Money and Time — Study Notes for Bihar TET Paper I

Overview

Money and Time form a foundational topic in primary mathematics that connects classroom learning directly to everyday life. For Bihar TET Paper I, this topic tests your ability to solve practical problems involving currency calculations, reading clocks, and understanding calendars — skills that primary teachers must effectively impart to Classes I–V students.

Questions typically appear in the Mathematics section (30 marks total) and often integrate with other topics like fractions, decimals, and basic operations. The pedagogy component may also ask how to teach these concepts using real-life contexts. Mastery requires fluency in Indian currency denominations, conversion between time units, and quick mental calculations for clock and calendar problems.

Students must be comfortable with rupee-paise conversions, reading both analog and digital clocks, calculating time intervals, and solving problems involving days, weeks, months, and years. These concepts frequently appear as word problems requiring careful reading and systematic solving.

Key Concepts

• **Indian Currency System**: India uses the decimal system — 1 Rupee (₹) = 100 Paise. Notes: ₹10, ₹20, ₹50, ₹100, ₹200, ₹500, ₹2000. Coins: 50 paise, ₹1, ₹2, ₹5, ₹10.

• **Money as Decimal**: ₹45.75 means 45 rupees and 75 paise. The decimal point separates rupees from paise, making money calculations excellent practice for decimal operations.

• **Clock Reading**: Analog clocks have hour hand (short, slow) and minute hand (long, fast). Hour hand completes one round in 12 hours; minute hand completes one round in 60 minutes.

• **Time Units Hierarchy**: 1 minute = 60 seconds, 1 hour = 60 minutes, 1 day = 24 hours, 1 week = 7 days, 1 year = 365 days (366 in leap year), 1 year = 12 months.

• **12-Hour vs 24-Hour Format**: 12-hour uses AM (midnight to noon) and PM (noon to midnight). 24-hour format runs 00:00 to 23:59. To convert PM time to 24-hour: add 12 to the hour (except 12 PM = 12:00).

• **Leap Year Rule**: A year is a leap year if divisible by 4, except century years which must be divisible by 400. So 2000 was a leap year, but 1900 was not.

• **Calendar Structure**: Months with 31 days — January, March, May, July, August, October, December. Months with 30 days — April, June, September, November. February — 28 or 29 days.

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 |

**Clock Angle Facts:**

• Minute hand moves 6° per minute (360° ÷ 60)
• Hour hand moves 0.5° per minute (30° ÷ 60)
• Hour hand moves 30° per hour

**Odd Days Calculation (for finding day of week):**

• Ordinary year = 1 odd day
• Leap year = 2 odd days
• 100 years = 5 odd days
• 400 years = 0 odd days

**Month Code for Day Calculation:** Jan=0, Feb=3, Mar=3, Apr=6, May=1, Jun=4, Jul=6, Aug=2, Sep=5, Oct=0, Nov=3, Dec=5

Worked Examples

### Example 1: Money Calculation **Problem:** Raju 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:**

• Step 1: Total cost = ₹35.50 + ₹12.75 = ₹48.25
• Step 2: Change = ₹100.00 − ₹48.25 = ₹51.75
• **Answer:** Raju received ₹51.75 as change.

### Example 2: Time Duration **Problem:** A train departs at 9:45 AM and arrives at 2:20 PM. What is the total journey time?

**Solution:**

• Step 1: From 9:45 AM to 12:00 PM = 2 hours 15 minutes
• Step 2: From 12:00 PM to 2:20 PM = 2 hours 20 minutes
• Step 3: Total = 2 hr 15 min + 2 hr 20 min = 4 hours 35 minutes
• **Answer:** Journey time is 4 hours 35 minutes.

### Example 3: Calendar Problem **Problem:** If 15th August 2023 was Tuesday, what day was 15th August 2024?

**Solution:**

• Step 1: Check if 2024 is a leap year — Yes (divisible by 4)
• Step 2: From Aug 15, 2023 to Aug 15, 2024 includes Feb 29, 2024
• Step 3: Total days = 366 (leap year)
• Step 4: Odd days = 366 ÷ 7 = 52 weeks + 2 days
• Step 5: Tuesday + 2 days = Thursday
• **Answer:** 15th August 2024 was Thursday.

### Example 4: Clock Problem **Problem:** What is the angle between the hour and minute hands at 3:30?

**Solution:**

• Step 1: At 3:30, minute hand is at 6 (180° from 12)
• Step 2: Hour hand at 3:00 is at 90°. In 30 minutes, it moves 30 × 0.5° = 15°
• Step 3: Hour hand position = 90° + 15° = 105°
• Step 4: Angle between hands = 180° − 105° = 75°
• **Answer:** The angle is 75°.

Common Mistakes

• **Forgetting to carry over in time addition** → When minutes exceed 60, convert to hours. Example: 2 hr 45 min + 1 hr 30 min = 3 hr 75 min = 4 hr 15 min, not 3 hr 75 min.

• **Confusing AM/PM in duration problems** → Students calculate 10 AM to 2 PM as 8 hours (10+2=12, then subtract incorrectly). Correct method: count hours forward or split at noon.

• **Decimal errors in money** → Writing ₹5.5 as 5 rupees 5 paise instead of 5 rupees 50 paise. Remember: two digits after decimal for paise.

• **Leap year miscalculation** → Assuming all years divisible by 4 are leap years. Century years (1900, 2100) are NOT leap years unless divisible by 400.

• **Clock hand confusion** → Assuming hour hand stays fixed between hours. At 4:30, the hour hand is halfway between 4 and 5, not exactly at 4.

Quick Reference

• ₹1 = 100 paise; always write paise as two-digit decimal (₹3.05, not ₹3.5 for 3 rupees 5 paise)
• 1 hour = 60 min = 3600 seconds; 1 day = 24 hours = 1440 minutes
• Minute hand: 6° per minute; Hour hand: 0.5° per minute
• Leap year: divisible by 4 (but centuries must divide by 400)
• "30 days has September, April, June and November" — rest have 31 except February
• For day calculation: count odd days (remainder when total days ÷ 7)