Money and Time
Overview
Money and Time is a foundational topic in the JKTET Paper I Mathematics section, testing a candidate's ability to handle everyday numerical situations that primary school teachers must explain to young learners. This topic bridges arithmetic operations with real-life applications—calculating totals, giving change, reading clocks, and working with calendars.
For the exam, expect questions on currency conversions (rupees and paise), bill calculations, elapsed time problems, and calendar-based reasoning (days, weeks, leap years). Mastery here demonstrates that you can teach children practical numeracy skills essential for daily life in any region of J&K.
The key challenge is unit conversion and careful arithmetic. Many errors stem from mixing rupees with paise or confusing 12-hour and 24-hour clock formats. A systematic approach to these conversions will help you score reliably.
Key Concepts
- Indian Currency System: 1 Rupee (₹) = 100 Paise. All money calculations must maintain consistent units before adding or subtracting.
- Reading and Writing Money: ₹45.75 means 45 rupees and 75 paise. The decimal point separates rupees from paise.
- Clock Reading: The short hand shows hours, the long hand shows minutes. Each number on a clock face represents 5 minutes for the minute hand.
- 12-hour vs 24-hour Format: 24-hour clock runs 00:00 to 23:59. To convert PM times: add 12 to the hour (3:00 PM = 15:00). AM times before 10:00 get a leading zero (9:00 AM = 09:00).
- Elapsed Time: Time duration between two events. Calculate by subtracting start time from end time, borrowing 60 minutes if needed.
- Calendar Structure: 1 year = 12 months = 52 weeks + 1 day (or +2 days in leap year). Ordinary year = 365 days; Leap year = 366 days.
- Leap Year Rule: A year is a leap year if divisible by 4, except century years must be divisible by 400. So 2000 was a leap year, but 1900 was not.
- Days in Months: January-31, February-28/29, March-31, April-30, May-31, June-30, July-31, August-31, September-30, October-31, November-30, December-31. Mnemonic: "30 days hath September, April, June and November."
Formulas / Key Facts
| Concept | Formula/Fact |
|---|---|
| Currency conversion | ₹1 = 100 paise; To convert paise to rupees: divide by 100 |
| Total cost | Total = Price per item × Number of items |
| Change returned | Change = Amount paid − Total cost |
| Minutes in an hour | 60 minutes = 1 hour |
| Seconds in a minute | 60 seconds = 1 minute |
| Hours in a day | 24 hours = 1 day |
| Days in a week | 7 days = 1 week |
| Leap year check | Divisible by 4 (and if century, divisible by 400) |
| Elapsed time | Duration = End time − Start time |
| 24-hour conversion (PM) | 24-hour time = 12-hour time + 12 (for PM, except 12 PM = 12:00) |
Worked Examples
Example 1: Money Calculation
Problem: Aisha buys 3 notebooks at ₹45.50 each and 2 pens at ₹12.75 each. She pays ₹200. How much change does she get?
Solution:
- Cost of notebooks = 3 × ₹45.50 = ₹136.50
- Cost of pens = 2 × ₹12.75 = ₹25.50
- Total cost = ₹136.50 + ₹25.50 = ₹162.00
- Change = ₹200.00 − ₹162.00 = ₹38.00
Example 2: Elapsed Time
Problem: A bus leaves Srinagar at 9:45 AM and reaches Jammu at 2:15 PM. How long is the journey?
Solution:
- From 9:45 AM to 12:00 noon = 2 hours 15 minutes
- From 12:00 noon to 2:15 PM = 2 hours 15 minutes
- Total duration = 2 hr 15 min + 2 hr 15 min = 4 hours 30 minutes
Alternative method: Convert to minutes from midnight, subtract, then convert back.
Example 3: Calendar Problem
Problem: If 15th August 2023 was a Tuesday, what day was 15th August 2024?
Solution:
- 2024 is a leap year (divisible by 4).
- From 15 Aug 2023 to 15 Aug 2024 = 366 days (includes Feb 29, 2024).
- 366 ÷ 7 = 52 weeks and 2 odd days.
- Tuesday + 2 days = Thursday
Example 4: Clock Problem
Problem: What is the time 3 hours 40 minutes after 10:50 AM?
Solution:
- Add hours: 10:50 + 3 hours = 1:50 PM
- Add minutes: 1:50 PM + 40 minutes = 2:30 PM
- Answer: 2:30 PM
Common Mistakes
- Mixing units in money: Adding ₹25 + 50 paise as ₹75 instead of ₹25.50. → Always convert to same unit (all rupees or all paise) before operations.
- Forgetting to borrow 60 in time subtraction: Calculating 3:15 − 1:45 as 2 hours 30 minutes instead of 1 hour 30 minutes. → When minutes to subtract are larger, borrow 1 hour (60 min) from hours column.
- Confusing 12-hour and 24-hour formats: Writing 12:30 AM as 12:30 in 24-hour format. → 12:30 AM is 00:30 in 24-hour format; 12:30 PM remains 12:30.
- Ignoring leap year in calendar problems: Counting 365 days for every year. → Always check if the period includes February of a leap year.
- Misremembering days in months: Assuming February always has 28 days or confusing 30/31 day months. → Use the knuckle method or the rhyme to verify.
Quick Reference
- ₹1 = 100 paise; always align decimal points when adding money.
- 1 hour = 60 minutes; 1 day = 24 hours; 1 week = 7 days.
- Leap year: divisible by 4 (century years must be divisible by 400).
- Ordinary year has 1 odd day; leap year has 2 odd days (for day-of-week calculations).
- PM to 24-hour: add 12 (except 12 PM stays 12:00); AM after midnight: 12 AM = 00:00.
- Elapsed time = End time − Start time (borrow 60 if minutes need it).