Money and Unitary Method

Overview

Money and Unitary Method forms a fundamental part of the MP TET Mathematics section, appearing consistently across all three Varg papers. This topic tests a candidate's ability to handle real-life arithmetic situations involving currency, proportional reasoning, and average calculations—skills essential for any primary or upper-primary teacher.

The unitary method, in particular, is the backbone of ratio-proportion problems and appears disguised in questions on time-work, speed-distance, and cost calculations. Mastering this topic builds computational fluency and helps teachers demonstrate practical mathematics to students using everyday examples like shopping, wages, and market transactions.

For the exam, expect 2–4 questions directly testing currency conversions, cost calculations using unitary method, and finding averages. The questions are typically word problems requiring careful reading and systematic calculation.

Key Concepts

• **Indian Currency System**: 1 Rupee (₹) = 100 Paise. All modern calculations use the decimal system where paise are written as decimal fractions of rupees (₹5.75 means 5 rupees and 75 paise).

• **Unitary Method**: A technique to find the value of a single unit first, then use it to find the value of any required number of units. It follows the principle: if more quantity costs more (direct proportion), or if more workers take less time (inverse proportion).

• **Direct Proportion in Unitary Method**: When two quantities increase or decrease together. Example: More items → More cost. Formula approach: Value of 1 unit = Total value ÷ Number of units.

• **Inverse Proportion in Unitary Method**: When one quantity increases while the other decreases. Example: More workers → Less time to complete work.

• **Average (Mean)**: The sum of all observations divided by the number of observations. It represents the central value of a data set.

• **Weighted Average**: When different items have different importance (weights), the average is calculated by multiplying each value by its weight, summing, and dividing by total weight.

• **Currency Conversion Logic**: Converting between rupees and paise requires multiplying by 100 (rupees to paise) or dividing by 100 (paise to rupees).

Formulas / Key Facts

| Concept | Formula | |---------|---------| | Rupees to Paise | Paise = Rupees × 100 | | Paise to Rupees | Rupees = Paise ÷ 100 | | Unitary Method (Direct) | Value of n units = (Value of given units ÷ Given units) × n | | Unitary Method (Inverse) | If M₁ workers take D₁ days, then M₂ workers take D₂ days where M₁ × D₁ = M₂ × D₂ | | Average | Average = Sum of all values ÷ Number of values | | Sum from Average | Sum = Average × Number of values | | New Average after addition | New Average = (Old Sum + New Value) ÷ (Old Count + 1) |