NCERT Solutions Class 8 Maths Part 2 Chapter 1: Fractions in Disguise (Hinglish)

Ganita Prakash Grade 8 (pehla edition December 2025, 2026-27 mein chalne wala) ke Part 2 Chapter 1, Fractions in Disguise, ke har sawaal ke jawab: har Figure it Out, text ke sawaal, Math Talk aur Try This, aur Peaceful Knights paheli. Page number book ke hisaab se hain (pages 1–32). Jo percentages poore nahi bante, unhe do decimal tak round kiya gaya hai. Short notes: Part 2 Chapter 1 ke notes.

Fractions as percentages (pages 1–5)

24% ko fraction mein likho. 24% = 24/100, jo 12/50, 6/25 ya 48/200 ke barabar hai.

Kaun sa biscuit zyada meetha hai? Variety 2: 13/45 ≈ 28.89%, jo 9/34 ≈ 26.47% se zyada hai.

Denominator 100 hi kyon? Koi bhi sankhya chal sakti thi, par 100 hamare das par tike system mein fit hai, isliye percentage seedha decimal ban jaata hai (31% = 0.31). Ye ek gol sankhya bhi hai jise samajhna aasaan hai, jabki zyaadatar kaam ke liye 10 bahut mota aur 1000 bahut baarik hai.

Figure it Out (pages 3–4)

1. (i) 3/5 = 60% (ii) 7/14 = 1/2 = 50% (iii) 9/20 = 45% (iv) 72/150 = 48% (v) 1/3 = 33⅓% ≈ 33.33% (vi) 5/11 = 45 5/11% ≈ 45.45%.

2. 15/25 × 100 = 60%, option (iv).

3. 15/80 × 100 = 18.75% students paidal school aate hain.

4. Start se har dhaavak ki doori line par naapne par: A ≈ 38%, B ≈ 55%, C ≈ 72% aur D ≈ 93%. 20% aur 84% wale options kaam nahi aate.

5. (i) > , kyunki 50%, 5% ka das guna hai. (ii) =, kyunki 5/10 aadha hai. (iii) <, kyunki 3/11 aadhe se kam hai aur 61% aadhe se zyada. (iv) <, kyunki 1/3 = 33⅓%.

Percentage of some quantity (pages 6–9)

Cheeni zyada kisne khaayi? Madhu: 120 g ka 25% = 30 g. Madhav: 95 g ka 35% = 33.25 g. Madhav ne zyada khaayi.

Mann se hisaab wali table. 100, 200, 50, 80, 10, 35 aur 287 ke liye: 25% se 25, 50, 12.5, 20, 2.5, 8.75, 71.75; 10% se 10, 20, 5, 8, 1, 3.5, 28.7; 20% se 20, 40, 10, 16, 2, 7, 57.4; 5% se 5, 10, 2.5, 4, 0.5, 1.75, 14.35. 40% yaani 20% ka double: 40, 80, 20, 32, 4, 14, 114.8. 15% = 10% + 5%: 15, 30, 7.5, 12, 1.5, 5.25, 43.05. Har 20% wali entry 10% wali ki doguni hai, aur 20% + 5% = 25%.

75%, 90%, 70%, 55% mann mein. 75% = 50% + 25% (ya teen chauthaai); 90% = 100% − 10%; 70% = 50% + 20% (ya 7 × 10%); 55% = 50% + 5%.

FDP table. 50% = 50/100 = 1/2 = 0.5; 100% = 1 = 1.0; 25% = 1/4 = 0.25; 75% = 3/4 = 0.75; 10% = 1/10 = 0.1; 1% = 1/100 = 0.01; 5% = 1/20 = 0.05; 43% = 43/100 = 0.43. Kisi maatra ka 10% nikaalne ke liye 0.1 se guna karo.

Example 3 (Zubin). 75 ka 80% = 0.8 × 75 = kam se kam 60 marks.

