Money and Time

Overview

Money and Time is a fundamental topic in CG TET Paper I Mathematics that tests a candidate's ability to perform everyday calculations involving Indian currency and time measurement. This topic directly connects classroom mathematics to real-life situations, making it essential for primary-level teaching.

In the CG TET exam, questions typically involve currency conversion, addition and subtraction of money amounts, calculating total cost or change, reading clocks, converting time units, and solving problems related to calendars and duration. The pedagogy aspect expects teachers to understand how children develop concepts of money and time through concrete experiences before moving to abstract calculations.

Mastery of this topic requires comfort with decimal operations (since rupees and paise work like decimals), understanding of the 12-hour and 24-hour clock systems, and familiarity with calendar patterns including leap years.

Key Concepts

• **Indian Currency System**: 100 paise = 1 rupee. Money is written as ₹X.YZ where X is rupees and YZ is paise (e.g., ₹45.75 means 45 rupees and 75 paise).

• **Place Value in Money**: When adding or subtracting money, align the decimal point. Paise are always written as two digits (₹5.05, not ₹5.5 for 5 rupees 5 paise).

• **Time Units Hierarchy**: 60 seconds = 1 minute; 60 minutes = 1 hour; 24 hours = 1 day; 7 days = 1 week; 12 months = 1 year.

• **12-Hour vs 24-Hour Clock**: 12-hour clock uses AM (midnight to noon) and PM (noon to midnight). 24-hour clock runs 00:00 to 23:59. To convert PM time to 24-hour format, add 12 to the hour (3:30 PM = 15:30).

• **Calendar Patterns**: Ordinary year has 365 days; leap year has 366 days. Leap year occurs when the year is divisible by 4, except century years must be divisible by 400.

• **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 has September, April, June and November")

• **Duration Calculation**: To find time elapsed, subtract start time from end time. If minutes become negative, borrow 1 hour (60 minutes).

Formulas / Key Facts

| Conversion | Formula | |------------|---------| | Rupees to Paise | Rupees × 100 = Paise | | Paise to Rupees | Paise ÷ 100 = Rupees | | Hours to Minutes | Hours × 60 = Minutes | | Minutes to Seconds | Minutes × 60 = Seconds | | Days to Hours | Days × 24 = Hours |

**Key Facts to Remember:**

• 1 decade = 10 years; 1 century = 100 years
• Leap year check: Divisible by 4 (but century years must be divisible by 400)
• 2000 was a leap year; 1900 was not a leap year; 2024 is a leap year
• Odd days in ordinary year = 1; odd days in leap year = 2
• Quarter past = 15 minutes past; Half past = 30 minutes past; Quarter to = 15 minutes before

Worked Examples

**Example 1: Money Calculation** Ravi bought a notebook for ₹35.50 and a pen for ₹12.75. He gave ₹100 to the shopkeeper. How much change did he receive?

*Solution:*

• Total cost = ₹35.50 + ₹12.75 = ₹48.25
• Change = ₹100.00 − ₹48.25 = ₹51.75
• **Answer: ₹51.75**

**Example 2: Time Duration** A train departs at 9:45 AM and arrives at 2:20 PM. Find the journey time.

*Solution:*

• Start time: 9:45 AM
• End time: 2:20 PM = 14:20 (in 24-hour format)
• Method: From 9:45 to 10:00 = 15 minutes; From 10:00 to 14:00 = 4 hours; From 14:00 to 14:20 = 20 minutes
• Total = 4 hours + 15 minutes + 20 minutes = 4 hours 35 minutes
• **Answer: 4 hours 35 minutes**

**Example 3: Calendar Problem** If 15th August 2023 was 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 + 2 odd days
• Tuesday + 2 days = Thursday
• **Answer: Thursday**

**Example 4: Converting Currency** Express 4523 paise in rupees and paise.

*Solution:*

• 4523 paise = 4523 ÷ 100 = 45 rupees and 23 paise
• **Answer: ₹45.23**

Common Mistakes

• **Forgetting to align decimals in money**: Students write ₹5.5 instead of ₹5.50, then miscalculate ₹5.5 + ₹3.25 as ₹8.75 instead of the correct ₹5.50 + ₹3.25 = ₹8.75. → Always write paise as two digits.

• **Adding time like regular numbers**: Students add 3 hours 45 minutes + 2 hours 30 minutes as 5 hours 75 minutes and stop there. → Convert 75 minutes to 1 hour 15 minutes, giving 6 hours 15 minutes.

• **Confusing AM/PM conversion**: Students convert 12:30 PM to 24:30 by adding 12. → 12 PM stays as 12:00-12:59 in 24-hour format; only 1 PM onwards becomes 13:00+.

• **Leap year errors with century years**: Students assume 1900 was a leap year because 1900 ÷ 4 = 475. → Century years need divisibility by 400. 1900 ÷ 400 ≠ whole number, so not a leap year.

• **Subtracting time across midnight**: Students struggle with duration from 10:30 PM to 2:15 AM. → Break into parts: 10:30 PM to 12:00 AM = 1 hr 30 min; 12:00 AM to 2:15 AM = 2 hr 15 min; Total = 3 hr 45 min.

Quick Reference

• 100 paise = ₹1; always write paise as two digits after decimal
• 60 sec = 1 min; 60 min = 1 hr; 24 hr = 1 day
• Leap year: divisible by 4 (century years must be divisible by 400)
• PM to 24-hour: add 12 (except 12 PM stays 12:00)
• Odd days in ordinary year = 1; in leap year = 2
• February has 28 days (29 in leap year); other months alternate 30/31