सोमवार, मई 04, 2020

Ratio ka basic concept and isske 10 question with solution

Hello friend !! Aaj hum aapko jo chapter padhne jaa rahe hai, uska naam hai-"Ratio" jisko hindi me "anupaat" (अनुपात) kahte hai. Ye chapter math ka ek very important chapter hai. Aaj hum aapko iss chapter ke baare me bilkul basic se padhane jaa rahe hai. Basic se padhane ka matalab ye hai ki, agar aap iss chapter ke baare me kuch bhi nahi jaante hai toh bhi aap humare iss bataye huye lesson se ekdam basic (zero) se sikh sakte hai.
Aaj hum aapko batayenge ki-
• Ratio ka Main basic concept kya hai?
• Ratio (Anupaat) kya hai?
• Tulya Anupaat kya hai?
• Kisi anupaat ka tulya anupaat kaise gyaat karte hai?
• Ratio ke 10 basic Question aur Solution with full details.


Toh chaliye aaj ka Ratio and proportion chapter start karte hai-:

Ratio ka Main Basic concept kya hai? 

Ratio ka main basic concept hai "ek sankhya ka kisi dusari sankhya se tulna karna." Toh iss chapter ki suruwaat hum iske main basic concept  "tulna karna (तुलना करना) compare" word se karenge.

Hum apne daily life me ek chij ki tulna (compare) dusri chij se karte hai.
Jaise-: (1). Ram ki age 46 years aur Mohan ki age 28 years hai. Toh hum dono ki age ki tulna karte huye kah sakte hai ki, "Ram , Mohan se 46-28=18 years bada (18 years old) hai."
             (2). Ek building ki height, kisi dusri building ki height se 75 feet adhik lambi hai. Toh ye bhi ek building ka dusri building ke hissab se tulna huaa.
             (3). Shanu , Raani se moti (fat) hai. Yaa Raani , Shanu se patali (thin) hai. Ye bhi ek tulna huaa.

Koi bhi chij ki tulna hum bada (big), chhota (small), lamba (long), naata (short), mota (fat), patalaa (thin) etc se karte hai.

Ab baat aati hai ki, hum tulna kitane prakaar se karte hai? Toh isska answer hai-"normally hum tulna 2 prakar se karte hai."
(1). Subtract karke.
(2). Divide karke.

(1). Subtract karke-: Yadi 2 diye huye numbers ke beech jyaada antar (difference) naa ho toh hum unki tulna Subtract karke kar sakte hai. Nichey diye gaye example ko dhyaan se samjhiye-:

Example-: Arun ka weight 56 kg aur Saloni ki weight 46 kg hai. Toh iss me hum subtract karke tulna kar sakte hai. Hum kah sakte hai ki, Arun ka weight Saloni ke weight se 56-46 = 10 kg adhik hai.

(2). Divide karke-: Kabhi - kabhi hume aise numbers ka tulna karna hota hai. Jinme anatar (difference) bahut jyaada hota hai. Toh yaha subtracte karke tulna karna sahi nahi hota hai. Isliye hum isme divide karke tulna karte hai. Nichey diye example ko samjhiye-:

Example-: Ek Math book A ki price ₹500 hai aur Math book B ki price ₹10 ki hai.

Ratio ka basic concept and isske 10 question with solution

Yadi hum inke price ki tulna subtract karke kare toh hum ₹500-₹10 = ₹490 milega. Joki sahi nahi hoga.

Yadi hum tulna bhaag karke kare toh wo iss prakar se hoga-:
Book A ki price/Book B ki price
= 500/10
= 50/1
Toh hum kah sakte hai ki, Book A ki price Book B ki price ka 50 guna hai.

Toh iss prakar se Subtract aur Divide karke hum tulna (compare) karte hai.


Ab tulna karte time ye humesha yaad rakhe ki, kisi bhi 2 chij ki tulna hum tabhi kar sakte hai jab wo 2 chij ek hi unit (ikaai) "इकाई" ke ho.

Jaise-: (1). Rahul ki height 5 feet aur Shreya ki height 2 meter ho toh dono ki height ki tulna kijiye.
            (2). Ekta ki age 18 years aur Soni ki age 84 month hai toh dono ki age ki tulna kijiye.

Uppar ke dono example (1) aur (2) me hum normally tulna nahi kar sakte kyuki example (1) me Ram ki height "feet" me aur Shreya ki height "meter" me hai. Toh "Feet" aur "meter" dono alag-alag raashiya hai.
Issi prakar example (2) me Ekta ki age "year" me toh Soni ki age "month" ne diya hai. Ye bhi alag-alag raashiya hai.

