Class 8 Maths · Chapter 7
Short answer: Class 8 Maths Ganita Prakash Chapter 7 'Proportional Reasoning-1' ratio, proportion, unitary method aur direct/inverse proportion sikhata hai — real-life examples (map scale, speed-time, work-time) ke saath step-by-step solutions.
Chapter 7 'Proportional Reasoning-1', NCERT ki naye Ganita Prakash textbook (Class 8, Part 1) ka last chapter hai, aur ye us foundation ko complete karta hai jo poore Class 8 aur aage Class 9-10 ke ratio-percentage-based real-life problems ke liye zaroori hai. Is chapter me ratio, proportion, unitary method, aur direct/inverse proportion jaise concepts ko real-world examples — jaise map scale, speed-distance, recipe scaling, work-time problems — ke through samjhaya gaya hai.
Ganita Prakash class 8 maths chapter 1 solutions se lekar is chapter tak, poori Part 1 book (chapters 1-7) me numeracy, algebra, aur geometry ka mix hai, aur Proportional Reasoning-1 unn sab me common quantitative-thinking skill build karta hai jo real life me kaam aati hai — jaise budget banate waqt, recipe scale karte waqt, ya map padhte waqt.
Chapter 7 Summary — 5 Minute Revision
Chapter 7 'Proportional Reasoning-1' Class 8 Maths ki Ganita Prakash Part 1 textbook ka concluding chapter hai jo ratio, proportion, unitary method, aur direct/inverse proportion ke core concepts ko real-life scenarios ke through build karta hai. Ye chapter students ko sikhata hai ki kaise do quantities ke beech relationship identify kiya jaye — kya woh saath badhti/ghatati hain (direct) ya opposite direction me move karti hain (inverse) — aur is understanding ko map scales, speed-distance-time, recipe scaling, aur work-time jaise practical problems me apply kiya jaye.
Poore Ganita Prakash Part 1 (chapters 1-7: A Square and A Cube, We Distribute Yet Things Multiply, Fractions in Disguise, Tales by Dots and Lines, Number Play, Exploring Some Geometric Themes/Quadrilaterals/Area-type geometry chapters, aur Proportional Reasoning-1) ka structure old single-book format se kaafi different hai — chapters ka naming aur sequence dono naye hain. Is naye do-part 'Ganita Prakash' format (2026-27 session) me exact rationalisation details — kaunse purane chapters drop/merge hue — official ncert.nic.in rationalisation PDF se is session me cross-verify nahi ho paye, isliye woh specific claim yahan nahi banayi gayi hai.
Exam preparation ke liye students ko ratio simplification, unitary method application, aur direct vs inverse proportion ki pehchaan par focus karna chahiye — ye teen skills is chapter ke saath-saath aage Class 9-10 ke commercial maths (simple/compound interest, speed-distance) ke liye bhi foundation banate hain.
In-Text Questions — Solutions
Do quantities x aur y is tarah related hain ki x = 4 par y = 20, aur x = 6 par y = 30. Kya ye direct proportion hai? Check karo.
y/x ratio check karo: 20/4 = 5, aur 30/6 = 5
Dono cases me ratio same (5) hai, isliye y directly proportional hai x ke — y = 5x.
Answer: Haan, direct proportion hai, constant k = 5
Agar 8 mazdoor ek kaam 6 din me karte hain, to 4 mazdoor same kaam kitne din me karenge?
Mazdoor kam ho rahe hain to din badhenge — inverse proportion.
8 × 6 = 4 × d
d = 48 ÷ 4 = 12 din
Answer: 12 din
Exercise Questions — Solutions (Q1–Q6)
Ek car 180 km ki doori 3 ghante me tay karti hai. Same speed se woh 450 km ki doori kitne ghante me tay karegi?
Speed = 180 ÷ 3 = 60 km/h
Yeh ek direct proportion ka case hai — distance aur time same ratio me badhte hain (speed constant).
Required time = 450 ÷ 60 = 7.5 ghante
Answer: 7.5 ghante (7 ghante 30 minute)
12 workers ek deewar 15 din me bana sakte hain. Same kaam agar 9 workers karein, to kitne din lagenge (assume equal efficiency)?
Workers aur days inverse proportion me hain — kam workers, zyada din.
Total work = 12 × 15 = 180 worker-days
Days for 9 workers = 180 ÷ 9 = 20 din
Answer: 20 din
₹2,400 ko A, B aur C me 2 : 3 : 5 ke ratio me baato.
Total ratio parts = 2 + 3 + 5 = 10
1 part ki value = ₹2,400 ÷ 10 = ₹240
A = 2 × 240 = ₹480
B = 3 × 240 = ₹720
C = 5 × 240 = ₹1,200
Check: 480 + 720 + 1200 = ₹2,400 ✓
Ek recipe me 250 g atta se 5 rotiyan banti hain. 900 g atta se kitni rotiyan banengi?
Unitary method use karenge — pehle 1 g atta se kitni roti, phir 900 g ke liye.
5 roti ↔ 250 g, to 1 roti ↔ 50 g atta
900 g atta se rotiyan = 900 ÷ 50 = 18 rotiyan
Answer: 18 rotiyan
Ek shop me kisi item ka price ₹80 se badh kar ₹100 ho gaya. Percentage increase nikalo.
Increase = 100 − 80 = ₹20
Percentage increase = (Increase ÷ Original) × 100
= (20 ÷ 80) × 100 = 25%
Answer: 25% increase
Common galti: students kabhi kabhi 20 ko 100 se divide kar dete hain — hamesha original value se divide karo.
Naksha (map) me 1 cm = 50 km scale hai. Agar do sheher naksha par 3.5 cm door hain, to actual doori kya hai?
Scale ek direct proportion hai — map distance aur real distance same ratio me.
