1 das hazaar + 2 hazaar + 4 saikde, yaani 10000 + 2000 + 400.
🟦 Square kya hai? Chhota ² ka matlab
Kisi number ko usi number se guna karna us number ka square (Hindi mein “varg”) kehlata hai. Ise number ke upar-right mein chhota ² likh kar dikhate hain. 5² padho “5 ka square” ya “5 square”, matlab 5 × 5 = 25. Dhyaan: 5² ka matlab 5 × 2 nahi hai (woh 10 hota)!
Naam “square” kyun? Square ka ek matlab hai chaukor (jiski chaaron bhujaayein barabar hon). 5 line banao, har line mein 5 dots: dots ka ek chaukor ban jaata hai, aur kul dots 5 × 5 = 25. To 5² = 25 dots ka chaukor.
| Square | Matlab | Jawab |
|---|---|---|
| 3² | 3 × 3 | 9 |
| 5² | 5 × 5 | 25 |
| 10² | 10 × 10 | 100 |
| 35² | 35 × 35 | 1225 (Post 6.1) |
➕1 Number × agla number (1 se 9 tak)
Aaj ki trick mein ek chhota guna baar-baar aayega: ek number × uske theek baad wala (agla) number. 3 ka agla number 4 hai (3 + 1 = 4). 8 ka agla 9. Neeche poori table hai. Har guna ko baar-baar jod se bhi nikaal sakte ho (GUNA box): 3 × 4 matlab 4 ko 3 baar jodo.
| Number × agla | Baar-baar jod se | Jawab |
|---|---|---|
| 1 × 2 | 2 | 2 |
| 2 × 3 | 3 + 3 | 6 |
| 3 × 4 | 4 + 4 + 4 | 12 |
| 4 × 5 | 5 + 5 + 5 + 5 | 20 |
| 5 × 6 | 6 + 6 + 6 + 6 + 6 | 30 |
| 6 × 7 | 7, 14, 21, 28, 35, 42 (running total) | 42 |
| 7 × 8 | 8, 16, 24, 32, 40, 48, 56 | 56 |
| 8 × 9 | 9, 18, 27, 36, 45, 54, 63, 72 | 72 |
| 9 × 10 | 9 ke peeche 0 (10 se guna) | 90 |
Pattern dekho: 2, 6, 12, 20, 30, 42, 56, 72, 90. jodne wala number har baar 2 badhta hai: 4, 6, 8, 10, 12, 14, 16, 18. (6 + 6 = 12, 12 + 8 = 20, 20 + 10 = 30, …) Yeh pattern bhool jaao to bhi chalega; table ya baar-baar jod kaafi hai.
🔁 Chhota sa warm-up
- 4 × 5 = ?
- 3 × 7 = ?
- 2000 + 21 = ?
Answers dekho
- 20
- 21
- 2021
Teeno aa gaye? 43 × 47 = 2021 tayyar!
— 📌 charumam.com
🎬 Kahani: Raksha Bandhan Ki Mithaai
Raksha Bandhan pe Meera ki dukaan pe 43 dabbe laddoo aaye, har dabbe mein 47 laddoo. Papa ne poocha: “Kul kitne laddoo?”
Meera ne dekha: 43 aur 47. “Dono ki dahai 4! Aur 3 + 7 = 10!” Usne CharuMam ki class yaad ki: “4 × 5 = 20, 3 × 7 = 21. 2021 laddoo!”
Papa ne calculator se check kiya: 2021. “Wah beta!” 🍬
CharuMam: “Yeh 35² wali trick ki bahan hai. Aaj dekhenge kab chalti hai, aur kab nahi.” 👯
— 📌 charumam.com
🪄 Trick Step by Step: Dahai × Agla, Phir Ikaiyon Ka Guna
💡 Is post ki ek badi baat: Do numbers jinki dahai same ho aur ikaiyon ka jod 10 ho: jawab = (dahai × agla) aur uske peeche (ikaiyon ka guna, do digit mein). 43 × 47: 4 × 5 = 20, 3 × 7 = 21 → 2021.
Step 1: Shartein check karo
Sawaal: 43 × 47. Dahai: 4 aur 4, same ✅. Ikai: 3 + 7 = 10 ✅. Dono shartein poori, trick lagegi.
Step 2: Dahai × agla number
4 ka agla 5. 4 × 5 = 20. (Yeh jawab ke saikde hain: 20 saikde = 2000.)
