Compensation: 47 + 29 = 47 + 30 − 1
CharuMam ka Udhaar-Wapsi Formula: mushkil number ko gol bana lo, aasan jod karo, aur jo udhaar liya tha woh wapas kar do 🤝
🔥 Kahani: Sharma Uncle ki dukaan aur ₹29 ki cold drink
School ke baad Golu Sharma Uncle ki dukaan pe gaya. Usne ₹47 ka chips ka bada packet liya aur ₹29 ki cold drink. Golu ungliyon pe ginne laga: “7 aur 9 = 16, 6 likho, 1 haasil…” 🤯
Uncle ne bina ruke bola: “₹77 mein se ek rupaya kam, ₹76.” Golu chaunka: “Uncle, 77 kahan se aaya?”
Uncle hanse: “₹29 ko main ₹30 maan leta hoon. 47 aur 30 = 77, yeh toh dimaag mein turant ho jaata hai. Par 30 asal mein 29 se ek zyada hai, toh woh ek rupaya wapas ghata deta hoon.”
Shaam ko Rohan aur Priya ko yeh baat batayi toh Priya boli: “Yeh toh udhaar lene jaisa hai! 29 ne 1 udhaar liya aur 30 ban gaya. Kaam hone ke baad udhaar wapas.” Aaj isi chaal ko samjhenge, jise maths mein Compensation (hisaab barabar karna) kehte hain.
✅ Prerequisite Checker
Yeh post samajhne ke liye itna aana chahiye:
- Gol number (10, 20, 30… ya 100, 200…) jodna, jaise 47 + 30 = 77 (MN-01: Place Value)
- Kisi number ka agla gol number aur kitna door hai: 29 se 30 tak 1, 98 se 100 tak 2 (MN-08: Number Bonds)
- Number ko tod ke jodna: 46 + 38 = 70 + 14 (MN-09: Mental Addition)
- Number line pe aage-peeche chalna (MN-04: Number Line)
Bas! Agar 47 + 30 aur 77 − 1 tum bina ungli ke kar lete ho, toh tum taiyaar ho. 🙂
📘 Concept: Udhaar lo, gol jodo, wapas karo
47 + 30 socho. Ikai ka 7 waisa ka waisa rehta hai, sirf dahai badalti hai: 4 dahai + 3 dahai = 7 dahai. Jawaab 77, ek second mein.
Kyun aasan? Kyunki 30 ki ikai 0 hai. 0 jodne se ikai nahi badalti, toh koi haasil nahi, koi tension nahi. Sirf ek ghar (dahai) mein kaam hua.
29 ke sabse paas ka gol number 30 hai. Aur 29 = 30 − 1. Yaani 29, 30 se sirf 1 kam hai.
Kyun yahi padosi? Number line pe 29 se 30 sirf ek kadam hai, jabki 20 nau kadam door hai. Jitna paas ka gol number, utna chhota hisaab baad mein barabar karna padega.
29 ki jagah 30 jodo: 47 + 30 = 77.
Kyun yeh theek hai? Hum jaante hain ki 30 jodne mein humne 29 se 1 zyada joda hai. Jab tak yeh baat yaad hai, kuch galat nahi hua. Bas 1 ka udhaar chadh gaya.
1 zyada joda tha, toh 1 ghatao: 77 − 1 = 76. Toh 47 + 29 = 47 + 30 − 1 = 76.
Kyun ghatana hai? 30 = 29 + 1. Toh 47 + 30 asal mein 47 + 29 + 1 hai. Woh extra “+ 1” hata do, toh bacha sirf 47 + 29. Yahi compensation hai: jo badla, uska hisaab barabar.
65 + 52 mein 52 = 50 + 2. Pehle 65 + 50 = 115, phir jo 2 kam joda tha woh jodo: 115 + 2 = 117.
Kyun ab jodna pada? Kyunki 50 jodne se humne 52 se 2 kam joda. Rule simple hai: gol number bada tha toh baad mein ghatao, gol number chhota tha toh baad mein jodo.
356 + 198 → 198 = 200 − 2. Toh 356 + 200 = 556, phir 556 − 2 = 554.
Kyun yahan sabse zyada faayda? 356 + 198 ko ghar-ghar jodo toh teen ghar mein haasil ki chinta. 200 jodna sirf saikde ka kaam hai. Jitna bada number aur jitna gol ke paas, utni badi bachat.
47 + 29 mein 47 se 1 nikaal ke 29 ko de do: 46 + 30 = 76. Same jawaab!
