UPSC Darpan

MathsMarichi · UPSC

AP aur GP: Simple vs Compound, Malthus ka Tark aur CSAT

Malthus ka tark tha ki aabaadi GP mein badhti hai aur anaaj AP mein — toh yeh tark exam mein kaise poocha jaata hai, aur aaj kitna tikta hai?

Socho pehle… phir dekho jawab

Malthus ke tark ka gaNit sahi hai: GP aakhir mein AP se aage nikal jaata hai. Par asli duniya mein technology se anaaj ki upaj bhi tez badhi, isliye uska nateeja saaf nahi tikta — Mains yahi dono pehlu maangta hai.

Concept: AP mein sthir farak d, a(n) = a + (n - 1)d; GP mein sthir anupaat r, a(n) = a x r^(n - 1). Simple interest AP banata hai, compound interest GP. Kisi bhi r > 1 wale GP ko lambe samay mein koi bhi AP peeche chhod deta hai.

Prelims/CSAT link: CSAT mein sequence, percentage aur compound interest ke sawaal aate hain. Shortcut: 'Rule of 72' ek anumaan hai — saalana dar r% par rakam lagbhag 72/r saal mein doguni hoti hai; 8% par lagbhag 9 saal (yeh exact nahi, anumaan hai). Trap: simple aur compound interest ko ek jaisa maan lena.

Mains link (GS1 — Society, population): Malthus ke 1798 ke essay ka tark tha ki aabaadi GP mein badhti hai aur khaadya utpaadan AP mein, isliye ant mein akaal aayega. Analysis: tark ka gaNit samajhne laayak hai, par technology (jaise Green Revolution) ne upaj ko tez badhaya, aur aabaadi ki dar bhi shiksha aur swasthya badhne se ghati. Isliye 'sthir r ya d' wala model asli duniya ka poora sach nahi hai.

Ghar pe try karo

150-word skeleton: intro (AP vs GP ka gaNit), body (Malthus ka tark aur uski seemayein: technology, demographic transition), conclusion (model ki seema aur neeti ka sabak).

Wow!

Rule of 72: 8% saalana par rakam lagbhag 9 saal mein doguni ho jaati hai — sirf anumaan, par exam mein kaam aata hai!

3 sawaal

  1. Malthus ke tark ke anusaar aabaadi aur khaadya utpaadan kaise badhte hain?
    Jawab dekho

    Aabaadi GP mein, khaadya AP mein. Malthus ka tark tha: aabaadi geometric, khaadya arithmetic.

  2. Simple interest kaun sa progression banata hai?
    Jawab dekho

    AP. Har saal sthir rakam judti hai, isliye AP.

  3. Rule of 72 ke anusaar 8% saalana par rakam lagbhag kitne saal mein doguni hoti hai?
    Jawab dekho

    Lagbhag 9 saal. 72/8 = 9; yeh ek anumaan hai.

NCERT se jodo: GS1 — Society (population aur uske mudde); CSAT — basic numeracy aur sequences; NCERT Class 10 Maths — arithmetic progressions; NCERT Class 11 Maths — sequences and series

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