Step 3: Ikaiyon ka guna, do digit mein
3 × 7 = 21 (7 + 7 + 7 = 21). Do digit hain, to waise hi.
Step 4: Saath likho
20 ke peeche 21: 2021. Yaani 2000 + 21. To 43 × 47 = 2021.
Kai examples
| Sawaal | Dahai × agla | Ikaiyon ka guna | Jawab |
|---|---|---|---|
| 43 × 47 | 4 × 5 = 20 | 3 × 7 = 21 | 2021 |
| 62 × 68 | 6 × 7 = 42 | 2 × 8 = 16 | 4216 |
| 24 × 26 | 2 × 3 = 6 | 4 × 6 = 24 | 624 |
| 81 × 89 | 8 × 9 = 72 | 1 × 9 = 9 → 09 | 7209 |
| 71 × 79 | 7 × 8 = 56 | 1 × 9 = 9 → 09 | 5609 |
| 34 × 36 | 3 × 4 = 12 | 4 × 6 = 24 | 1224 |
| 35 × 35 | 3 × 4 = 12 | 5 × 5 = 25 | 1225 (Post 6.1!) |
| 98 × 92 | 9 × 10 = 90 | 8 × 2 = 16 | 9016 |
09 kyun, sirf 9 kyun nahi?
81 × 89 matlab 72 saikde + 9, yaani 7200 + 9. 7200 ki dahai aur ikai mein 0 0 hain. 9 sirf ikai mein jaata hai, dahai mein 0 hi rehta hai: 7200 + 9 = 7209. Agar “72” ke peeche sirf “9” likhte to 729 ban jaata, jo 72 saikde nahi, sirf 7 saikde hai. Isliye ikaiyon ka guna hamesha do khaane leta hai: 9 → 09.
Kab NAHI chalegi (dhokha)
| Sawaal | Kyun nahi |
|---|---|
| 43 × 57 | Dahai alag (4 aur 5) |
| 42 × 47 | Ikaiyon ka jod 2 + 7 = 9, 10 nahi |
| 46 × 46 | Ikaiyon ka jod 6 + 6 = 12, 10 nahi |
Aise sawaal seedhe tareeke (tukdon mein guna) se karo. Jaise 42 × 47: 42 ko 40 baar = 1680 (420 ko 4 baar: 420, 840, 1260, 1680), 42 ko 7 baar = 294, kul 1680 + 294 = 1974. Trick lagate to galat “2014” aata!
🆘 Atak gaye? Aise socho
- Dono shartein yaad: dahai same, ikai ka jod 10. Ek bhi na ho to trick mat lagao.
- Ikai guna ek digit ka? Aage 0 lagao: 9 → 09, 4 → 04 (jaise 21 × 29: 2 × 3 = 6, 1 × 9 = 09 → 609).
- Ikaiyon ka jod nahi, guna: 3 × 7 = 21 (3 + 7 nahi).
- Check: seedha tareeka (40 baar + 7 baar), ya andaaza: 43 × 47 to 40 × 50 = 2000 ke paas.
— 📌 charumam.com
🔍 Yeh Kaam Kyun Karta Hai?
Tiles ka aayat socho: 43 × 47 matlab 43 line, har line mein 47 tile. 47 = 40 + 7 aur 43 = 40 + 3. To aayat ke 4 hisse (chitra):
- Neela bada chaukor: 40 × 40 = 1600 (4 × 4 = 16, peeche 00)
- Naarangi patti: 40 ko 7 baar
- Hari patti: 40 ko 3 baar
- Gulaabi kona: 3 × 7 = 21
Ab dekho: naarangi aur hari patti milkar 40 ko (7 + 3) baar = 40 ko 10 baar = 400. Yahin ikaiyon ka jod 10 kaam aata hai! Neela + dono patti: 1600 + 400 = 2000. Aur 2000 = 40 × 50 (yaani 4 × 5 = 20, peeche 00): “dahai × agla”.
Gulaabi kona alag: 3 × 7 = 21. Kul: 2000 + 21 = 2021.
Agar ikaiyon ka jod 10 na hota (jaise 2 + 7 = 9), to dono patti milkar 40 ko 9 baar banti, 10 baar nahi, aur “× agla” wala hissa galat ho jaata. Isliye jod 10 shart zaroori hai.
— 📌 charumam.com
✏️ Solved Examples (Har Ek Normal Tareeke Se Check)
Example 1: 62 × 68 = ?
