Mental Ability · Lesson 6

Measurement, Time & Calendar

Climb the metric ladder for length, mass and capacity, read any clock, switch between a.m./p.m. and railway time, work out journey times — and find the day of any date with a neat counting trick.

~45 min read8 quick checksTest: 20 questions

1Metric units and the conversion ladder

We measure length (how long), mass (how heavy) and capacity (how much liquid a container holds). The metric system makes every unit 10, 100 or 1000 times another — so converting is just multiplying or dividing.

Quantity	Units you must know	Used for
Length	1 km = 1000 m 1 m = 100 cm 1 cm = 10 mm so 1 m = 1000 mm	km: distance between cities; m: a room; cm: a pencil; mm: an ant
Mass	1 kg = 1000 g 1 g = 1000 mg (also 1 quintal = 100 kg, 1 tonne = 1000 kg)	kg: a person, a bag of rice; g: a biscuit; mg: medicine
Capacity	1 L = 1000 mL 1 kL = 1000 L	L: a bucket, a bottle; mL: a spoon, a cup; kL: a water tank

The length ladder. Mass (kg → g → mg) and capacity (L → mL) work the same way with × 1000.

Remember: King Henry Died By Drinking Chocolate Milk = kilo, hecto, deca, Base unit (metre, gram, litre), deci, centi, milli. Each step down the list is × 10. So kilo is 1000 × the base unit and milli is one-thousandth of it.

Prefix	Meaning	Length	Mass	Capacity
kilo (k)	× 1000	1 km = 1000 m	1 kg = 1000 g	1 kL = 1000 L
hecto (h)	× 100	1 hm = 100 m	1 hg = 100 g	1 hL = 100 L
deca (da)	× 10	1 dam = 10 m	1 dag = 10 g	1 daL = 10 L
base	× 1	metre (m)	gram (g)	litre (L)
deci (d)	÷ 10	1 dm = 0.1 m	1 dg = 0.1 g	1 dL = 0.1 L
centi (c)	÷ 100	1 cm = 0.01 m	1 cg = 0.01 g	1 cL = 0.01 L
milli (m)	÷ 1000	1 mm = 0.001 m	1 mg = 0.001 g	1 mL = 0.001 L

💡 Sense check

When you change to a smaller unit you need more of them, so the number gets bigger (2 m = 200 cm). When you change to a bigger unit the number gets smaller (3500 g = 3.5 kg). If your answer goes the wrong way, you multiplied when you should have divided.

2Converting mixed units

Many answers are written in two units, like 3 km 45 m or 6 kg 75 g. To change these into one unit, convert the big part and add the small part.

✏️ Worked examples — to the smaller unit

3 km 45 m = 3 × 1000 m + 45 m = 3000 + 45 = 3045 m (not 3450 m!).
5 km 7 m = 5000 + 7 = 5007 m.
7 m 5 cm = 700 + 5 = 705 cm.
3 L 400 mL = 3000 + 400 = 3400 mL.
2.5 km = 2.5 × 1000 = 2500 m (point hops 3 places right).

✏️ Worked examples — to the bigger unit

6075 g: 1000 g make 1 kg, so 6075 g = 6 kg and 75 g left over = 6 kg 75 g = 6.075 kg.
2350 mL = 2 L 350 mL = 2.35 L.
45 mm = 4 cm 5 mm = 4.5 cm.
365 cm = 3 m 65 cm = 3.65 m.

⚠️ Olympiad trap — the missing zero

3 km 45 m is not 3450 m and not 345 m. A kilometre has 1000 metres, so the metres part always takes three places: 3 km 45 m = 3045 m, and 3 km 5 m = 3005 m. Same with grams and millilitres. Centimetres take two places (1 m = 100 cm): 7 m 5 cm = 705 cm.

✏️ Worked example — which is longest?

1 km 50 m, 1005 m, 1 km 500 m, 15000 cm

Change all to metres: 1050 m, 1005 m, 1500 m, and 15000 cm ÷ 100 = 150 m.
Longest: 1 km 500 m. (15000 looks biggest but it is only 150 m!)

Reading a ruler

Each small gap on a centimetre ruler is 1 mm; 10 small gaps make 1 cm. If an object does not start at 0, subtract the start mark from the end mark.

The bar starts at 3 cm and ends at 7.5 cm, so its length = 7.5 − 3 = 4.5 cm = 45 mm.

5 km 8 m is equal to:

5800 m
5080 m
5008 m
508 m

5 km = 5000 m. 5000 + 8 = 5008 m. The metres part needs three places: 5 km 008 m.

3Adding, subtracting and word problems

Write measures in columns — big unit under big unit, small unit under small unit. When the small unit reaches 1000 (or 100 for cm), carry 1 to the big unit. When you can't subtract, borrow 1 big unit = 1000 small units.

