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) |

**Key Facts to Remember**:

• 1 Rupee = 100 Paise (not 50 or 10)
• In unitary method, always find the value of ONE unit first
• Average can be a decimal even when all values are whole numbers
• When finding average of averages, use total sum method, not average of averages directly

Worked Examples

**Example 1: Currency and Unitary Method Combined**

*If 15 notebooks cost ₹262.50, find the cost of 23 notebooks.*

**Solution**:

• Step 1: Find cost of 1 notebook
• Cost of 1 notebook = ₹262.50 ÷ 15 = ₹17.50
• Step 2: Find cost of 23 notebooks
• Cost of 23 notebooks = ₹17.50 × 23 = ₹402.50

**Answer**: ₹402.50

---

**Example 2: Inverse Proportion (Unitary Method)**

*If 12 workers can build a wall in 20 days, how many days will 15 workers take to build the same wall?*

**Solution**:

• This is inverse proportion (more workers → less days)
• Step 1: Total work = 12 × 20 = 240 worker-days
• Step 2: Days for 15 workers = 240 ÷ 15 = 16 days

**Answer**: 16 days

---

**Example 3: Average Calculation**

*The marks of 5 students are 72, 85, 68, 91, and 79. Find the average marks.*

**Solution**:

• Step 1: Sum = 72 + 85 + 68 + 91 + 79 = 395
• Step 2: Average = 395 ÷ 5 = 79

**Answer**: 79 marks

---

**Example 4: Finding Missing Value from Average**

*The average of 6 numbers is 24. If five of the numbers are 18, 22, 26, 30, and 25, find the sixth number.*

**Solution**:

• Step 1: Total sum = Average × Count = 24 × 6 = 144
• Step 2: Sum of five numbers = 18 + 22 + 26 + 30 + 25 = 121
• Step 3: Sixth number = 144 − 121 = 23

**Answer**: 23

Common Mistakes

• **Confusing direct and inverse proportion** → Before solving, ask: "If one quantity increases, does the other increase (direct) or decrease (inverse)?" More items cost more (direct); more workers need fewer days (inverse).

• **Forgetting to convert units consistently** → When the problem mixes rupees and paise, convert everything to one unit first. ₹3.50 + 75 paise should become 350 paise + 75 paise = 425 paise = ₹4.25.

• **Calculating average of averages directly** → Wrong: Average of class A (60) and class B (70) is not 65 unless both classes have equal students. Correct method: Find total marks of both classes, then divide by total students.

• **Skipping the unitary step in complex problems** → Students often try to find the answer directly without finding the value of one unit. Always write the intermediate step: "Cost of 1 item = ..."

• **Placing decimal point incorrectly in currency** → ₹17.5 means ₹17 and 50 paise, not ₹17 and 5 paise. Write ₹17.05 for 17 rupees and 5 paise.

Quick Reference

• **Unitary Method Mantra**: Find value of 1 → Multiply by required number

• **Direct proportion check**: Both increase or both decrease together

• **Inverse proportion check**: One increases while other decreases

• **Average = Total Sum ÷ Count** (works both ways—rearrange to find sum or count)

• **Currency rule**: Rupees to paise → ×100; Paise to rupees → ÷100

• **For missing value problems**: Sum needed = Average × Total count, then subtract known values