Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।
Exam strategyपरीक्षा रणनीतिRarely taughtकम सिखाई जाने वाली
Back-solve from the middle option
Use it when:कब इस्तेमाल करें: The question is easy to check but slow to set up as an equation (ages, mixtures, “find the number”).
Options on this site are in ascending order (as in most printed papers), so start with B or C.
Plug it into the question. Too big? The answer is above it. Too small? Below.
At most two checks find the answer.
Exampleउदाहरण
The father is 3 times his son’s age; in 12 years he will be twice the son’s age. Son’s age? (a) 10 (b) 12 (c) 14 (d) 16
→ Try 12: father 36; in 12 years 48 and 24 → 2 times. Done.
Why it works, and when it failsयह क्यों काम करती है, और कब नहीं
Why:क्यों: Checking a candidate is a few multiplications; with sorted options each check halves the choices, so two checks cover four options.
Limits:सीमाएँ: Not for “cannot be determined” options or questions with several unknowns. Write the equation then.
Solved examplesहल किए गए उदाहरण
Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।
Example 1उदाहरण 1 · Partnership: sharing profit · Easyआसान
Kabir invested ₹15,000, Lakshmi invested ₹80,000 in a small business in Guwahati. At the end of the year the profit is ₹26,600. What is Lakshmi's share?
₹17,900
₹22,400
₹24,600
₹26,900
Answer:उत्तर:₹22,400
Kabir: 15,000 × 12 = 1,80,000.
Lakshmi: 80,000 × 12 = 9,60,000.
Ratio = 3 : 16 (sum 19).
Lakshmi's share = 26,600 × 16/19 = ₹22,400.
Example 2उदाहरण 2 · Partnership: sharing profit · Mediumमध्यम
Isha invested ₹50,000, Arjun joined after 6 months with ₹55,000 in a small business in Nagpur. At the end of the year the profit is ₹40,300. What is Arjun's share?
₹11,400
₹14,300
₹17,200
₹17,900
Answer:उत्तर:₹14,300
Isha: 50,000 × 12 = 6,00,000.
Arjun: 55,000 × 6 = 3,30,000.
Ratio = 20 : 11 (sum 31).
Arjun's share = 40,300 × 11/31 = ₹14,300.
Example 3उदाहरण 3 · Partnership: sharing profit · Hardकठिन
Rohan invested ₹15,000, Lakshmi joined after 4 months with ₹75,000, Tenzin joined after 6 months with ₹15,000 in a small business in Surat. At the end of the year the profit is ₹26,100. What is Tenzin's share?
₹2,000
₹2,400
₹2,700
₹3,400
Answer:उत्तर:₹2,700
Rohan: 15,000 × 12 = 1,80,000.
Lakshmi: 75,000 × 8 = 6,00,000.
Tenzin: 15,000 × 6 = 90,000.
Ratio = 6 : 20 : 3 (sum 29).
Tenzin's share = 26,100 × 3/29 = ₹2,700.
Example 4उदाहरण 4 · Partnership: sharing profit · Mediumमध्यम
Priya invested ₹50,000, Meera joined after 4 months with ₹35,000 in a small business in Bhopal. At the end of the year the profit is ₹26,400. What is Priya's share?
₹13,500
₹18,000
₹21,600
₹22,500
Answer:उत्तर:₹18,000
Priya: 50,000 × 12 = 6,00,000.
Meera: 35,000 × 8 = 2,80,000.
Ratio = 15 : 7 (sum 22).
Priya's share = 26,400 × 15/22 = ₹18,000.
Example 5उदाहरण 5 · Partnership: sharing profit · Mediumमध्यम
Priya invested ₹15,000, Isha joined after 6 months with ₹90,000 in a small business in Bhopal. At the end of the year the profit is ₹7,600. What is Priya's share?
₹1,400
₹1,700
₹1,900
₹2,400
Answer:उत्तर:₹1,900
Priya: 15,000 × 12 = 1,80,000.
Isha: 90,000 × 6 = 5,40,000.
Ratio = 1 : 3 (sum 4).
Priya's share = 7,600 × 1/4 = ₹1,900.
Example 6उदाहरण 6 · Partnership: sharing profit · Mediumमध्यम
Ananya invested ₹15,000, Vihaan joined after 3 months with ₹80,000 in a small business in Kochi. At the end of the year the profit is ₹500. What is Vihaan's share?
₹200
₹300
₹400
₹500
Answer:उत्तर:₹400
Ananya: 15,000 × 12 = 1,80,000.
Vihaan: 80,000 × 9 = 7,20,000.
Ratio = 1 : 4 (sum 5).
Vihaan's share = 500 × 4/5 = ₹400.
Common mistakesआम गलतियाँ
Using capital alone when the time periods differ.
Sharing the whole profit before taking out a working partner’s salary.
Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न
How is profit divided in a partnership?
In the ratio of capital × time for each partner.
What if a partner joins after a few months?
Count only the months their money was in the business.
Is partnership asked in bank exams?
Yes, usually as one question in prelims and in arithmetic DI sets in mains.