Kyun? Socho do jebein hain, ek mein ₹47, doosri mein ₹29. Ek jeb se ₹1 nikaal ke doosri mein daal do. Kul paise wahi ₹76 rahenge. Jod mein ek ko badhao aur utna hi doosre ko ghatao, toh kul nahi badalta.
83 − 29 → 83 − 30 = 53. Ab socho: 29 ghatana tha, humne 30 ghata diya, yaani 1 zyada ghataya. Toh 1 wapas jodo: 53 + 1 = 54.
Kyun yahan +1? Ghatana matlab cheez le jaana. 29 ki jagah 30 le gaye, toh ek cheez zyada chali gayi. Use wapas laana padega. Jod mein zyada diya toh wapas lo (−), ghatav mein zyada liya toh wapas do (+). Andaaza bhi bata deta hai: 83 − 30 = 53, aur 29 thoda kam hai, toh jawaab 53 se thoda zyada hoga.
🎯 CharuMam ka Udhaar-Wapsi Formula
“Gol padosi dhundho, udhaar lo, gol number se kaam karo, phir udhaar wapas karo. Zyada joda toh ghatao, zyada ghataya toh jodo.”
Dukaan ka sach: 47 + 29 = 47 + 30 − 1 = 77 − 1 = ₹76. Sharma Uncle bilkul sahi the! ✅
🖼️ Picture se samjho: 29 ne 1 udhaar liya
Upar: 29 ko das-das ki line mein dekho. Teesri line mein ek dabba khaali hai. Woh 1 udhaar le lo, toh poore 30 ban jaate hain. Neeche: number line pe 47 se +30 ki badi chhalaang 77 tak, phir udhaar wapas karne ke liye 1 kadam peeche, 76 pe.
✏️ Examples: aasan se mushkil tak
Example 1: 56 + 19
19 ka gol padosi 20 (19 = 20 − 1). 56 + 20 = 76. 1 zyada joda, toh 76 − 1 = 75.
Kyun? 20 jodna sirf dahai ka kaam hai (5 dahai + 2 dahai = 7 dahai). Phir sirf 1 ka hisaab. Ghar-ghar jodte toh 6 + 9 = 15 aur haasil ki baat aati.
Example 2: 64 + 38 (udhaar 2 ka)
38 = 40 − 2. 64 + 40 = 104. 2 zyada joda, toh 104 − 2 = 102.
Balancing se bhi: 64 se 2 nikaal ke 38 ko do → 62 + 40 = 102 ✅
Kyun 2 ghataya, 1 nahi? Kyunki 38 se 40 tak 2 kadam hain. Jitna udhaar liya, utna hi wapas karna hai. Udhaar hamesha “gol number − asli number” jitna hota hai.
Example 3: 245 + 198
198 = 200 − 2. 245 + 200 = 445. Udhaar wapas: 445 − 2 = 443.
Andaaza: 250 + 200 = 450, aur 443 uske paas hai ✅
Kyun 200 chuna, 190 nahi? 190 bhi gol hai, par 198 se 8 door hai. 200 sirf 2 door hai. Gol padosi woh chuno jo sabse paas ho, taaki wapsi ka hisaab chhota rahe.
Example 4: Jeb mein ₹500, shirt ₹198. Kitne bache?
500 − 198 → pehle 500 − 200 = 300. Par 198 ki jagah 200 de diye, yaani ₹2 zyada. Woh wapas lo: 300 + 2 = ₹302.
Kyun +2? Socho dukaandaar ko ₹200 diye aur shirt ₹198 ki thi. Dukaandaar ₹2 wapas karega! Ghatav mein zyada ghataya toh wapas jodna padta hai. 500 − 198 ko column se karte toh 0 mein se udhaar lene ka lamba jhanjhat hota.
🧮 Khud karke dekho: CharuMam Udhaar-Wapsi Machine
💡 0 se 9999 tak ke do poore number daalo aur jod ya ghatav chuno. Machine doosre number ka gol padosi dhundhegi, gol number se kaam karegi, aur dikhayegi ki udhaar kaise wapas hua. 47 + 29 ke baad 245 + 198, 83 − 29 aur 500 − 198 try karo!
📕 Textbook yeh nahi batata
1. ₹99 aur ₹199 wale daam isi chaal ke liye bane lagte hain. Dukaanon mein daam aksar ₹49, ₹99, ₹199 hote hain. Dimaag “₹199” ko “lagbhag ₹200” sunta hai, par sahi total ke liye compensation chahiye: ₹199 + ₹299 = ₹200 + ₹300 − ₹2 = ₹498. Har ₹99 wala daam gol number se sirf ₹1 kam hai.
