Money and Time

Overview

Money and Time form essential life-skill topics in the OTET Paper I Mathematics section. These concepts test a candidate's ability to handle everyday calculations involving currency, clocks, and calendars—skills that primary teachers must confidently teach young learners.

For OTET, expect questions on currency conversion, bill calculations, finding total cost and change, reading analog and digital clocks, calculating time duration, and solving calendar-based problems (days, dates, leap years). These are typically straightforward but require careful attention to units and carry-over calculations. Mastery of this topic ensures quick marks and builds the foundation for teaching transactional mathematics to Classes I–V.

Students must be comfortable with the Indian currency system, 12-hour and 24-hour clock formats, and basic calendar arithmetic including identifying leap years and counting days between dates.

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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.

• **Conversion**: To convert rupees to paise, multiply by 100. To convert paise to rupees, divide by 100. Example: ₹7.50 = 750 paise.

• **Bill Calculation**: Total cost = Sum of (Quantity × Rate) for each item. Change = Amount paid − Total cost.

• **Clock Basics**: A clock has 12 hours marked, 60 minutes in 1 hour, 60 seconds in 1 minute. The minute hand completes one full rotation in 60 minutes; the hour hand in 12 hours.

• **12-hour vs 24-hour Format**: 12-hour uses AM (midnight to noon) and PM (noon to midnight). 24-hour format: 1:00 PM = 13:00, 11:00 PM = 23:00. Add 12 to PM hours (except 12 PM = 12:00).

• **Time Duration**: Duration = End time − Start time. When minutes are insufficient to subtract, borrow 1 hour (= 60 minutes) from the hour column.

• **Calendar Facts**: Ordinary year = 365 days. Leap year = 366 days. Leap year occurs when the year is divisible by 4 (except century years must be divisible by 400).

• **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. Mnemonic: "30 days hath September, April, June, and November."

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Formulas / Key Facts

| Concept | Formula / Fact | |---------|----------------| | Rupees to Paise | Paise = Rupees × 100 | | Paise to Rupees | Rupees = Paise ÷ 100 | | Total Cost | Total = Σ (Quantity × Unit Price) | | Change | Change = Amount Paid − Total Cost | | Time Duration | Duration = End Time − Start Time | | 24-hour Conversion | PM time (except 12 PM) → Add 12 to hour | | Leap Year Test | Divisible by 4; century years by 400 | | Odd Days in a Year | Ordinary year = 1 odd day; Leap year = 2 odd days | | Minutes in a Day | 24 × 60 = 1440 minutes | | Seconds in an Hour | 60 × 60 = 3600 seconds |

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Worked Examples

### Example 1: Money Calculation

**Problem**: Ravi bought 3 notebooks at ₹45 each and 2 pens at ₹12.50 each. He paid ₹200. Find the total cost and change received.

**Solution**:

• Cost of notebooks = 3 × 45 = ₹135
• Cost of pens = 2 × 12.50 = ₹25
• Total cost = 135 + 25 = ₹160
• Change = 200 − 160 = **₹40**

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### Example 2: Time Duration

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

**Solution**:

• Convert to same format: 9:45 AM and 2:20 PM
• From 9:45 AM to 12:00 noon = 2 hours 15 minutes
• From 12:00 noon to 2:20 PM = 2 hours 20 minutes
• Total duration = 2 hr 15 min + 2 hr 20 min = **4 hours 35 minutes**

*Alternative method*: Convert to 24-hour format.

• 9:45 and 14:20
• 14:20 − 9:45 → Borrow: 13:80 − 9:45 = 4:35 → **4 hours 35 minutes**

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### Example 3: Calendar Problem

**Problem**: If 15th August 2023 is a Tuesday, what day is 15th August 2024?

**Solution**:

• 2024 is a leap year (divisible by 4).
• From 15 Aug 2023 to 15 Aug 2024 = 366 days (leap year).
• Odd days = 366 ÷ 7 = 52 weeks + 2 days → 2 odd days.
• Tuesday + 2 days = **Thursday**

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Common Mistakes

1. **Forgetting unit conversion** → Students add ₹5 and 50 paise as ₹55. **Fix**: Always convert to the same unit (either all rupees or all paise) before adding.

2. **Ignoring AM/PM while calculating duration** → Adding 9:00 AM to 3:00 PM as 3 − 9 = negative. **Fix**: Break the problem at 12:00 noon or convert to 24-hour format.

3. **Subtracting time without borrowing** → Writing 3:15 − 1:45 = 2:30. **Fix**: 3:15 → 2:75, then 2:75 − 1:45 = 1:30.

4. **Leap year confusion for century years** → Assuming 1900 is a leap year. **Fix**: Century years must be divisible by 400. So 1900 is not a leap year, but 2000 is.

5. **Miscounting days in months** → Forgetting that February has 28 or 29 days. **Fix**: Use the "30 days hath September" rhyme and check for leap year.

6. **Confusing 12-hour notation** → Writing 12:30 AM as afternoon. **Fix**: 12:00 AM = midnight; 12:00 PM = noon.

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Quick Reference

• **₹1 = 100 paise** — always convert before operating on mixed units.

• **Leap year**: divisible by 4; century years must be divisible by 400.

• **Ordinary year = 365 days = 52 weeks + 1 odd day.**

• **PM to 24-hour**: Add 12 (except 12 PM stays 12:00).

• **Time subtraction**: Borrow 60 minutes when needed, reduce hour by 1.

• **Days in Feb**: 28 normally, 29 in a leap year.