MathsMarichi · UPSC
Threshold ka Khel: ₹2,000 aur Bill Todne ki Maths
Agar ₹2,000 se upar ke UPI payment pe fee lage, to dukaandaar ₹2,400 ka bill kaise 'ghata' dega?
Socho pehle… phir dekho jawab
Bill ko ₹2,000 aur ₹400 mein tod dega! Jab rule ek threshold pe achanak lagta hai, log uske theek neeche aa jaate hain. Yeh 'bunching' ki maths hai — aur policy design ka sabse bada sabak.
Pehle simple percentage: 0.4% ka matlab har ₹100 pe 40 paise. Illustration ke liye maano fee poore amount pe lagti hai, to ₹2,500 pe ₹10. Chhoti rakam lagti hai, par lakhon transactions pe jud kar badi ho jaati hai — yahi aggregate thinking hai.
Ab threshold: agar rule 'sirf ₹2,000 se upar' hai, to ₹1,999 aur ₹2,001 mein 2 rupaye ka farak hai par fee mein poora farak. Aisi 'cliff' pe log behaviour badalte hain — bill split karna, do payment karna. Isliye economists graph mein threshold ke theek neeche transactions ka dher (bunching) dhoondhte hain.
CSAT aur Mains dono ka sabak: percentage vs percentage point. Agar rate 5% se 6% hua, to yeh 1 percentage point badhna hai, par 20% (relative) badhna hai. Aur 50% badhne ke baad 50% ghatne pe wapas wahin nahi aate — 100 → 150 → 75.
Policy mein yeh maths isliye zaroori hai ki rule ka asli asar sirf formula se nahi, logon ke jawab (incentive) se tay hota hai.
Ghar pe try karo
Ek number lo, jaise 200. Pehle 25% badhao, phir 25% ghatao. Kya wapas 200 aaye? Ab 20% ghata kar 25% badha kar dekho. Pattern samjho.
Wow!
Har threshold ek chhupa hua 'invitation' hai — log uske theek neeche aane ka raasta dhoondh hi lete hain.
3 sawaal
- Ek cheez ka daam 100 se 50% badha, phir naye daam se 50% ghata. Antim daam?
Jawab dekho
75. 100 → 150 → 75. Percentage alag base pe lagta hai.
- Trap: Inflation 4% se 5% hui. Sahi kathan?
Jawab dekho
Inflation 1 percentage point badhi, jo relative roop mein 25% badhotri hai. 5 − 4 = 1 percentage point; (1/4) × 100 = 25% relative badhotri.
- ₹2,000 threshold ke theek neeche transactions ka achanak dher dikhna kya darshata hai?
Jawab dekho
Logon ka incentive ke jawab mein behaviour badalna (bunching). Threshold pe cost ka jump logon ko uske neeche aane ke liye prerit karta hai.
NCERT se jodo: GS3 — Indian Economy (digital payments); Prelims CSAT (GS Paper II) — percentage aur basic numeracy; NCERT Class 8 Maths — comparing quantities (percentage)