2. Yeh chaal sirf jod tak nahi rukti. Guna mein bhi yahi soch chalti hai: 99 × 47 ko “100 × 47, phir 47 kam” ki tarah kar sakte hain. Yeh aage MN-21 mein aayega. Aaj ki samajh wahan ki neev hai.
3. Do raaste = muft check. 47 + 29 ko MN-09 ke Tod-Jod se karo (40 + 20 = 60, 7 + 9 = 16, 60 + 16 = 76) aur Udhaar-Wapsi se karo (77 − 1 = 76). Dono same aaye toh pakka sahi. Alag aaye toh kahin galti hai. Exam mein yeh 10 second ka check bahut kaam aata hai.
🧠 Bachche yahan galti karte hain
❌ Galti 1: Udhaar wapas karne ki jagah aur de dena: 47 + 29 = 47 + 30 + 1 = 78.
Yeh galat kyun hai? 30 jodne mein pehle hi 1 zyada juda hai. Ab +1 karoge toh 2 zyada ho gaye! Sahi: 77 − 1 = 76. Check: 47 + 29 ka jawaab 47 + 30 (= 77) se kam hona chahiye, kyunki 29 chhota hai 30 se.
❌ Galti 2: Ghatav mein bhi jod wala rule laga dena: 83 − 29 = 83 − 30 − 1 = 52.
Kyun galat? 83 − 30 mein humne 1 zyada ghataya, toh 1 wapas jodna hai: 53 + 1 = 54. Andaaza socho: 29 kam ghatana tha 30 se, toh jawaab 53 se zyada hona chahiye, kam nahi.
❌ Galti 3: Udhaar ka amount galat lena ya bhool jaana: 64 + 38 = 64 + 40 − 1 = 103, ya seedha 104 likh dena.
Kyun galat? 38 se 40 tak 2 kadam hain, toh udhaar 2 ka hai: 104 − 2 = 102. Shuru mein hi likh lo “38 = 40 − 2”, taaki yaad rahe kitna aur kis taraf wapas karna hai.
🌍 Real Life mein kahan?
🛒 Dukaan: T-shirt ₹299 aur cap ₹149. ₹300 + ₹150 = ₹450, udhaar ₹1 + ₹1 = ₹2 wapas. Total ₹448.
💰 Change ginna: ₹200 diye, saamaan ₹97 ka. 200 − 100 = 100, ₹3 zyada ghataya toh wapas jodo: ₹103 wapas milne chahiye.
🏏 Cricket: Team 138 pe hai, aur 59 run chahiye. Target kitna? 138 + 60 − 1 = 198 − 1 = 197.
📱 Mobile recharge: Is mahine ₹239 ka plan aur ₹19 ka data booster. 239 + 20 − 1 = ₹258.
⏰ Time: 2:45 baje se 55 minute ka tuition. 55 minute = 1 ghanta − 5 minute. 2:45 + 1 ghanta = 3:45, phir 5 minute peeche = 3:40. Yahan gol number 1 ghanta (60 min) hai, 100 nahi! Time ki baat MN-44 mein.
⚖️ Kab use karein, kab nahi
| ✅ Udhaar-Wapsi use karo jab… | ⚠️ Dhyaan rakho / mat karo jab… |
|---|---|
| Number gol ke bahut paas ho: ikai 8 ya 9 (29, 38, 198), ya 1 ya 2 (51, 302) | Number gol se door ho (45, 64, 136): udhaar bada, faayda kam. Wahan MN-09 ka Tod-Jod behtar |
| Dukaan ke ₹49, ₹99, ₹199 wale daam jodne ho | Ghatav mein: zyada ghataya toh wapas jodo, ghatao nahi |
| Jawaab ko doosre tareeke se check karna ho | Time mein gol number 60 minute hai, 100 nahi |
| ❌ Kabhi nahi: udhaar wapas karna bhool jaana, ya bina likhe yaad rakhna ki kitna udhaar liya (38 = 40 − 2, toh 2). | |
📝 Self-Check Quiz
Q1. 36 + 19 ko Udhaar-Wapsi se karo. Sahi kaunsa? (a) 36 + 20 − 1 = 55 (b) 36 + 20 + 1 = 57 (c) 36 + 10 − 1 = 45 (d) 36 + 20 = 56
✅ (a): 19 = 20 − 1. 36 + 20 = 56, 1 zyada joda toh 56 − 1 = 55.
(b) galat: 1 zyada pehle hi juda tha, aur +1 kar diya (Galti 1). 2 zyada ho gaye.
(c) galat: 19 ka gol padosi 20 hai, 10 nahi. 10 toh 19 se 9 door hai.
(d) galat: 20 jod diya par udhaar wala 1 wapas nahi kiya (Galti 3).
