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) |