NCERT Solutions Class 8 Maths Part 2 Chapter 3: Proportional Reasoning-2 (Hinglish)

Ganita Prakash, Grade 8 Part 2, ke Chapter 3, Proportional Reasoning-2, ke har sawaal ke jawaab: text ke sawaal, Math Talk ke prashn aur chaaron Figure it Out. Page numbers book ke hisaab se hain (pages 55–69). Chhote notes: Part 2 Chapter 3 ke notes.

Samaanupaat recap (page 55)

Kya Viswanath aur Puneet ki idli ek jaisi lagengi? Bahut sambhav hai, haan. 6 : 3 aur 4 : 2 ka cross-multiplication 6 × 2 = 12 aur 3 × 4 = 12 deta hai, isliye chaawal aur urad dal ke anupaat samaanupaati hain; agar baaki saamagri bhi anupaat mein ho to idli ek jaisi lagni chahiye.

Naksha mein anupaat (pages 56–57)

RF 1 : 60,00,000 ka matlab. Naksha par naapa gaya har 1 cm zameen par seedhi rekha mein 60,00,000 cm dikhaata hai.

60,00,000 cm ko kilometre mein badlo. 60,00,000 cm ÷ 100 = 60,000 m, aur 60,000 m ÷ 1000 = 60 km. Yaani naksha par 1 cm = 60 km.

Bengaluru se Chennai aur Mangaluru se Chennai ki doori. Har doori ruler se naapo aur centimetre ko 60 km se guna karo. Sahi 1 : 60,00,000 naksha par Bengaluru se Chennai lagbhag 4.8 cm, yaani lagbhag 290 km, aur Mangaluru se Chennai lagbhag 9.8 cm, yaani lagbhag 585 km, hai. Ye bhaugolik (seedhi rekha ki) dooriyaan hain; sadak ki dooriyaan lambi hoti hain. Book ka chhota naksha ‘not to scale’ likha hai, isliye chhape page par ruler se alag aankda aa sakta hai; atlas ka naksha aur uska apna RF lo.

Kya alag paimaane wale naksha wahi dooriyaan dete hain? Lagbhag haan. Bade RF number wale naksha mein shehar paas-paas dikhte hain, par har centimetre ki badi zameeni doori se guna karne par lagbhag wahi jawaab aata hai; chhote antar naapne ki galti aur mote bindu se aate hain.

Naksha banaane ki activity. 1 : 50 par kaagaz ka 1 cm kamre ke 50 cm ke barabar hai, isliye 8 m × 6 m ka classroom 16 cm × 12 cm ka rectangle banta hai, aur 1 m lambi desk 2 cm lambi banti hai.

Do se zyada padon wale anupaat (pages 57–58)

Puneet ki saamagri. Unke paas 2 mirch hain, Viswanath ki 4 ki aadhi, isliye ve sab kuch aadha karte hain: 4 chammach dhaniya ke beej, ek chammach toor dal aur 0.5 chammach methi ke beej.

Example 1: baingani rang ka kul aayatan. 4 + 6 + 10 = 20 litre.

Poore ko anupaat mein baantna (pages 58–60)

Hal kiye gaye udaaharan 110 ikai concrete ke liye 20, 30 aur 60 ikai, 50 mL baingani rang ke liye 10, 15 aur 25 mL, aur 1 : 3 : 5 anupaat wale triangle ke liye 20°, 60° aur 100° kon dete hain.

Figure it Out (page 60)

1. 3 + 4 + 3 + 5 = 15 hisse, aur ek hissa 150 ÷ 15 = 10 minute. Warm-up aur cool-down: 30 minute; batting: 40 minute; bowling: 30 minute; fielding: 50 minute.

2. Odiya kitaabein 3 hisse hain, isliye ek hissa 288 ÷ 3 = 96 kitaabein. Hindi: 2 × 96 = 192. English: 96.

3. 4 + 3 + 2 + 1 = 10 hisse, isliye ek hissa 10 sikke: ₹10 ke chaalees sikke (₹400), ₹5 ke tees (₹150), ₹2 ke bees (₹40) aur ₹1 ke das (₹10). Kul: ₹600.

4. Ek hissa 1 cm maankar 3 cm, 4 cm aur 5 cm ki bhujaayein banao: 3 cm aur 4 cm bhujaaon ke beech ka kon samkon aata hai. Nahi, saare triangle sarvaangsam nahi hain. 6, 8 aur 10 cm, ya 1.5, 2 aur 2.5 cm ki bhujaayein bhi 3 : 4 : 5 anupaat mein hain; in sabke kon aur aakaar ek jaise hain par size alag, isliye ye samaroop (similar) hain, sarvaangsam nahi.

5. Nahi. Triangle mein kinhi do bhujaaon ka jod teesri se zyada hona chahiye. Yahan do chhoti bhujaayein milkar 1 + 3 = 4 hisse hain, jo 5 se kam hai, isliye ve milkar triangle band nahi kar sakti.