Example 4 (millet kanji). Millet mishran ka 2/9 hai, lagbhag 22.22%; paani lagbhag 77.78%. 500 ml mein millet 2/9 × 500 ≈ 111.1 ml.

Hissa, poora aur 100 se zyada percentages (pages 10–12)

Cyclist. 40% = 92 km, to 20% = 46 km aur baaki 60% = 138 km; poora safar 230 km.

Kishanlal ki bikri. Day 5: 7800/5000 × 100 = 156%. Day 6: 9550/5000 × 100 = 191%. Day 7 par 150% yaani 1.5 × 5000 = ₹7500, aur Day 8 par 210% yaani 2.1 × 5000 = ₹10,500.

Table. 90% = 9/10 = 0.9; 110% = 11/10 = 1.1; 200% = 2/1 = 2; 250% = 5/2 = 2.5; 15% = 3/20 = 0.15; 173% = 173/100 = 1.73; 358% = 179/50 = 3.58; 28.9% = 289/1000 = 0.289; 305% = 61/20 = 3.05. 0 se 4 wali line par har point apni decimal value par aata hai: 0.15 aur 0.289 shuru ke paas, 0.9 1 se thoda pehle, 1.1 uske thoda baad, 1.73 2 se pehle, 2 aur 2.5, 3.05 3 ke thoda aage, aur 3.58 3 aur 4 ke beech se thoda aage.

Example 7 (gehun). 650/260 × 100 = 250%, yaani is saal ki fasal pichhle saal ki 2.5 guna hai.

Figure it Out (pages 12–14)

1. (ii) Bar ke 10 barabar hisse hain, to ek hissa 10% hai; 90 ke das mein se chhah hisse yaani 90 ka 60% = 54. (iii) Bar ke 4 hisse hain, to ek hissa 25% hai; 140 ke chaar mein se teen hisse yaani 140 ka 75% = 105.

2. (i) 160 ka 25% = 40 (ii) 250 ka 16% = 40 (iii) 360 ka 62% = 223.2 (iv) 40 ka 140% = 56 (v) 1 ghante ka 1% = 0.6 minute = 36 second (vi) 10 kg ka 7% = 0.7 kg = 700 g. Har bar model mein poore ko 100% banao aur hissa bhar do; 140% ke liye ek poori bar aur doosri ka 40% banao.

3. Laal rang = 60 ml ka 3/4 = 45 ml.

4. (i) < (ii) < (iii) < (iv) < (12 banaam 20) (v) > (90 banaam 49) (vi) > (24 banaam 15.36).

5. (i) 140, 210, 280. (ii) 21.5, 2.15, 12.9. (iii) 27, 54, 300. (iv) Jaise: q ka 25% = 40, to q ka 50% = 80 aur q ka 100% = 160; aur w ka 20% = 9, to w ka 10% = 4.5 aur w ka 60% = 27.

6. (i) 3/300 = 1/100, to khaali jagah mein 1. (ii) 4 ka 40% = 1.6. (iii) Agar kisi sankhya ka 80% = 40, to 10% = 5 aur sankhya 50.

7. Haan. Din ka 10% = 2.4 ghante = 144 minute; hafte ka 1% = 1.68 ghante = 100.8 minute. Ek aur sawaal: kya saal ka 1% din ke 25% se lamba hai? (Haan: 87.6 ghante banaam 6 ghante.)

8. Din 1: 1/2 = 50%; Din 2: 2/3 ≈ 66.67%; Din 3: 3/4 = 75%; Din 4: 4/5 = 80%; Din 9: 9/10 = 90%; Din 99: 99/100 = 99%. Khaaye gaye chaare ka percentage badhta jaata hai, har baar chhote kadam se, 100% ke kareeb aata jaata hai par kabhi pahunchta nahi.

9. 20% mein 18 din lagte hain, to 100% mein 5 × 18 = 90 din. Ye maanna zaroori hai kyunki agar mazdooron ki ginti, mausam ya berries ka pakna badle, to kaam samay ke anupaat mein nahi rahega.