Iss type ke question me tulna karne ke liye hume example (1) me "feet" ko "meter" me yaa phir "meter" ko "feet" me badalana (convert) hoga.
Matalab,  Feet     ⇨   Meter 
Or             Meter  ⇨   Feet
Issi prakaar example (2) me "year" ko "month" me yaa "month" ko "year" me badalana (convert) hoga.
Matalab,  Year     ⇨   Month
Or             Month  ⇨   Year

Toh Hume ummid hai ki ab aap tulna karna sikh gaye honge. Ab hum baat karenge Anupaat (Ratio) ki.

Ratio - Anupaat kya hai?


Jab hum two ya two se jaada number ke tulna karte hai toh iss method ko hum Ratio kahte hai.
Anupaat ko agar hum simple me kahe toh, "bhaag karke tulna karna hi Anupaat kahlata hai." Matalab Anupaat hume ye batata hai ki, koi ek chij, kisi dusri chij se kitane guna hai. Anupaat ko hum ":" sign se dikhate hai.
Jaise-: (1). Anil ke paas ₹45 aur Amir ke paas ₹135 hai. Amir ke paas , Anil se kitne guna hai?

Solution-: Amir ke paas =₹135 aur Anil ke paas = ₹45 toh bhaag karne par- 
   Amir ke paas ₹     =    135    =    3  
    Anil ke paas ₹             45           1

Toh bhaag karne ke baad hum dekh sakte hai ki, Amir ke paas, Anil se 3 guna rupye hai.

Ab issko hum Anupaat me iss prakar se likh sakte hai-:
Amir ke paas ke rupye ka Anil ke paas ke rupye ka Anupaat = 3/1 = 3:1
(2). Shahil ki height 5ft aur ek tree ki height 40ft hai toh tree ki height, Shahil ki height ka kitna guna hai?

Solution-: Shahil ki height = 5ft aur Tree ki height = 40 toh bhaag karne par- 
   Tree ki height     =    40    =    8   
 Shahil ki height           5           1

Hum dekh sakte hai ki, Tree ki height, Shahil ki height ka 8 guna hai.
Anupaat me likhane par-:
Tree ki height ka Shahil ki height ke saath Anupaat = 8/1 = 8:1



Ab hum baat karenge tulya Anupaat (Equivalent Ratio) ki. Tulya Anupaat kya hota hai? Kisi bhi diye Anupaat ka tulya Anupaat kaise nikaalate hai? Aayiye sikh lete hai-:

Tulya Anupaat (Equivalent Ratio)-:


Tulya anupaat kya hai ? Ye jaanane ke liye nichey diye dono examples ko dekhiye-:
Example-(1). 27 aur 81 ka anupaat gyaat kijiye.

Solution-: 27:81 = 27/81
                             = 1/3
                             = 1:3

Example-(2). 18 aur 54 ka anupaat gyaat kijiye.

Solution-: 18:54  = 18/54
                              = 1/3
                              = 1:3

Dono example (1) aur (2) me hum dekhte hai ki, 27:81 aur 18:54 ka lowest form me anupaat 1:3 ek samaan (equal) hai. Issi ko hum tulya anupaat (Equivalent ratio) kahte hai.
Matlab 27:81 aur 18:54, 1:3 ka tulya anupaat hai.

Kisi anupaat ka Tulya anupaat kaise gyaat karte hai?


Hum kisi bhi Anupaat ka tulya Anupaat gyaat karne ke liye Ansh (numerator) aur har (denominator) me ek hi number se multiply yaa divide karke nikaal sakte hai.
Jaise-: (1). 2:3 ka ek tulya anupaat bataye.

Solution-: 2:3 = 2/3
                         = (2×5)/(3×5)
                         = 10/15
                         = 10:15
∴2:3 ka ek tulya anupaat = 10:15

(2). 25:75 ka tulya anupaat gyaat kijiye.

Solution-: 25:75 = 25/75
                             = (25÷5)/(75÷5)
                             = 5/15
                             = 1/3
                             = 1:3
∴25:75 ka ek tulya anupaat = 1:3

Toh upar ke dono example me aapne dekha ki, diye huye aunpaat me hum ek hi number se multiply aur divide karke hum tulya anupaat gyaat kar sakte hai.

Ratio ke 10 Basic Question aur Solution-:


#Q-1. 4 m aur 40cm ka anupaat gyaat kijiye.

