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

Ye chapter kis baare mein hai?

Sale ke board par 50% off likha hota hai, report card par 83% aata hai, aur bank ke notice par FD par 6% p.a. likha hota hai. In sabmein % ka nishaan hai, jise ‘per cent’ padhte hain. Chapter dikhata hai ki percentage asal mein bhes badla hua fraction hai: aisa fraction jiska denominator 100 par tika diya gaya ho. Isi ek idea se shopping, marks, recipe, daam, profit-loss, tax aur bachat ke sawaal hal hote hain.

Percentages bhi fractions hain

‘Per cent’ Latin ke per centum se aaya hai, matlab ‘har sau par’. Isliye 20% = 20/100 = 1/5, aur kisi maatra s ka 50% yaani 50/100 × s, s ka aadha. Fraction ko percentage banane ke do raaste hain: 100 denominator wala barabar fraction dhoondho (3/4 = 75/100 = 75%), ya fraction ko 100 se guna karo (3/5 × 100 = 60, to 3/5 = 60%). 100 hi kyon? Hamara number system das par tika hai, isliye percentage seedha decimal ban jaata hai (31% = 0.31), aur alag denominator wale do fractions se do percentages ki tulna kahin aasaan hai. Ye idea puraana hai: Kautilya ke Arthashastra mein bhi interest ‘per cent’ mein bataaya gaya hai. Padho percentage kya hai?

Kisi maatra ka percentage

Madhu ke biscuits mein 25% cheeni thi aur Madhav ke biscuits mein 35%. Sirf percentage dekhkar nahi keh sakte ki cheeni zyada kisne khaayi; maatra bhi chahiye. Madhu ke 120 g mein 25/100 × 120 = 30 g cheeni thi, aur Madhav ke 95 g mein 35/100 × 95 = 33.25 g. Aam taur par z ka y% = y/100 × z. Kai percentages mann mein nikal jaate hain: 10% yaani 10 se bhaag, 5% uska aadha, 20% uska double, 25% chauthaai; 15% = 10% + 5%, aur 75% = 50% + 25%. Ek hi value ka fraction, decimal aur percentage milkar FDP trio banate hain, isliye 75 ka 80% chahe 4/5 × 75 karo ya 0.8 × 75, dono 60 dete hain.

Hisse se poora, aur 100 se zyada percentages

Ek cyclist Delhi se Agra ke raaste ka 40% hissa, yaani 92 km, tay kar chuke hain. Tab 20% = 46 km, aur baaki 60% = 138 km; ya poora safar 92 × 100/40 = 230 km. Anupaat bhi percentage ban sakta hai: millet aur paani 2 : 7 mein milaayein to millet kanji ka 2/9 hai, lagbhag 22.22%. Percentage 100 se aage bhi jaata hai. Kishanlal ka roz ka sales target ₹5000 hai, to ₹6000 ki bikri target ka 120% hai, yaani 20% zyada, aur ₹9550 target ka 191% hai.

Tulna aur badlaav

Eesha ke English mein 50 mein se 42 aur Science mein 80 mein se 70 marks aaye. 100 mein badlo to ye 84% aur 87.5% hain, yaani Science mein kaam behtar raha, chaahe wahan zyada marks kate. Labels bhi aise hi padhe jaate hain: do badam drink mix ke grams ko percentage mein badlo to pata chalta hai kismein badam zyada hai. Percentages badlaav bhi naapte hain. Tamatar ₹30 se ₹42 kilo ho jaayein to vriddhi 12/30 × 100 = 40% hai; theatre ke darshak 160 se 100 reh jaayein to kami 37.5% hai. Badlaav ko hamesha shuruaati maatra se bhaag dete hain. Padho pratishat vriddhi aur kami.

Profit, loss, discount aur GST

Cost price wo hai jo bechne wale ne chukaaya, marked price wo jo bataaya gaya, aur selling price wo jo grahak aakhir mein dete hain. Ek sweater manufacturer se wholesaler aur phir Kishanlal ki dukaan tak pahunchta hai, aur ek ka selling price agle ka cost price ban jaata hai. Kishanlal use ₹300 mein khareed kar ₹430 mein bechte hain: ₹130 ka profit, jo 130/300 × 100 ≈ 43.3% hai. Loss bhi isi tarah nikalta hai. ₹1800 ke cooker par 35% discount ke baad 65% daam bachta hai, yaani ₹1170. GST jaise tax bhi percentage hain: ₹450 par 9% CGST aur 9% SGST milkar ₹81 jodte hain.

Growth aur compounding

10% p.a. dene wala bank ₹6000 par saal ka ₹600 interest deta hai. Agar interest har saal bahar de diya jaaye to jama ₹6000 hi rehta hai aur 3 saal mein kul ₹7800 milte hain. Agar har saal ka interest waapas jod diya jaaye to jama ₹6600, phir ₹7260, phir ₹7986 ho jaata hai: yahi compounding hai. Aam taur par principal p, rate r par t saal mein bina compounding ke p(1 + rt) aur compounding ke saath p(1 + r)ᵗ banta hai. Padho simple aur compound interest.

Girawat aur tricky percentages

Cheezein keemat kho bhi sakti hain. ₹21,000 ka TV agar ek saal mein 5% depreciate ho to uski keemat 0.95 × 21,000 = ₹19,950 reh jaati hai, aur 1250 logon ka gaon jo har dashak lagbhag 10% ghatta hai, teen dashak baad lagbhag 910 logon ka reh jaata hai. Laaparwaahi mein percentages dhokha de sakte hain: ₹200 ke cake par pehle 30% aur phir 20% off ke baad ₹112 dene padte hain, jo 50% off ke ₹100 se zyada hai, aur Surbhi ka 50% markup ke baad 50% discount aakhir mein 25% ka loss deta hai.

Saar mein

Percentage 100 mein se ek fraction hai. Hisaab ke liye use fraction ya decimal mein badlo, hamesha poochho ki poora ya base kya hai, hisaab se pehle andaaza lagao, aur sawaal uljha lage to ek rough bar model banao. Chapter shatranj ki ek paheli par khatm hota hai, jismein aath ghodon ko aise rakhna hai ki koi kisi par hamla na kare. Har sawaal ke jawab Part 2 Chapter 1 ke NCERT solutions mein hain.