Dahai 6 same, 2 + 8 = 10 ✅. 6 × 7 = 42, 2 × 8 = 16 → 4216.
✔️ Normal tareeke se check: Seedha: 62 ko 60 baar = 620 ko 6 baar: 620, 1240, 1860, 2480, 3100, 3720. 62 ko 8 baar: 62, 124, 186, 248, 310, 372, 434, 496. Kul 3720 + 496 = 4216 ✅
Example 2: 81 × 89 = ?
8 × 9 = 72, 1 × 9 = 9 → 09. Jawab 7209.
✔️ Normal tareeke se check: Seedha: 81 ko 80 baar = 810 ko 8 baar: 810, 1620, 2430, 3240, 4050, 4860, 5670, 6480. 81 ko 9 baar = 81 ko 10 baar se ek kam: 810 − 81 = 729. Kul 6480 + 729 = 7209 ✅
Example 3: 24 × 26 = ?
2 × 3 = 6, 4 × 6 = 24 → 624.
✔️ Normal tareeke se check: Seedha: 24 ko 20 baar = 240 + 240 = 480. 24 ko 6 baar: 24, 48, 72, 96, 120, 144. Kul 480 + 144 = 624 ✅
Example 4: 98 × 92 = ?
9 × 10 = 90, 8 × 2 = 16 → 9016.
✔️ Normal tareeke se check: Ch 3 wali round soch: 92 ko 98 baar = 92 ko 100 baar se 2 baar kam. 9200 − 184 = 9016 ✅ (92 ko 2 baar = 184)
— 📌 charumam.com
🕉️ Vedic Maths Connection
Vedic Maths ki kitabon mein yeh “Ekadhikena Purvena” ki hi ek aur roop mein milti hai, jahan ikaiyon ka jod 10 ho (kai kitabein ise “Antyayordashake’pi” se bhi jodti hain, rough matlab “aakhri digits ka jod 10 ho tab bhi”). Hamare liye asli baat chitra hai: dono pattiyaan milkar 40 ko 10 baar.
— 📌 charumam.com
🧭 Kab Use Karein, Kab Nahi
| Situation | Trick use karein? | Kyun |
|---|---|---|
| Dahai same aur ikaiyon ka jod 10 (43 × 47) | ✅ Haan | Do second: dahai × agla, ikai × ikai. |
| 35 × 35, 75 × 75 | ✅ Haan | Yeh bhi isi ka hissa (5 + 5 = 10). |
| Dahai alag (43 × 57) | ❌ Nahi | Pehli shart toot gayi. |
| Ikaiyon ka jod 10 nahi (42 × 47) | ❌ Nahi | Doosri shart toot gayi; seedha tareeka lo. |
| 3-digit, aage ka hissa same (112 × 118) | ✅ Chalegi | 11 × 12 = 132, 2 × 8 = 16 → 13216 (Challenge). |
| Teacher ne steps maange | ❌ Answer sheet pe nahi | Sheet pe seedha tareeka, rough mein trick. |
— 📌 charumam.com
❌→✅ Common Mistakes
Galti 1: 09 ki jagah 9
Sawaal: 81 × 89
❌ Galat: 72 aur 9 → 729.
✅ Sahi: 72 aur 09 → 7209. Andaaza: 81 × 89 to 80 × 80 = 6400 se bada, 729 bahut chhota.
Galti 2: Agle ki jagah wahi dahai
Sawaal: 43 × 47
❌ Galat: 4 × 4 = 16, 3 × 7 = 21 → 1621.
✅ Sahi: 4 × 5 = 20 → 2021.
Galti 3: Shart check nahi ki
Sawaal: 42 × 47
❌ Galat: 4 × 5 = 20, 2 × 7 = 14 → 2014.
✅ Sahi: 2 + 7 = 9, 10 nahi! Trick nahi lagegi. Seedha: 1680 + 294 = 1974.
Galti 4: Ikaiyon ka jod likh diya
Sawaal: 43 × 47
❌ Galat: 20, phir 3 + 7 = 10 → 2010.
✅ Sahi: ikaiyon ka guna: 3 × 7 = 21 → 2021.
🧠 Rule of thumb: Pehle shartein (dahai same, ikai jod 10). Phir dahai × agla | ikai × ikai (do digit mein).
— 📌 charumam.com
🏃 Speed Drill: 15 Sawaal, Timer Ke Saath
Timer lagao. 15 sawaal, sab mein shartein poori hain. Target: 4 minute.
