Money and Time — Study Notes for JTET Paper I

Overview

Money and Time forms a practical, everyday mathematics topic that appears consistently in JTET Paper I. This topic tests a candidate's ability to perform arithmetic operations involving Indian currency and solve problems related to clocks, calendars, and duration calculations. Since JTET assesses readiness to teach Classes I–V, questions typically involve real-life contexts—shopping scenarios, fare calculations, reading clocks, and computing elapsed time.

Mastery here requires comfort with decimal operations (since paise work like two-decimal-place amounts), unit conversions between rupees and paise, and understanding the 12-hour and 24-hour clock systems. Calendar-based questions on days, weeks, and months also appear. The pedagogy component may ask how to teach money concepts using play money or how to introduce clock-reading in early grades.

Expect 2–4 direct questions from this sub-topic. They are usually straightforward calculation problems but can trip students who confuse units or misread clock positions.

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Key Concepts

**Indian Currency System**: 1 Rupee (₹) = 100 Paise. Notes: ₹10, ₹20, ₹50, ₹100, ₹200, ₹500, ₹2000. Coins: 50 paise, ₹1, ₹2, ₹5, ₹10.

**Converting Between Rupees and Paise**: To convert rupees to paise, multiply by 100. To convert paise to rupees, divide by 100. Example: ₹7.50 = 750 paise; 825 paise = ₹8.25.

**Operations on Money**: Addition, subtraction, multiplication, and division of money amounts follow decimal rules—align decimal points before operating.

**Clock Basics**: A clock face has 12 hours; the hour hand completes one full rotation in 12 hours, the minute hand in 1 hour (60 minutes).

**Minute Hand Movement**: The minute hand moves 360° in 60 minutes, i.e., 6° per minute. The hour hand moves 360° in 12 hours, i.e., 0.5° per minute.

**12-Hour vs 24-Hour Format**: 12-hour uses AM/PM; 24-hour format runs 00:00 to 23:59. Conversion: Add 12 to PM hours (except 12 PM stays 12:00); subtract 12 from hours ≥13 for 12-hour format.

**Duration / Elapsed Time**: Time difference between two events. Count forward from start time to end time, borrowing 60 minutes when needed.

**Calendar Facts**: 1 week = 7 days; 1 year = 12 months = 365 days (366 in leap year). Leap year: divisible by 4, but century years must be divisible by 400.

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Formulas / Key Facts

| Concept | Formula / Fact | |---------|----------------| | Rupees to Paise | Paise = Rupees × 100 | | Paise to Rupees | Rupees = Paise ÷ 100 | | Angle traced by minute hand | θ = 6° × minutes | | Angle traced by hour hand | θ = 0.5° × minutes (from 12 o'clock reference) | | Angle between hands | \|30H − 5.5M\| where H = hour, M = minutes; if >180°, subtract from 360° | | Hands overlap | 12 times in 12 hours (not 11, because 12 o'clock counts once) | | Hands at right angle (90°) | 22 times in 12 hours | | Hands opposite (180°) | 11 times in 12 hours | | Elapsed time | End time − Start time (borrow 60 min if needed) | | Days in months | Jan 31, Feb 28/29, Mar 31, Apr 30, May 31, Jun 30, Jul 31, Aug 31, Sep 30, Oct 31, Nov 30, Dec 31 |

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Worked Examples

### Example 1: Money Addition and Subtraction

**Problem**: Ravi bought a notebook for ₹45.75 and a pen for ₹18.50. He gave the shopkeeper ₹100. How much change did he receive?

**Solution**: 1. Total cost = ₹45.75 + ₹18.50 = ₹64.25 2. Change = ₹100.00 − ₹64.25 = ₹35.75

**Answer**: ₹35.75

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### Example 2: Elapsed Time Calculation

**Problem**: A train departs at 9:45 AM and arrives at 2:20 PM. What is the total travel time?

**Solution**: 1. From 9:45 AM to 12:00 PM = 2 hours 15 minutes 2. From 12:00 PM to 2:20 PM = 2 hours 20 minutes 3. Total = 2 h 15 min + 2 h 20 min = 4 hours 35 minutes

**Answer**: 4 hours 35 minutes

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### Example 3: Angle Between Clock Hands

**Problem**: What is the angle between the hour and minute hands at 3:30?

**Solution**: Using the formula: Angle = |30H − 5.5M|

H = 3, M = 30
Angle = |30 × 3 − 5.5 × 30| = |90 − 165| = |−75| = 75°

**Answer**: 75°

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### Example 4: 24-Hour to 12-Hour Conversion

**Problem**: Convert 17:45 to 12-hour format.

**Solution**:

17 − 12 = 5
Time = 5:45 PM

**Answer**: 5:45 PM

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Common Mistakes

1. **Forgetting to align decimal points when adding money**

*Wrong*: Adding ₹5.50 + ₹12.5 as 5.50 + 12.5 = 17.100
*Correct*: Write ₹12.5 as ₹12.50, then add: ₹5.50 + ₹12.50 = ₹18.00

2. **Confusing AM/PM while calculating elapsed time across noon**

*Wrong*: 10:30 AM to 1:15 PM calculated as 1:15 − 10:30 directly
*Correct*: Split at 12:00 PM—10:30 to 12:00 is 1 h 30 min; 12:00 to 1:15 is 1 h 15 min; total = 2 h 45 min

3. **Using wrong multiplier for angle calculations**

*Wrong*: Minute hand moves 5° per minute
*Correct*: Minute hand moves 6° per minute (360° ÷ 60 min)

4. **Assuming clock hands overlap 11 times in 12 hours**

*Wrong*: Hands overlap at every hour mark
*Correct*: They overlap approximately every 65.45 minutes, totaling 11 overlaps between 12:00 and 12:00 (not counting the starting 12:00 again), but including the 12:00 position gives 12 overlaps in a 12-hour span.

5. **Ignoring leap year in calendar problems**

*Wrong*: February always has 28 days
*Correct*: Check if the year is a leap year (divisible by 4; century years by 400)

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Quick Reference

₹1 = 100 paise; always convert to same unit before operating.
Minute hand: 6° per minute; Hour hand: 0.5° per minute.
Angle between hands at H:M = |30H − 5.5M|; if result >180°, use 360° − result.
Elapsed time: count from start to end; borrow 60 minutes when subtracting.
24-hour to 12-hour: subtract 12 from hours ≥13 and add PM.
Leap year test: divisible by 4; century years must be divisible by 400.

Money and Time