1 cm ↔ 50 km
3.5 cm ↔ 3.5 × 50 = 175 km
Answer: 175 km actual doori
Important Equations — Ek Nazar Me
| Concept | Formula / Rule |
|---|---|
| Ratio | a : b = a/b (b ≠ 0), simplest form me common factor cancel karo |
| Proportion (four terms) | a : b :: c : d ⟹ a × d = b × c (cross-multiplication / product of extremes = product of means) |
| Unitary Method | Pehle 1 unit ki value nikalo, phir required units se multiply karo |
| Direct Proportion | x/y = constant k, ya x₁/y₁ = x₂/y₂ (dono badhte/ghatte saath saath) |
| Inverse Proportion | x × y = constant k, ya x₁y₁ = x₂y₂ (ek badhe to doosra ghate) |
| Percentage | Percentage = (Part ÷ Whole) × 100 |
| Percentage Change | % change = (New value − Original value) ÷ Original value × 100 |
| Speed-Distance-Time (direct proportion base) | Speed = Distance ÷ Time (constant speed pe Distance ∝ Time) |
↔ Table ko side me swipe karein
Common Mistakes — Yahan Marks Kat te Hain
- Ratio simplify karte waqt dono terms ko same number se divide na karke sirf ek term change kar dena — hamesha dono sides ko common factor se divide karo.
- Direct aur inverse proportion me confuse ho jaana — pehle socho: agar ek quantity badhne se doosri bhi badhti hai (same direction) to direct, agar ghatati hai to inverse.
- Percentage change nikalte waqt original value ki jagah new value se divide kar dena — formula hamesha Original value ko denominator me rakhta hai.
- Unitary method me units convert karna bhool jaana — jaise km ko m, ya ghante ko minute me convert kiye bina calculation karna, jisse final answer galat unit me aata hai.
- Proportion ke four terms likhte waqt order galat rakhna (a:b :: c:d ki jagah a:b :: d:c) — cross-multiplication se pehle order double-check karo.
- Word problem me kaunsi quantities proportional hain ye identify kiye bina seedha formula laga dena — pehle relationship samjho, phir formula apply karo.
Board-Style Important Questions
- Note: Ye chapter naye rationalised Ganita Prakash syllabus (2026-27 session) ka hissa hai, isliye is exact naam/structure ke official board-level previous year questions abhi available nahi hain — koi exam year ya paper code yahan claim nahi kiya ja raha.
- Purane NCERT syllabus me similar 'Comparing Quantities' / 'Direct and Inverse Proportions' chapters se practice-style questions school-level tests me common the — jaise ratio-based distribution, unitary method word problems, aur percentage change calculations.
- School unit tests aur term exams me is tarah ke ratio/proportion identification aur word problem (map scale ya work-time type) questions puche jaa sakte hain — exact marks-weightage school/board ke syllabus document par depend karta hai, isliye specific marks yahan claim nahi kiye ja rahe.
- Students ko practice ke liye NCERT textbook ke in-text exercises aur end-of-chapter 'Figure it Out' sections thoroughly solve karne chahiye, kyunki school assessments inhi se directly adapt hoti hain.
Aksar Poochhe Jaane Wale Sawaal
Class 8 Maths Proportional Reasoning 1 vs 2 me kya difference hai?
Ganita Prakash Part 1 ka Chapter 7 'Proportional Reasoning-1' basic ratio, unitary method, direct aur inverse proportion, aur percentage-linked real-life applications cover karta hai — foundation level. Part 2 me aage jo proportional reasoning ka extension hoga (agar textbook me hai), woh usually harder multi-step word problems, compound proportion, aur applications jaise simple interest/speed-time-distance ke saath deeper integration karta hai. Is session ke liye exact Part 2 chapter naam aur content ncert.nic.in se cross-verify nahi ho paya, isliye specific claim nahi banayi ja rahi.
NCERT Class 8 Maths ka naya book name 2026-27 session ke liye kya hai?
2026-27 session se NCERT ne Class 8 Maths ko purani single-book format se hata kar do-part 'Ganita Prakash' (Part 1 aur Part 2) me rationalise kar diya hai — total 14 chapters, Part 1 me chapters 1 se 7 aur Part 2 me 8 se 14.
Kya Ganita Prakash Class 8 Chapter 1 'A Square and A Cube' hai?
Haan, Ganita Prakash Class 8 Part 1 ka Chapter 1 'A Square and A Cube' hai, jisme squares, cubes, square roots aur cube roots ke concepts basic level se cover kiye gaye hain — geometric aur numeric dono angle se.
Class 8 Maths me Baudhayana ka Pythagoras theorem chapter kaunsa hai?
Baudhayana theorem (jo Pythagoras theorem se pehle Indian mathematician Baudhayana dwara likha gaya tha) 'Exploring Some Geometric Themes' chapter ke antargat cover hota hai, jaha right-angled triangle ke sides ka relationship geometric proof ke saath dikhaya jata hai.
Chapter 7 'Proportional Reasoning-1' me kaunse topics important hain exam ke liye?
Ratio simplification, unitary method, direct aur inverse proportion identify karna, percentage-to-ratio conversion, aur real-life word problems (speed-distance-time, work-time, scale/map problems) — ye sab is chapter ke high-weightage areas hain jinki practice zaroor karo.
'We Distribute Yet Things Multiply' chapter ka Proportional Reasoning se koi connection hai?
'We Distribute Yet Things Multiply' primarily algebraic identities aur distributive property (jaise a(b+c) = ab+ac) par focus karta hai, jo algebra ka topic hai — proportional reasoning se directly connect nahi hai, lekin dono hi Ganita Prakash Part 1 ke chapters hain jo real-life quantitative reasoning build karte hain.
Class 8 Maths — Saare Chapters
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