10. Warm-up 90 ka 10% = 9 minute, khel 80% = 72 minute, cool-down 9 minute.

11. 2025 mein duniya ki aabaadi lagbhag 8.2 billion hai, to 90% lagbhag 7.4 billion log hain.

12. (i) Anupaat wahi rehta hai, 40% rava, 40% cheeni aur 20% ghee; sirf maatra doguni hoti hai. (ii) Rava 800 g, cheeni 800 g aur ghee 400 g.

Using percentages (pages 14–19)

Eesha ke marks. English 42/50 = 84%; Science 70/80 = 87.5%. Science ke marks behtar rahe. Vishu ki baat sahi hai ki alag maximum wale marks seedhe nahi milaa sakte, par percentage mein badalne se faisla ho jaata hai.

Know your contents. DEF (150 g): cheeni 66%, milk solids 20%, badam 8%, food chemicals 6%. Zacni (400 g): cheeni 68%, milk solids 16%, badam 10%, food chemicals 6%. Zacni mein badam ka hissa zyada hai; food chemicals dono mein barabar hain. Har line ka jod 100% hai.

Wholesaler aur manufacturer. Wholesaler: CP ₹253, SP ₹300, profit 47/253 × 100 ≈ 18.58%. Manufacturer: CP ₹230, SP ₹253, profit 23/230 × 100 = 10%.

Shambhavi. Notebook ka SP = ₹36 ka 120% = ₹43.20. Crayons: cost ka 125% = ₹50, to cost = 50/1.25 = ₹40.

Raghu, har kg par. CP ₹35, SP ₹30, har kg ₹5 loss: 5/35 × 100 ≈ 14.29%, 10 kg wala hi jawab.

Example 6 (Shyamala). Pehle andaaza: 18% ek-paanchve se thoda kam hai, to ₹2100 se thoda zyada milega. Theek hisaab: 2650 ka 82% = ₹2173.

Snehal ki strawberries. ₹80 cost price ka 88% hai, to CP = 80/0.88 ≈ ₹90.91 kilo.

Cooker. SP = 1800 ka 65% = ₹1170. Profit = 1170 − 900 = ₹270, jo cost ka 30% hai.

Bill. Sahi hai: 3 × 150 = 450; 450 ka 9% = 40.50, CGST aur SGST dono; 450 + 81 = 531.

Figure it Out (pages 19–20)

Is exercise ka doosra hissa, page 20 par, phir se 3 se gina gaya hai; yahan use 6 se 12 tak aage badhaaya hai.

1. Profit = 110 − 75 = ₹35; cost par 35/75 × 100 ≈ 46.67%.

2. 475 ka 150% = ₹712.50.

3. Agar 25% margin revenue par hai, jaisa company ke liye aam hai, to profit = ₹2.5 crore ka 25% = ₹0.625 crore aur kharch = ₹1.875 crore. (Agar margin cost par hota, to kharch × 1.25 = 2.5 crore se ₹2 crore aata.)

4. 300 ka 75% = ₹225.

5. 60 par 40 ki vriddhi, yaani 66.67%, option (iv).

6 (chhapa 3). ₹4,40,000 daam ka 85% hai, to daam 4,40,000/0.85 ≈ ₹5,17,647 tha.

7 (chhapa 4). 500/1600 × 100 = 31.25%. Baaki candidates mein 1100 vote bante, har ek ke 500 se kam, to kam se kam 3 aur candidates chahiye: kul kam se kam 4 candidates.

8 (chhapa 5). Mehngai = 4/38 × 100 ≈ 10.53%.

9 (chhapa 6). Sankhya ka 120% = 90, to sankhya = 90/1.2 = 75.

10 (chhapa 7). Pehli bhains: CP = 80,000/1.05 ≈ ₹76,190.48. Doosri: CP = 80,000/0.90 ≈ ₹88,888.89. Kul CP ≈ ₹1,65,079.37 aur SP ₹1,60,000: kul milaakar lagbhag ₹5,079.37 ka loss, kareeb 3.08%.

