Arithmetic and Debu: Discussion of Important Mathematical Questions

Objective

• Achieving an 80% hit rate and 90% accuracy
• Solution in minimal time
• If it is a Level 1 question, it should be solved in 32-45 seconds, and medium to difficult questions should be completed in 1-1.5 minutes.

Methodology

• Every individual should focus on strong traits in percentages and arithmetics.
• We have been doing arithmetic since childhood, but due to struggles, it seems challenging.

Important Questions

Profit and Loss

• Under the profit and loss topic:
  • Calculate profit and discount between cost price, selling price, and marked price.
  • Example: A profit of 20% on a cost price of 100 will be 120.
• Margin: Often applied in companies.
  • For instance, calculate a 50% markup and a 20% discount.
• Successive Changes: Simple formula: A + B + A.B/100.
  • Change perspective, multiply by percentage.

Interest

• Basic concepts of Simple Interest and Compound Interest
  • Example: If the principal is 1000 rupees and the rate is 10%, calculate the simple interest for the given time.
• The more frequently interest is calculated in installments, the more it accrues. Core principles⟿ consider the percentage with N periods.
• Example: How long will it take to double 1000 rupees at compound interest?

Time Speed Distance

• Distance = Speed X Time.
  • Example: If an object moves at x speed, what will be its distance?
• Use of reciprocals:
  • If speed is constant, time is constant. This can be considered in time speed distance questions.
  • Simple example: Covering 100 meters in 32 seconds.
• Escalator Question: The distance will always remain, mention the speed.
  • The concept of height remains, as given in Uncle's example.

Mixture and Allegation

• Use simple average mixture and allegation
  • Mixing concentrations and finding the average concentration, such as mixing 30% and 60% and calculating the percentage.
• Replacement formula: (Original concentration)x(1-fake)/ (Total-1/number of times) completed.
  • Example: 10 liters of milk and 10 liters of water case.

Work and Time

• Solution by LCM method: or solving days using LCM. Also, count using one-day work method.
  • Example: A task can be completed in 10 days by one person and in 20 days by another. How many days will it take if they work together?

The Challenge

• Revise respective time speed distance, work and time individual percentages, and return on investment.
  • Rate count, total work, and allegation.
• Questions should balance personal experience and effort.