- 43 × 47 = ?
- 62 × 68 = ?
- 24 × 26 = ?
- 71 × 79 = ?
- 33 × 37 = ?
- 51 × 59 = ?
- 84 × 86 = ?
- 96 × 94 = ?
- 12 × 18 = ?
- 45 × 45 = ?
- 57 × 53 = ?
- 38 × 32 = ?
- 69 × 61 = ?
- 75 × 75 = ?
- 91 × 99 = ?
Mera time: ______ · Sahi: ____ / 15
Answers dekho (pehle khud karo!)
- 2021
- 4216
- 624
- 5609
- 1221
- 3009
- 7224
- 9024
- 216
- 2025
- 3021
- 1216
- 4209
- 5625
- 9009
Kaise kiya (kuch): 51 × 59: 5 × 6 = 30, 1 × 9 = 09 → 3009. 12 × 18: 1 × 2 = 2, 2 × 8 = 16 → 216. 91 × 99: 9 × 10 = 90, 1 × 9 = 09 → 9009.
— 📌 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.
- 13 × 17 = ?
- 22 × 28 = ?
- 34 × 36 = ?
- 46 × 44 = ?
- 58 × 52 = ?
- 63 × 67 = ?
- 77 × 73 = ?
- 82 × 88 = ?
- 95 × 95 = ?
- 19 × 11 = ?
| Rating | Kitne sahi, kitne time mein |
|---|---|
| 🌱 Beginner | 60 second mein 5 se 7 sahi. Badhiya shuruaat! |
| 🚀 Pro | 60 second mein 8 ya 9 sahi |
| 🏆 Champion | 10 mein 10 sahi, 60 second ke andar |
Answers dekho
- 221
- 616
- 1224
- 2024
- 3016
- 4221
- 5621
- 7216
- 9025
- 209
Dhyaan: 19 × 11: dahai dono 1, ikai 9 + 1 = 10 ✅. 1 × 2 = 2, 9 × 1 = 09 → 209.
5 se kam sahi? Koi baat nahi! Trick wala section ek baar aur padho aur kal phir try karo. Har din thoda better, bas yahi chahiye. 💪
— 📌 charumam.com
📝 10 MCQs (Har Option Ka Kaaran)
MCQ matlab ek sawaal ke chaar jawab (options) diye hote hain, unme se ek sahi chunna hai.
Q1. 43 × 47 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 2021
- (a) galat ❌: 2010 mein ikaiyon ka jod (10) likh diya; guna (21) chahiye.
- (b) galat ❌: 2121 mein 4 × 5 ko 21 maan liya; 4 × 5 = 20.
- (c) sahi ✅: 4 × 5 = 20, 3 × 7 = 21 → 2021.
- (d) galat ❌: 1621 mein 4 × 4 kiya; agla 5 lena tha.
Q2. Yeh trick kis sawaal pe lagegi?
Jawab aur kaaran dekho
Sahi jawab: (b) 62 × 68
- (a) galat ❌: 2 + 2 = 4, 10 nahi.
- (b) sahi ✅: Dahai 6 same, 2 + 8 = 10 ✅.
- (c) galat ❌: Dahai alag (6 aur 7).
- (d) galat ❌: 2 + 7 = 9, 10 nahi.
Q3. 81 × 89 = ?
Jawab aur kaaran dekho
Sahi jawab: (a) 7209
- (a) sahi ✅: 8 × 9 = 72, 1 × 9 = 09 → 7209.
- (b) galat ❌: 729 mein 09 ki jagah 9 likha; 72 saikde ka hisaab bigad gaya.
- (c) galat ❌: 7290 mein 9 galat khaane (dahai) mein chala gaya.
- (d) galat ❌: 6409 mein 8 × 8 kiya; agla 9 lena tha.
Q4. Trick ki do shartein kya hain?
Jawab aur kaaran dekho
Sahi jawab: (d) Dahai same, aur ikaiyon ka jod 10
- (a) galat ❌: Ulta hai; dahai same honi chahiye.
- (b) galat ❌: Sirf 35 × 35 jaise; 43 × 47 mein 5 nahi phir bhi chalti hai.
- (c) galat ❌: Juft hona shart nahi (43, 47 taaq hain).
- (d) sahi ✅: Yahi do shartein: 43 aur 47 jaise.
Q5. 24 × 26 = ?
