Money and Time

Overview

Money and Time form a foundational topic in Paper I Mathematics, testing a candidate's ability to handle everyday calculations that primary school teachers must teach confidently. Questions typically involve currency conversions, bill calculations, reading clocks, and calendar-based problems. This topic carries moderate weightage but offers easy scoring opportunities for well-prepared candidates.

The practical nature of this topic means questions often appear as word problems set in real-life contexts—shopping scenarios, travel schedules, or event planning. Mastery requires not just computational skill but also the ability to visualise clock faces and mentally navigate calendar structures. Since Assam TET emphasises linking mathematics to community life, expect problems involving local contexts like weekly haats, Bihu festival timings, or tea garden wage calculations.

Key Concepts

• **Indian Currency System**: 1 Rupee = 100 Paise. Notes available: ₹10, ₹20, ₹50, ₹100, ₹200, ₹500, ₹2000. Coins: 50 paise, ₹1, ₹2, ₹5, ₹10.

• **Conversion between units**: Always convert to the same unit (all rupees or all paise) before adding, subtracting, or comparing amounts.

• **Clock as a circle**: A clock face is divided into 12 hours, 60 minutes. Each hour mark represents 5 minutes. The minute hand completes one full rotation in 60 minutes; the hour hand in 12 hours.

• **Angle between hands**: In 1 minute, the minute hand moves 6° and the hour hand moves 0.5°. The relative speed is 5.5° per minute.

• **12-hour vs 24-hour format**: AM covers midnight to noon (12:00 AM to 11:59 AM); PM covers noon to midnight. In 24-hour format, add 12 to PM hours (3:00 PM = 15:00).

• **Calendar structure**: A regular year has 365 days (52 weeks + 1 odd day). A leap year has 366 days (52 weeks + 2 odd 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. Memory aid: "30 days has September, April, June and November."

• **Odd days concept**: The remainder when total days are divided by 7 gives the odd days, used to find the day of the week.

Formulas / Key Facts

| Concept | Formula/Fact | |---------|--------------| | Rupees to Paise | ₹1 = 100 paise | | Total cost | Total = Rate per unit × Number of units | | Change returned | Change = Amount given − Total cost | | Minutes to hours | Hours = Minutes ÷ 60 | | Angle of minute hand | Angle from 12 = Minutes × 6° | | Angle of hour hand | Angle from 12 = (Hours × 30) + (Minutes × 0.5°) | | Angle between hands | |Hour angle − Minute angle| (take smaller of two) | | Leap year test | Divisible by 4; century years must be divisible by 400 | | Odd days in regular year | 1 odd day | | Odd days in leap year | 2 odd days | | Time duration | End time − Start time (borrow 60 if needed for minutes) |

Worked Examples

**Example 1: Money Calculation**

*Rina buys 3 notebooks at ₹45.50 each and 2 pens at ₹12.75 each. She pays ₹200. What change does she receive?*

Step 1: Cost of notebooks = 3 × ₹45.50 = ₹136.50 Step 2: Cost of pens = 2 × ₹12.75 = ₹25.50 Step 3: Total cost = ₹136.50 + ₹25.50 = ₹162.00 Step 4: Change = ₹200 − ₹162 = **₹38.00**

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**Example 2: Clock Angle Problem**

*Find the angle between the hour and minute hands at 3:20.*

Step 1: Hour hand position = (3 × 30) + (20 × 0.5) = 90 + 10 = 100° from 12 Step 2: Minute hand position = 20 × 6 = 120° from 12 Step 3: Angle between = |120 − 100| = **20°**

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**Example 3: Time Duration**

*A bus leaves Guwahati at 9:45 AM and reaches Jorhat at 2:15 PM. What is the journey time?*

Step 1: From 9:45 AM to 12:00 noon = 2 hours 15 minutes Step 2: From 12:00 noon to 2:15 PM = 2 hours 15 minutes Step 3: Total = 2h 15m + 2h 15m = **4 hours 30 minutes**

Alternative method: Convert to minutes, subtract, convert back.

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**Example 4: Calendar Problem**

*If 15th August 2023 was a Tuesday, what day was 15th August 2024?*

Step 1: Check if 2024 is a leap year → 2024 ÷ 4 = 506 (yes, leap year) Step 2: Period from 15 Aug 2023 to 15 Aug 2024 includes Feb 2024 (leap year) Step 3: Total days = 366 (one complete year with Feb 29) Step 4: Odd days = 366 ÷ 7 = 52 weeks + 2 odd days Step 5: Tuesday + 2 days = **Thursday**

Common Mistakes

• **Forgetting to align units** → Students add ₹45 and 50 paise as ₹95. Fix: Convert everything to paise (4500 + 50 = 4550 paise = ₹45.50) or keep decimals aligned.

• **Confusing AM/PM boundaries** → Calculating duration from 10:30 AM to 1:15 PM incorrectly by subtracting directly. Fix: Break the problem at 12:00 noon, calculate each segment, then add.

• **Using 30° per hour for minute hand** → The hour hand moves 30° per hour; the minute hand moves 360° per hour (6° per minute). Fix: Remember minute hand is faster—it completes full circle in one hour.

• **Miscounting odd days** → Forgetting that the starting day should not be counted, or double-counting endpoints. Fix: Count from the day after the start date to the end date inclusive.

• **Leap year errors with century years** → Treating 1900 as a leap year. Fix: Century years (1800, 1900, 2100) are NOT leap years unless divisible by 400 (2000 was a leap year).

• **Clock angle exceeding 180°** → Reporting 340° instead of the acute/obtuse angle. Fix: If calculated angle exceeds 180°, subtract from 360° to get the smaller angle.

Quick Reference

• ₹1 = 100 paise; always convert to same unit before operations

• Minute hand: 6° per minute; Hour hand: 0.5° per minute

• Leap year: divisible by 4 (centuries must be divisible by 400)

• Regular year = 1 odd day; Leap year = 2 odd days

• Duration across noon: split at 12:00, calculate separately, then add

• Months with 30 days: April, June, September, November