Q2. 58 + 97 = ? (a) 161 (b) 155 (c) 158 (d) 145
✅ (b) 155: 97 = 100 − 3. 58 + 100 = 158, phir 158 − 3 = 155.
(a) galat: 3 ghatane ki jagah 3 jod diye: 158 + 3 = 161 (Galti 1).
(c) galat: 100 joda par 3 ka udhaar wapas nahi kiya.
(d) galat: 97 ka gol padosi galti se 90 le liya: 58 + 90 − 3 = 145. Asal mein 97 = 100 − 3, toh gol padosi 100 hai.
Q3. 84 − 29 = ? (a) 84 − 30 − 1 = 53 (b) 84 − 30 + 1 = 55 (c) 84 − 20 + 1 = 65 (d) 84 − 30 = 54
✅ (b) 55: 30 ghataya, yaani 1 zyada ghataya. 84 − 30 = 54, phir 54 + 1 = 55.
(a) galat: ghatav mein jod wala rule laga diya (Galti 2). Zyada ghataya toh wapas jodna tha.
(c) galat: 29 ka gol padosi 30 hai, 20 nahi. Yahan 9 kam ghataya gaya.
(d) galat: 30 ghata diya par udhaar wala 1 wapas nahi joda.
Q4. 47 + 29 = 46 + 30 (ek se 1 liya, doosre ko diya). Isi tarah 65 + 38 kis jodi ke barabar hai? (a) 63 + 40 (b) 67 + 40 (c) 65 + 40 (d) 62 + 40
✅ (a) 63 + 40: 38 ko 40 banane ke liye 2 chahiye. Woh 2 65 se lo: 63 + 40 = 103. Check: 65 + 38 = 103 ✅
(b) galat: 38 ko 2 diye aur 65 ko bhi 2 de diye. Dono badh gaye, toh kul 4 zyada: 107.
(c) galat: 38 ko 2 diye par kisi se liye nahi. Kul 2 zyada: 105.
(d) galat: 65 se 3 le liye par 38 ko sirf 2 chahiye the. Kul 1 kam: 102.
Q5. Priya ke paas ₹125 the. Usne ₹98 ki kitaab li. Kitne bache? (a) ₹23 (b) ₹27 (c) ₹25 (d) ₹37
✅ (b) ₹27: 98 = 100 − 2. 125 − 100 = 25. ₹2 zyada ghataye, toh wapas jodo: 25 + 2 = 27.
(a) galat: 2 wapas jodne ki jagah aur ghata diye: 25 − 2 = 23 (Galti 2).
(c) galat: 100 ghataya par ₹2 wapas nahi kiye.
(d) galat: 98 ko 100 ki jagah 90 maan ke ghataya: 125 − 90 + 2 = 37. 90 toh 98 se 8 door hai.
💪 Practice Zone
Har sawaal mein pehle likho “asli number = gol number ± udhaar”, phir gol se kaam karo, aur aakhir mein udhaar sahi taraf wapas karo.
- 34 + 19 = ?
- 45 + 28 = ?
- 67 + 39 = ?
- 156 + 99 = ?
- 74 − 29 = ?
- 132 − 98 = ?
- 388 + 297 = ?
- Bill: ₹249 + ₹149 + ₹99 = ? (teeno ko gol karo, phir kul udhaar wapas)
Answer Key (click karo)
1) 34 + 20 = 54, 54 − 1 → 53 · 2) 45 + 30 = 75, 75 − 2 → 73 · 3) 67 + 40 = 107, 107 − 1 → 106 · 4) 156 + 100 = 256, 256 − 1 → 255 · 5) 74 − 30 = 44, 44 + 1 → 45 · 6) 132 − 100 = 32, 32 + 2 → 34 · 7) 388 + 300 = 688, 688 − 3 → 685 · 8) ₹250 + ₹150 + ₹100 = ₹500, udhaar 1 + 1 + 1 = 3, toh 500 − 3 → ₹497
Answer Key — charumam.com exclusive
🚀 Challenge (HOTS)
Q1. Rohan kehta hai: “47 + 29 mein 30 jodke 1 ghataya. Toh 47 − 29 mein bhi 30 ghatake 1 ghatana hoga: 47 − 30 − 1 = 16.” Kya Rohan sahi hai? Number line ya paison se samjhao.
Solution
Nahi, Rohan galat hai. Sahi jawaab 47 − 29 = 18.
47 − 30 = 17. Par ghatana sirf 29 tha, humne 30 ghata diye, yaani 1 zyada le gaye. Woh 1 wapas karo: 17 + 1 = 18.
