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.
They are usually straightforward calculation problems but can trip students who confuse units or misread clock positions.
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.
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 |
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:
- Total cost = ₹45.75 + ₹18.50 = ₹64.25
- Change = ₹100.00 − ₹64.25 = ₹35.75
Answer: ₹35.75
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:
- From 9:45 AM to 12:00 PM = 2 hours 15 minutes
- From 12:00 PM to 2:20 PM = 2 hours 20 minutes
- Total = 2 h 15 min + 2 h 20 min = 4 hours 35 minutes
Answer: 4 hours 35 minutes
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°
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
Common Mistakes
- 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
- 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
- Using wrong multiplier for angle calculations
- Wrong: Minute hand moves 5° per minute
- Correct: Minute hand moves 6° per minute (360° ÷ 60 min)
- 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.
- 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)
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.