Jawab aur kaaran dekho
Sahi jawab: (c) 624
- (a) galat ❌: 6024 mein 6 aur 24 ke beech extra 0 lag gaya; 24 pehle se do digit hai.
- (b) galat ❌: 644 mein 4 × 6 ko 44 maan liya.
- (c) sahi ✅: 2 × 3 = 6, 4 × 6 = 24 → 624.
- (d) galat ❌: 424 mein 2 × 2 kiya.
Q6. Chitra mein dono pattiyaan milkar kya banti hain?
Jawab aur kaaran dekho
Sahi jawab: (b) 40 ko 10 baar = 400
- (a) galat ❌: Yeh bada neela chaukor hai.
- (b) sahi ✅: 7 + 3 = 10, to 40 ko 10 baar = 400. Isi se “dahai × agla” banta hai.
- (c) galat ❌: Yeh sirf ek (naarangi) patti hai.
- (d) galat ❌: Yeh kone ka hissa hai, patti nahi.
Q7. 42 × 47 ka sahi jawab kya hai? (Dhyaan: shart!)
Jawab aur kaaran dekho
Sahi jawab: (a) 1974
- (a) sahi ✅: 2 + 7 = 9, trick nahi lagti. Seedha: 1680 + 294 = 1974.
- (b) galat ❌: 2014 trick galti se lagane pe aata hai; shart toot gayi thi.
- (c) galat ❌: 1934 mein 294 ki jagah 254 jod diya.
- (d) galat ❌: 2074 mein 42 ko 40 baar 1780 maan liya; sahi 1680.
Q8. 71 × 79 = ?
Jawab aur kaaran dekho
Sahi jawab: (d) 5609
- (a) galat ❌: 569 mein 09 ki jagah 9.
- (b) galat ❌: 5690 mein 9 dahai mein chala gaya.
- (c) galat ❌: 4909 mein 7 × 7 kiya.
- (d) sahi ✅: 7 × 8 = 56, 1 × 9 = 09 → 5609.
Q9. 35 × 35 is trick ka hissa kyun hai?
Jawab aur kaaran dekho
Sahi jawab: (c) Dahai same (3) aur 5 + 5 = 10
- (a) galat ❌: 3 + 5 = 8 se kuch tay nahi hota.
- (b) galat ❌: 35 taaq hai, aur juft hona shart bhi nahi.
- (c) sahi ✅: Dono shartein poori: dahai 3 aur 3, ikai 5 + 5 = 10. Isliye 3 × 4 | 25.
- (d) galat ❌: Bada hona shart nahi.
Q10. 98 × 92 = ?
Jawab aur kaaran dekho
Sahi jawab: (b) 9016
- (a) galat ❌: 9006 mein 8 × 2 ko 6 maan liya; 8 × 2 = 16.
- (b) sahi ✅: 9 × 10 = 90, 8 × 2 = 16 → 9016.
- (c) galat ❌: 8116 mein 9 × 9 = 81 kiya; agla 10 lena tha.
- (d) galat ❌: 916 mein 90 ka 0 chhoot gaya; 90 ke peeche 16 likhna tha.
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🧠 Challenge: HOTS Aur Olympiad Style
HOTS matlab Higher Order Thinking Skills, yaani aise sawaal jinme sirf trick nahi, thoda dimaag bhi lagana padta hai. Olympiad ek maths competition (pratiyogita) hota hai.
Q1. 112 × 118 = ? (3-digit bahan)
Solution dekho
Aage ka hissa same: 11 aur 11. Ikai: 2 + 8 = 10 ✅. 11 × 12 = 132 (Post 6.2). 2 × 8 = 16. Saath likho: 13216.
Check: 112 ko 100 baar = 11200, 112 ko 18 baar = 1120 + 896 = 2016 (112 ko 8 baar: 112, 224, 336, 448, 560, 672, 784, 896). Kul 11200 + 2016 = 13216 ✅
Q2. 6□ × 6△ = 4216, aur □ + △ = 10. □ aur △ kya hain?
Solution dekho
(△ = doosra khaali dabba, □ ki tarah.) Trick se: 6 × 7 = 42 aage, to peeche ka 16 = □ × △. Kaunse do digit jinka jod 10 aur guna 16? Jaldi list: 1 + 9 (guna 9), 2 + 8 (guna 16) ✅. To number 62 aur 68.
Check: 62 × 68: 6 × 7 = 42, 2 × 8 = 16 → 4216 ✅
Q3. 91 × 99 aur 95 × 95 mein kaunsa bada?