Paise se: ₹47 mein se ₹29 dene the, galti se ₹30 de diye. Saamne wala ₹1 lautayega, toh tumhare paas ₹17 + ₹1 = ₹18.
Kyun yeh important hai? Jod mein gol number “zyada dena” hai, isliye baad mein ghatate hain. Ghatav mein gol number “zyada lena” hai, isliye baad mein jodte hain. Rule yaad karne ki jagah poochho: maine zyada diya ya zyada liya?
Q2. Golu dono numbers ko gol karna chahta hai. (i) 48 + 39 ko 50 + 40 se karo. (ii) 52 + 39 ko 50 + 40 se karo. Har baar kitna aur kis taraf hisaab barabar karna padega?
Solution
(i) 48 = 50 − 2 aur 39 = 40 − 1. Dono mein zyada joda: 2 + 1 = 3. Toh 50 + 40 = 90, phir 90 − 3 = 87. Check: 48 + 39 = 87 ✅
(ii) 52 = 50 + 2 (yahan 2 kam joda) aur 39 = 40 − 1 (yahan 1 zyada joda). Kul hisaab: +2 − 1 = +1. Toh 90 + 1 = 91. Check: 52 + 39 = 91 ✅
Kyun yeh kaam ka hai? Har number ka udhaar alag likh lo, phir sab udhaar ek saath barabar karo. Kuch udhaar kat bhi jaate hain, jaise (ii) mein +2 aur −1 milke sirf +1 bacha.
❓ FAQ
29 ko 30 banane ke liye 1 joda, phir 1 ghatate kyun hain?
Kyunki woh 1 humara nahi tha, udhaar tha! Sawaal 47 + 29 ka tha. 30 jodne mein humne 29 + 1 jod diya. Jawaab sahi karne ke liye woh extra 1 hatana hi padega. Udhaar lo toh wapas karo, maths mein bhi aur zindagi mein bhi. 🙂
Ghatav mein rule ulta kyun ho jaata hai?
Kyunki ghatav mein hum cheez le jaate hain. 83 − 29 mein 30 le gaye, toh 1 cheez zyada chali gayi. Use wapas laana matlab +1. Jod mein 30 diya toh 1 zyada de diya, use wapas lena matlab −1. Har baar bas poochho: maine zyada diya ya zyada liya?
Kya har number ko gol karke jodna chahiye?
Nahi. Yeh chaal tab chamakti hai jab number gol ke bilkul paas ho (29, 98, 199, 51). 45 ya 64 jaise number gol se 5 ya 4 door hain, wahan udhaar bada ho jaata hai aur faayda kam. Wahan MN-09 ka Tod-Jod ya seedha jod behtar hai. Achha mathematician sahi tareeka chunta hai, ek hi tareeka har jagah nahi ghusata.
46 + 30 (balancing) aur 47 + 30 − 1 (udhaar-wapsi) mein kaunsa sahi hai?
Dono sahi, dono ka jawaab 76. Udhaar-wapsi mein hisaab baad mein barabar karte hain. Balancing mein pehle hi 47 se 1 lekar 29 ko de dete hain, toh baad mein kuch yaad nahi rakhna. Jo tumhe aasan lage wahi chuno. Bas dhyaan rahe: balancing jod mein chalta hai, ghatav mein iska niyam alag hai.
🔁 Recap
- Gol number (30, 200) ke saath jod-ghatav sabse aasan hai
- Mushkil number ka gol padosi dhundho: 29 = 30 − 1, 198 = 200 − 2, 52 = 50 + 2
- Jod: 47 + 29 = 47 + 30 − 1 = 76 (zyada joda, toh ghatao)
- Ghatav: 83 − 29 = 83 − 30 + 1 = 54 (zyada ghataya, toh jodo)
- Balancing: 47 + 29 = 46 + 30, ek se lo, doosre ko do
- Chaal tab use karo jab number gol ke bahut paas ho, aur udhaar ka amount pehle likh lo
💖 CharuMam Motivation
29 ne 1 udhaar liya, 30 ban gaya, kaam aasan ho gaya, aur kaam hote hi udhaar lauta diya. Na koi chori, na koi galti. Bas seedha, imaandaar hisaab. 🙂
Zindagi mein bhi kabhi-kabhi kisi dost se madad leni padti hai, kisi teacher se samjhna padta hai, ya ek kadam aage jaake ek peeche aana padta hai. Isme koi sharm nahi, beta. Bas Sharma Uncle ki tarah yaad rakhna ki kitna liya tha, aur waqt aane pe imaandaari se lauta dena. Jo apna hisaab saaf rakhta hai, uska jawaab hamesha sahi aata hai! 🌱
— CharuMam
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