11 (chhapa 8). (iv) p × 1.05.

12 (chhapa 9). Sirf (iii): 85% girne se aaj ki maang das saal pehle wali ki 15% reh gayi.

Growth and compounding (pages 20–24)

Example 7. Bina compounding: har saal ₹600 bahar milte hain, kul ₹7800. Compounding ke saath: ₹6600, ₹7260, phir ₹7986. Example 8: 7800/6000 = 130%, yaani 30% fayda; 7986/6000 = 133.1%, yaani 33.1% fayda.

Figure it Out (pages 22–24)

1. Bina compounding: 20,000 + 2 × 2000 = ₹24,000. Compounding ke saath: 20,000 × 1.1² = ₹24,200, yaani ₹200 zyada.

2. Bina compounding: 20,000 + 4 × 1000 = ₹24,000. Compounding ke saath: 20,000 × 1.05⁴ ≈ ₹24,310.13, yaani ₹310.13 zyada.

3. Bina compounding dono ₹24,000 dete hain, kyunki 2 saal ka 10% aur 4 saal ka 5% dono 20% jodte hain. Compounding ke saath 4 saal wala jama zyada kamaata hai, kyunki interest zyada baar waapas judta hai.

Kul interest ke formula. Bina compounding: prt. Compounding ke saath: p(1 + r)ᵗ − p.

4. (vii) p + (p × 0.06 × 4).

5. Bina compounding: 50,000 × 0.07 × 3 = ₹10,500. Compounding ke saath: 50,000 × 1.07³ ≈ ₹61,252.15, to interest ₹11,252.15, lagbhag ₹752.15 zyada.

6. Giridhar: 12,500 × 0.12 × 3 = ₹4500. Raghava: 12,500 × 1.1³ − 12,500 = ₹4137.50. Giridhar ₹362.50 zyada chukaate hain.

7. Bina compounding ₹1000 har saal ₹100 kamaata hai aur 10 saal mein doguna hota hai. Compounding ke saath 1.1⁷ ≈ 1.95 aur 1.1⁸ ≈ 2.14, to 7 saal se thoda zyada samay lagta hai (8ve saal ke aakhir tak). Haan: compounding har saal ek hi factor se guna karti hai (exponential growth), jabki bina compounding har saal wahi rakam judti hai (linear growth).

8. 1.5 crore × 1.03³ ≈ 1.639 crore, yaani lagbhag 1.64 crore log.

9. 5,06,000 × 1.025² ≈ 5,31,616 bacteria.

Girawat aur tricky percentages (pages 24–27)

Example 10 (TV). 21,000 ka 95% = ₹19,950. Example 11 (gaon). 1250 × 0.9³ ≈ 911; book ki tarah har kadam par round karne se 912 aata hai, to lagbhag 910.

Would you rather? Option A mein ₹100 par ₹200 ka fayda, yaani 200%. Option B mein ₹1000 par ₹500 ka fayda, yaani 50%. A ka percentage bada hai par B zyada paisa deta hai, isliye ek hi chunna ho to B behtar hai.

Stock clearance sale. (i) ₹180: 20% = ₹36, to ₹50 off lo. (ii) ₹225: 20% = ₹45, to phir ₹50 off lo. (iii) ₹300: 20% = ₹60, to 20% discount lo. ₹250 par dono barabar hain.

Example 12 (cake). Cakely: ₹200 → ₹140 → ₹112. Cakify: ₹100. Cakify chuno.

Example 13 (Surbhi). (i) Loss hua: aakhri daam cost ka 1.5 × 0.5 = 0.75 hai, yaani 25% loss. (ii) 0.75x = 12,000 se x = 16,000, to ₹4000 ka loss, jo 25% hai. (iii) Ek-tihaai yaani 33.33% discount 1.5x ko waapas x par le aata hai.