Solution-: Diya hai -: 4m = 400cm aur 40cm
Tab 4m aur 40cm ka anupaat = 400/40
= 80/8
= 10/1
∴ 4m aur 40cm ka anupaat = 10:1 Ans.

#Q-2. 25 minutes ka 2 hours ke saath Anupaat bataye.

Solution-: Diya hai-: 25 minutes aur 2 hours = 120 minutes
Tab 25 min aur 120 min ka anupaat = 25/120
= 5/24
∴25 aur 2 hours ka anupaat = 5:24  Ans.

#Q-3. ₹8 ka 40 paise ke saath Anupaat bataye.

Solution-: Diya hai- ₹8 = 800 paise aur 40 paise
Tab 800 paise aur 40 paise ka anupaat = 800/40
                 = 20/1
∴₹8 ka 40 paise ke saath anupaat = 20:1 Ans.

#Q-4. Ek class me 30 boys aur 42 girls hai. Boys ka Girls ke saath anupaat bataye.

Solution-: Boys = 30 aur Girls = 42
∴ Boys ka Girls ke saath anupaat = 30/42 = 10/14
           = 5/7
           = 5:7  Ans.

#Q-5. Garden me 15 mango tree aur 51 banana tree hai. Banana tree ka mango tree ke saath anupaat bataye.

Solution-: Mango tree = 15 aur Banana tree = 51
∴ Banana tree ka Mango tree ke saath anupaat = 51/15
                           = 17/5
                           = 17:5  Ans.

#Q-6. Ek class me 35 Students math aur baaki students Science padhate hai. Yadi class me total 56 students ho toh Science ke students ka math ke students ke saath Anupaat gyaat kijiye.

Solution-: Diya hai-: Math ke students = 35 aur Total students = 56
Tab, Science ke students = 56-35 = 21
∴ Science ke students ka Math ke students se anupaat = 21/35
                                     = 3/5
                                     = 3:5  Ans.

#Q-7. Ek Garden me 24 gulaab ke aur 51 lily ke plants hai. Toh Anupaat gyaat kijiye-:
(i) Gulaab ke plants ka total plants se.
(ii) Lily ke plants ka Gulaab ke plants se.

Solution-: Diya hai- Gulaab ke plants = 24
Lily ke plants = 51
Total plants = 24+51 = 75

(i) Gulaab ke plants ka total plants ke saath anupaat = 24/75
                                = 8/25
                                = 8:25  Ans.

(ii) Lily ke plants ka Gulaab ke plants ke saath anupaat = 51/24
                                             = 17/8
                                             = 17:8 Ans.

#Q-8. 2:5 ka tulya anupaat gyaat kijiye.

Solution-: 2:5 = 2/5
                         = (2×2)/(5×2)
                         = 4/10
                         = 4:10
∴2:5 ka tulya anupaat = 4:10 Ans.

#Q-9. 4:8 ka three tulya anupaat gyaat kijiye.

Solution-: 4:8 = 4/8
                         = (4÷2)/(8÷2)
                         = 2/4
                         = 2:4 ........(i)
2:4 = (2÷2)/(4÷2)
      = 1/2
      = 1:2 .........(ii)
And 4:8 = 4/8
               = (4×2)/(8×2)
               = 8/16
               = 8:16 ...........(iii)
∴4:8 ka three tulya anupaat = 2:4, 1:2 and 8:16 Ans.

【Note-: Question-9. me humne tulya anupaat nikalne ke liye divide aur multiply dono ka use kiya hai. Ye jaruri nahi hai ki aap bhi dono kare. Aap kewal multiply karke bhi tulya anupaat gyaat kar sakte hai.】

#Q-10. Ek aayatakaar maidaan (Rectangular field) ki length (लम्बाई) , width (चौड़ाई) ki 4 guni hai toh length (लम्बाई) ka width (चौड़ाई) ke saath anupaat bataye.

Solution-: Suppose Field ki width = x hai.
Tab Field ki length = 4x
Length ka width ke saath anupaat = 4x/x
= 4/1
= 4:1 Ans.

Ye bhi padh kar sikhiye-:
❒ Perfect Square ka Square root long division method se kaise nikalte hai?
❒ Circle ka basic concept and isske 10 important parts
❒ Rational numbers operations full details in hindi

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1 टिप्पणी:

  1. hi, aapki is post bahut acchi lagi isliye aapki post ka link hamne hindinotes.org par share kiya hai, yadi aapko koi problem hai to aap bata sakte hain, nahi to aap khud bhi apni nayi post ka link wahan share kar sakte hain.

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