✏️ Worked example — adding with a carry

4 kg 650 g + 2 kg 575 g

Grams: 650 + 575 = 1225 g = 1 kg 225 g → write 225 g, carry 1 kg.
Kilograms: 4 + 2 + 1 = 7 kg.
Answer: 7 kg 225 g.

✏️ Worked example — subtracting with a borrow

A tank has 10 L of water. 3 L 750 mL is used. How much is left?

Write 10 L as 9 L 1000 mL (borrow 1 L = 1000 mL).
mL: 1000 − 750 = 250 mL. L: 9 − 3 = 6 L.
Answer: 6 L 250 mL. Check: 6 L 250 mL + 3 L 750 mL = 10 L ✓

✏️ Worked example — how many pieces?

A ribbon is 5 m long. How many pieces of 25 cm can be cut from it?

Use the same unit: 5 m = 500 cm.
500 ÷ 25 = 20 pieces.
Similarly, a 2 L bottle fills 2000 ÷ 250 = 8 glasses of 250 mL.

Water is at 600 mL. To fill up to 1 L, add 1000 − 600 = 400 mL.

5 equal tins balance 2 kg. One tin = 2000 g ÷ 5 = 400 g.

3 kg 700 g + 1 kg 450 g = ?

4 kg 1150 g
5 kg 150 g
4 kg 150 g
5 kg 50 g

700 g + 450 g = 1150 g = 1 kg 150 g. Carry 1 kg: 3 + 1 + 1 = 5 kg. Answer 5 kg 150 g. ("4 kg 1150 g" has the same value but is not written properly — grams must be less than 1000.)

4Reading clocks and a.m. / p.m.

An analogue clock has a short, thick hour hand and a long minute hand (many clocks also have a thin second hand). The minute hand goes all the way round in 60 minutes; each small mark is 1 minute and each number is 5 minutes. The hour hand takes 12 hours to go round once.

4:40 — minute hand on 8 (8 × 5 = 40); hour hand two-thirds of the way from 4 to 5.

9:15 (quarter past 9) — minute hand on 3; hour hand just past 9.

⚠️ Olympiad trap — the hour hand moves too

At 4:40 the hour hand is not on 4 — it has moved 40/60 = two-thirds of the way towards 5. Also, when the hour hand is between two numbers, the hour is the smaller number (between 4 and 5 → it's 4-something). Pink = hour hand, blue = minute hand in the pictures.

a.m. and p.m.

a.m. (ante meridiem = before midday): from 12 midnight to just before 12 noon.
p.m. (post meridiem = after midday): from 12 noon to just before 12 midnight.
12 noon is written 12:00 p.m.; 12 midnight is 12:00 a.m. — the start of a new day.
Morning school at 8:00 a.m.; lunch at 1:00 p.m.; dinner at 8:00 p.m.

At 9:15, where exactly is the hour hand?

Exactly on 9
A little past 9, towards 10
Exactly on 3
Between 8 and 9

In 15 minutes the hour hand moves a quarter of the way from 9 to 10, so it is a little past 9.

5The 24-hour clock (railway time)

Railways, airlines and phones often use the 24-hour clock. The hours run from 00:00 (midnight) to 23:59, so there is no need for a.m. or p.m. It is always written with four digits.

One day = 24 hours. After 12 noon, the 24-hour clock keeps counting: 13, 14, 15 … 23.

Rule	12-hour	24-hour
a.m. (1 to 11): same, add a 0 in front if needed	6:05 a.m.	06:05
p.m. (1 to 11): add 12 to the hour	3:15 p.m.	15:15
p.m.: add 12	11:40 p.m.	23:40
12 noon hour: stays 12	12:45 p.m.	12:45
12 midnight hour: becomes 00	12:30 a.m.	00:30
24-hour to 12-hour: hour above 12 → subtract 12, p.m.	6:20 p.m.	18:20

⚠️ Olympiad trap — the two twelves

12:30 a.m. is half an hour after midnight → 00:30. 12:30 p.m. is half an hour after noon → 12:30. Don't add 12 to a 12 p.m. time (that would give 24:30, which doesn't exist!).

A train leaves at 18:45. What is this in 12-hour time?

8:45 p.m.
6:45 a.m.
6:45 p.m.
18:45 p.m.

18 is more than 12, so subtract 12: 18 − 12 = 6. It is after noon → 6:45 p.m.

6Converting units of time

Bigger unit	Equals
1 minute	60 seconds
1 hour	60 minutes = 3600 seconds
1 day	24 hours
1 week	7 days
1 year	12 months = 52 weeks and 1 day (365 days); a leap year has 366 days
half an hour / quarter of an hour	30 minutes / 15 minutes

✏️ Worked examples

248 minutes = ? 60 goes into 248 four times (240), 8 left → 4 h 8 min.
3 h 20 min = 3 × 60 + 20 = 180 + 20 = 200 min.
2 days 5 hours = 2 × 24 + 5 = 53 hours.
7200 seconds = 7200 ÷ 60 = 120 min = 2 hours.
45 days = 6 weeks and 3 days (6 × 7 = 42, 3 left).