Solution dekho
91 × 99: 9 × 10 = 90, 1 × 9 = 09 → 9009. 95 × 95: 90, 25 → 9025. 95 × 95 bada, 16 se. Pattern: jab do numbers ka jod same rahe (91 + 99 = 190, 95 + 95 = 190), to jitne paas, guna utna bada: 95 × 95 = 9025, 91 × 99 = 9009.
Check: 9025 − 9009 = 16 ✅
Q4. Ek aayat (rectangle) khet 53 metre lamba, 57 metre chauda. Kshetrafal (area)?
Solution dekho
(Area = lambai × chaudai, yaani kitni 1 metre × 1 metre tile.) 53 × 57: dahai 5 same, 3 + 7 = 10 ✅. 5 × 6 = 30, 3 × 7 = 21 → 3021 varg metre.
Check: 53 ko 50 baar = 2650 (530 ko 5 baar: 530, 1060, 1590, 2120, 2650). 53 ko 7 baar = 371. Kul 2650 + 371 = 3021 ✅
— 📌 charumam.com
🎯 Exam Mein Kahan Kaam Aayega?
| Exam | Kahan kaam aayega |
|---|---|
| School exam (Class 6–8) | Guna aur area (lambai × chaudai) wale sawaal mein tez check. |
| Maths Olympiad | Missing digit (6□ × 6△) aur “kaunsa bada” jaise pattern sawaal. |
| NTSE / MAT | Mental calculation mein 2-digit × 2-digit. |
| SSC / Bank (aage) | Simplification mein aise jode bahut aate hain. |
Shabdon ka matlab: Olympiad = school ke bachchon ki maths pratiyogita (competition). NTSE = Class 10 ke bachchon ka ek national scholarship (vazifa) exam. MAT = Mental Ability Test, yaani sochne-samajhne ki pariksha (NTSE ka ek hissa). SSC / Bank exam = badon ke sarkari naukri ke exam. Simplification = lambe hisaab ko chhota karke jawab nikaalna. Mental calculation = bina copy-pencil ke, mann mein hisaab karna. Class 6–8 = school ki chhathi se aathvi kaksha.
— 📌 charumam.com
👩🏫 CharuMam Ka Tip
Guna dekhte hi do sawaal poocho: “Dahai same? Ikai ka jod 10?” Dono haan, to trick. Ek bhi na, to seedha tareeka. Shart check hi asli samajhdaari hai! 👯
— 📌 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)
Dahai same (4), ikaiyon ka jod 3 + 7 = 10 ✅. Dahai × agla: 4 × 5 = 20. Ikaiyon ka guna: 3 × 7 = 21. Saath likho: 2021 ✅
| 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 din ki practice chahiye. Phir yeh purane tareeke 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 galti hone pe samjhayega:
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❓ FAQs (Bachchon Ke Asli Sawaal)
1. Kya ikai ka jod 10 ki jagah dahai ka jod 10 ho to bhi chalti hai?
Uski alag trick hai (jaise 37 × 77). Yeh is post ki trick nahi; ise baad mein dekhenge.
2. 09 likhna zaroori kyun?
Kyunki ikaiyon ka guna jawab ke aakhri do khaane (dahai, ikai) leta hai. 9 ikai mein, 0 dahai mein: 7200 + 9 = 7209.
3. Kya 3-digit pe bhi?
Haan, agar aage ka hissa same ho aur ikai ka jod 10 (112 × 118 = 13216, Challenge).
4. Agle post mein kya hai?
Post 6.4: Chapter 6 ke tricky sawaal: ulte sawaal, pattern aur dhokhe.
— 📌 charumam.com
🟢 Recap: Aaj Kya Seekha
- Shartein: dahai same, ikaiyon ka jod 10.
- Jawab: dahai × agla | ikai × ikai.
- 43 × 47 = 2021, 62 × 68 = 4216.
- Ikai guna ek digit ka ho to 09: 81 × 89 = 7209.
- Chitra: dono pattiyaan milkar 40 ko 10 baar, isliye “× agla”.
- Shart na ho (42 × 47) to trick mat lagao.
— charumam.com 🎯
👉 Aage Kya?
Ab Chapter 6 ka aakhri post: Square Ending in 5 Ke Tricky Sawaal: ulte sawaal, pattern aur dhokhe!
Koi doubt? CharuMam AI Tutor se poochho, ya comment mein likho! 💬
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- 🌐 Website: charumam.com
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