Ariba aur Arun. Arun ke paas Ariba ke kanchon ka 100/120 = 5/6 hai, to Arun keh sakte hain, ‘Mere paas Ariba ke kanchon ka lagbhag 83.33% hai’, ya ‘Mere paas Ariba se 16.67% kam hain’.

Figure it Out (pages 28–30)

1. 50 lakh ka 250% = 125 lakh = 1.25 crore.

2. Germany: 83 million ÷ 8.2 billion ≈ 1%. India: 1.46 billion ÷ 8.2 billion ≈ 18%. Bangladesh: 175 million ≈ 2%. USA: 347 million ≈ 4.2%, jo chhape hue kisi option se mel nahi khaata.

3. (v) aur (vi): 8250 × 1.18 = 8250 + 8250 × 0.18 = ₹9735.

4. (ii) aur (vi): 1.05 × 0.98 × 0.97 ≈ 0.998, to aabaadi p se thodi kam reh jaati hai.

5. Loss: 1.35 × 0.70 = 0.945, yaani cost ke 94.5% par bikri, 5.5% loss.

6. Square 8 × 8 = 64 chhote squares ka hai. A = 16, B = 24, C = 8, aur D aur E ek 4 × 4 square ke do aadhe hain, 8-8. E = 8/64 = 12.5%.

7. 40 ka 5% = 2 = 5 ka 40%; 12 ka 25% = 3 = 25 ka 12%; 60 ka 15% = 9 = 15 ka 60%. Aam taur par y ka x% = xy/100 = x ka y%.

8. (i) 40% ka 60% = 0.6 × 0.4 = 24% students Grade 8 ki ladkiyan hain. (ii) 160 ka 24% = 38.4, to lagbhag 38 ladkiyan; diye gaye percentages se 160 ka ye hissa poori sankhya nahi banta.

9. Ek pencil ki cost c maano. Teen pencils 5c mein bikti hain, to ek 5c/3 mein. c par 2c/3 ka profit, yaani 66.67% profit.

10. 1.03 × 1.04 = 1.0712: kul 7.12% vriddhi.

11. Nayi chaudaai purani ki 1/1.1 = 10/11 hai, to wo 1/11 = 9 1/11% ≈ 9.09% kam ho jaati hai.

12. Aaloo 65 g ka 70% = 45.5 g; vegetable oil 24% = 15.6 g; namak 3% = 1.95 g; masale 3% = 1.95 g.

13. (i) A: 2 items ₹100 mein, ₹50 ek. B: 3 items ₹200 mein, ₹66.67 ek. C: 4 items ₹300 mein, ₹75 ek. Saste se mehenge: A, B, C. (ii) A: 2 mein se 1 item ka paisa nahi lagta, 50% off; B: 3 mein se 1, 33.33%; C: 4 mein se 1, 25%. (iii) Shop A: wahan 2 items ka paisa dekar 4 items ₹200 mein milte hain, jabki B aur C dono mein 4 items ₹300 ke padte hain.

14. Right-handed sirf 1 hai. Us 1 ko 2% banane ke liye kamre mein 50 log hone chahiye, to 50 left-handed logon ko bahar jaana hoga.

15. Sahi: (i), (ii) aur (v). (iii) sahi nahi: graph percentages dikhata hai, logon ki ginti nahi. (iv) sahi nahi: thirties mein sirf 14% auratein aur 25% mard computer chala paate hain, to kul milaakar chauthaai se kam. (vi) sahi nahi: aankde 26% aur 37% hain, aadhe nahi.

Peaceful Knights (page 32)

Ghoda hamesha ek ya do line upar ya neeche jaata hai, aur hamesha doosre rang ke khaane par girta hai. Isliye ek hi line mein rakhe aath ghode kabhi ek doosre par hamla nahi kar sakte; na hi ek hi rang ke khaanon par rakhe aath ghode, jaise upar ki do lines ke halke khaane.

Short notes aur zyada practice topic pages par hai: pratishat kya hai?, pratishat vriddhi aur kami aur simple aur compound interest.