Pie chart (pages 60–63)

Kya 12 : 10 : 8 : 6 : 4 ko chhota kar sakte hain? Haan. Padon ka HCF 2 hai, isliye ye 6 : 5 : 4 : 3 : 2 ban jaata hai, aur kon 108°, 90°, 72°, 54° aur 36° aate hain.

Figure it Out, 1. Sardi: 360 − 90 − 120 = 150 log. 360 logon mein har vyakti 1° hai, isliye tukde garmi 90°, baarish 120° aur sardi 150°.

2. Har 1% = 3.6°: entertainment 50% → 180°, sports 25% → 90°, news 15% → 54°, information 10% → 36°.

3. Har student se ek pasand lo, phir kon = (us vishay ke students ÷ class ka size) × 360°. Jaise, 36 ki class mein Language 6, Arts Education 3, Vocational Education 3, Social Science 5, Physical Education 7, Maths 7 aur Science 5 hon, to har student 10° hai, aur tukde 60°, 30°, 30°, 50°, 70°, 70° aur 50° ke hain.

Vyutkram samaanupaat (pages 63–65)

Example 2: kya ise 30 : 60 :: 3 : x likh sakte hain? Samay badhega ya ghatega? Nahi. Wo kathan tez car ko zyada samay (x = 6 ghante) dega. Chaal badhne par safar ka samay ghatta hai.

Baaki saadhanon ki jaanch. Motorcycle se car: chaal × 2, samay ÷ 2 (3 → 1.5). Cycle se motorcycle: chaal × 2, samay ÷ 2 (6 → 3). Paidal se car: chaal × 12, samay ÷ 12 (18 → 1.5). Har baar chaal aur samay ek hi gunak se ulti disha mein badalte hain, aur chaal × samay = 90 km.

1.5 ÷ 18 kitna hai? 0.0833…, jo 5 ÷ 60 ke barabar hai.

Figure it Out (page 65), 1. (i) Har gunanphal 800, isliye haan. (ii) Gunanphal 800, 800, 312.5 aur 128, isliye nahi; yahan x ÷ y hamesha 2 hai, jo seedha samaanupaat hai. (iii) Har gunanphal 450, isliye haan.

2. k = 16 × 9 = 144. x = 12 ke liye y = 144 ÷ 12 = 12; y = 48 ke liye x = 144 ÷ 48 = 3; x = 36 ke liye y = 144 ÷ 36 = 4.

Example 6: kaam aur laga samay seedhe ya vyutkram samaanupaat mein? Seedhe: dugna kaam, dugna samay. Isliye 5/3 : 1 :: 1 : x, aur x = 3/5 ghanta, yaani 36 minute.

Figure it Out (pages 67–68)

1. Vyutkram samaanupaat: (i) nal aur tanki bharne ka samay, (ii) painter aur deewar rangne ke din, aur (iv) cyclist ki chaal aur nishchit raaste ka samay. (iii), (v) aur (vi) seedhe samaanupaat mein hain.

2. Ek pencil ₹120 ÷ 24 = ₹5 ki, isliye 20 pencil ₹100 ki.

3. 20 parivaar 6 din = 120 parivaar-din ka paani. 30 parivaaron ke liye ye 120 ÷ 30 = 4 din chalega. Maanyataayein: har parivaar roz utna hi paani lagaata hai, upyog nahi badalta, aur tanki dobaara nahi bhari jaati.

4. Ring charts se, jahan gehra hissa neend hai: giraffe 2.5 ghante, haathi 3.5, insaan 8, kutta 10.5, billi 13, gilahri 15, ajgar 18 aur chamgaadad 20.

5. Tukde hain bus 120°, paidal 90°, cycle 60°, two-wheeler 60°, aur car bacha hua 30°. (i) Bus. (ii) 30° ÷ 360° = 1/12. (iii) 18 × 12 = 216 bachchon ne hissa liya. Chart mein taxi ka tukda nahi hai, isliye koi bachcha taxi se nahi aata. (iv) Cycle aur two-wheeler, 60° har ek (36-36 bachche).

6. 3 mazdoor × 4 din = 12 mazdoor-din, isliye 4 mazdoor 12 ÷ 4 = 3 din lenge. Maanyataayein: sab ek hi raftaar se rangte hain aur ek-doosre ko dheema nahi karte.

7. Ye seedha samaanupaat hai: 2 tanki ke 6 ghante yaani ek tanki ke 3 ghante, isliye 5 tanki ke 15 ghante.

8. 25 × 12 = 300 kursiyaan, isliye 300 ÷ 20 = 15 qataar.

9. Din mein 8 × 45 = 360 minute, isliye 9 period mein har ek 360 ÷ 9 = 40 minute.

10. Ek ghante mein chhota pump 1/3 tanki aur bada 1/2 bharta hai. Saath mein ghante mein 1/3 + 1/2 = 5/6 tanki, isliye tanki 6/5 ghante, yaani 1 ghanta 12 minute, mein bharegi.

11. 42 × 63 = 2646 machine-din, isliye 2646 ÷ 54 = 49 machines chahiye.

12. Doori = 60 × 2 = 120 km, isliye 80 km/h par 120 ÷ 80 = 1.5 ghante.