Lagnever AI English

Pratishat vriddhi aur kami (percentage increase and decrease)

Short mein jawab

Pratishat vriddhi ya kami = badlaav ÷ shuruaati maatra × 100. Agar tamatar ₹30 se ₹42 kilo ho jaayein, to ₹12 ki vriddhi 12/30 × 100 = 40% hai. Profit aur loss bhi aise hi nikalte hain, jahan cost price shuruaati maatra hota hai, aur discount marked price mein pratishat kami hai.

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Badlaav ko per cent mein naapna

Daam, aabaadi aur darshakon ki ginti badalti rehti hai, aur percentage batata hai ki badlaav shuruaat ke mukable kitna bada hai. 1 kg tamatar teen saal pehle ₹30 ke the aur ab ₹42 ke hain. Vriddhi ₹12 hai, aur 12/30 × 100 = 40%, yaani daam 40% badha. Ek theatre mein COVID se pehle har show mein ausatan 160 darshak aate the aur ab 100 aate hain. Kami 60 hai, aur 60/160 × 100 = 37.5%. Dono baar:

Pratishat badlaav = badlaav ÷ shuruaati maatra × 100.

Shuruaati maatra ko base kehte hain. Uski jagah nayi maatra se bhaag dena sabse aam galti hai.

Pratishat vriddhi aur kami: tamatar ₹30 se ₹42, yaani 40% vriddhi; darshak 160 se 100, yaani 37.5% kami
Pratishat vriddhi aur kami

Ek hi baat, do tarah se

‘1991 ki aabaadi 1961 ki aabaadi ka 165% hai’ aur ‘1961 se 1991 tak aabaadi 65% badhi’ ek hi baat kehte hain. Agar pehle ki aabaadi p thi, to baad wali dono tarah se p + 0.65p = 1.65p hai. Isliye x% vriddhi ka matlab 1 + x/100 se guna, aur x% kami ka matlab 1 − x/100 se guna. 5% badhna 1.05 se guna hai; 85% ghatne par pehle ki value ka sirf 15% bachta hai.

Profit aur loss

Dukaandaar cost price (CP) chukaate hain, marked price (MP) bataate hain, aur aakhir mein selling price (SP) paate hain. SP, CP se zyada ho to profit hai; kam ho to loss. Kishanlal ek sweater ₹300 mein khareedte hain, us par ₹480 likhte hain aur mol-bhaav ke baad ₹430 mein bechte hain. Unka profit ₹130 hai, aur 130/300 × 100 ≈ 43.3%. Profit aur loss percentage cost price par nikaalte hain, kyunki ye sawaal ka jawab dete hain ki ‘jo lagaaya uske mukable kitna kamaaya?’. Ulta bhi chalta hai: Shyamala ko ₹2650 ka guldaan 18% loss par bechna pada, to unhe 2650 ka 82% mila, yaani ₹2173.

Sweater ka safar: manufacturer se wholesaler aur retailer tak, har kadam par cost, marked aur selling price
CP, MP aur SP

Kabhi profit ko bikri ke saamne bhi naapte hain. Manisha ki dukaan par khaad ki bori ₹500 mein aati hai aur ₹750 mein bikti hai: profit cost ka 50% hai par selling price ka sirf 33.33%. Businesses aksar kharchon ke baad ka net profit revenue ke percentage mein bataate hain.

Discount aur GST

Discount marked price mein pratishat kami hai. ₹1800 ke marked cooker par 35% off ho to wo 1800 ke 65% mein bikta hai, yaani ₹1170; agar dukaan ne use ₹900 mein khareeda tha, to profit ₹270 yaani 30% hai. GST pratishat vriddhi hai: ₹8250 ke mobile phone par 18% GST lagne se wo 8250 × 1.18 = ₹9735 ka padta hai. Bill par ye 18% kabhi 9% CGST aur 9% SGST ke roop mein dikhta hai.

GST wala bill check karna: ₹450 plus 9% CGST aur 9% SGST milkar ₹531
GST wala bill check karna

Badlaav par badlaav

Jab ek pratishat badlaav ke baad doosra aata hai, doosra nayi rakam par lagta hai, isliye badlaav judte nahi, guna hote hain. ‘30% + 20%’ off dene wali bakery ₹200 ke cake par pehle discount ke baad ₹140 aur doosre ke baad ₹112 leti hai, jabki seedha 50% discount ₹100 deta hai. Kiraaye mein pehle 3% aur phir 4% vriddhi kul milaakar 7.12% vriddhi hai. Poora chapter Chapter 1 ke notes mein hai, basics pratishat kya hai? mein, aur har exercise NCERT solutions mein.

Tricky percentages: 30% plus 20% off banaam 50% off, 50% markup ke baad 50% discount, aur bada percentage banaam badi rakam
Tricky percentages

Practice karo

  1. Petrol ₹60 se ₹100 litre ho gaya. Pratishat vriddhi lagbhag kitni hai?

    1. (a) 40%
    2. (b) 60%
    3. (c) 66.67%
    4. (d) 140%
    Jawab dekho

    Jawab: (c) 66.67%

  2. ₹300 ki shirt par 25% discount hai. Selling price kitna hai?

    1. (a) ₹75
    2. (b) ₹225
    3. (c) ₹275
    4. (d) ₹375
    Jawab dekho

    Jawab: (b) ₹225

  3. Ek sankhya 20% badhkar 90 ho jaati hai. Sankhya kya hai?

    1. (a) 70
    2. (b) 72
    3. (c) 75
    4. (d) 108
    Jawab dekho

    Jawab: (c) 75

  4. ₹75 mein khareedi geometry box ₹110 mein biki. Cost par profit percentage kitna hai?

    Jawab dekho

    Jawab: Profit = 110 − 75 = ₹35. Profit % = 35/75 × 100 ≈ 46.67%, jo ₹75 ke cost price par nikala gaya.

  5. Daam pehle 35% badhaaya aur phir 30% ghataaya. Aakhri daam shuru se zyada hai ya kam?

    Jawab dekho

    Jawab: Kam. Daam 1.35 × 0.70 = 0.945 guna ho jaata hai, yaani 5.5% kam, kyunki 30% ki kami bade, badhe hue daam par lagti hai.

Students ke sawal

Pratishat vriddhi kaise nikaalte hain?

Nayi value mein se puraani value ghatao, vriddhi ko puraani value se bhaag do, aur 100 se guna karo. Chawal ₹38 se ₹42 kilo ho to vriddhi 4 hai, aur 4/38 × 100 ≈ 10.53%. Isi ko us cheez ki mehngai ki dar (rate of inflation) bhi kehte hain.

Profit aur loss percentage kaise nikaalte hain?

Profit % = (selling price − cost price) ÷ cost price × 100, aur loss % = (cost price − selling price) ÷ cost price × 100. Raghu ne chawal ₹35 kilo khareeda aur 10 kg ₹300 mein becha, to ₹350 par ₹50 ka loss hua, lagbhag 14.29%.

Markup aur discount mein kya farq hai?

Markup cost price par joda gaya percentage hai jisse selling ya marked price tay hota hai. Discount marked price se ghataaya gaya percentage hai. Dono alag rakam par lagte hain, isliye 50% markup ke baad 50% discount daam ko cost par waapas nahi laata; isse 25% loss hota hai.

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