⚠️ Olympiad trap — time is not decimal!

1 hour = 60 minutes, not 100. So 2.5 hours = 2 h 30 min (not 2 h 50 min), and 1 h 45 min + 30 min = 2 h 15 min (not 1 h 75 min). Whenever minutes reach 60, carry 1 hour.

✏️ Worked example — ages in years and months (real olympiad question)

Mrs Tendulkar is three times as old as her daughter, who is 9 years 6 months old. How old is Mrs Tendulkar?

3 × 9 years = 27 years; 3 × 6 months = 18 months.
18 months = 1 year 6 months (12 months = 1 year).
27 years + 1 year 6 months = 28 years 6 months.

4 hours 25 minutes is how many minutes?

4 × 60 = 240; 240 + 25 = 265 minutes.

7Elapsed time and timetables

Elapsed time is how much time passes between a start and an end. The safest method is the bridge method: hop to the next full hour, then jump whole hours, then add the leftover minutes.

✏️ Worked example — same day

A class trip left at 10:45 a.m. and returned at 2:15 p.m. How long was it?

10:45 → 11:00 = 15 min.
11:00 a.m. → 2:00 p.m. = 3 h (11 → 12 → 1 → 2).
2:00 → 2:15 = 15 min.
Total = 3 h + 15 + 15 min = 3 h 30 min.

Overnight journey 22:40 → 05:15: 20 min + 6 h + 15 min = 6 h 35 min.

✏️ Worked example — railway timetable

Station	Arrives	Departs
Asanpur	—	06:45
Bela Junction	09:20	09:30
Chandnagar	13:05	—

Asanpur → Bela: 06:45 → 07:00 (15 min) → 09:00 (2 h) → 09:20 (20 min) = 2 h 35 min.
Halt (stop) at Bela = 09:30 − 09:20 = 10 min.
Bela → Chandnagar: 09:30 → 10:00 (30 min) → 13:00 (3 h) → 13:05 (5 min) = 3 h 35 min.
Whole journey: 06:45 → 13:05 = 6 h 20 min. Check: 2 h 35 + 10 min + 3 h 35 = 6 h 20 min ✓

✏️ Worked example — finding the end or the start

A film starts at 4:50 p.m. and lasts 2 h 45 min. It ends at 4:50 + 2 h = 6:50, + 45 min = 7:35 p.m.
A bus reaches at 1:10 p.m. after a 3 h 25 min ride. Go back: 1:10 − 3 h = 10:10 a.m.; 10:10 − 25 min = 9:45 a.m.

✏️ Worked example — "in … hours it will be" (real olympiad question)

If it will be 10 a.m. in 11 hours, then it was 10 a.m. how many hours ago?

Find "now": 10 a.m. − 11 hours = 11 p.m. (of the day before).
Go back from 11 p.m. to the previous 10 a.m.: 10 a.m. → 10 p.m. is 12 h, plus 1 h to 11 p.m. = 13 h.
Answer: 13 hours ago. Shortcut: the two 10 a.m.s are 24 h apart, so 24 − 11 = 13.

A night train leaves at 20:50 and arrives at 04:10 the next morning. How long is the journey?

8 h 40 min
16 h 40 min
7 h 40 min
7 h 20 min

20:50 → 21:00 = 10 min; 21:00 → 04:00 = 7 h; 04:00 → 04:10 = 10 min. Total 7 h 20 min.

8The calendar and leap years

A year has 12 months. Some months have 31 days, some 30, and February has 28 (or 29 in a leap year). The knuckle trick helps you remember:

Make fists: every knuckle (blue) is a 31-day month; every gap (orange) is 30 days, except February. July and August are two knuckles in a row.

Remember: "Thirty days has September, April, June and November. All the rest have thirty-one, except February alone, which has 28 days clear, and 29 in each leap year."

Leap years

An ordinary year has 365 days. A leap year has 366 days — the extra day is 29 February.
Rule 1: a year divisible by 4 is a leap year: 2016, 2020, 2024, 2028. (Check the last two digits: 24 ÷ 4 = 6 ✓.)
Rule 2: a century year (ending in 00) must be divisible by 400: 2000 and 1600 were leap years; 1900 and 2100 are not.
365 days = 52 weeks + 1 day. 366 days = 52 weeks + 2 days.

⚠️ Olympiad trap — century years

1900 ÷ 4 works, but 1900 is not a leap year because 1900 ÷ 400 does not divide exactly. 2000 ÷ 400 = 5 exactly, so 2000 was a leap year.

Counting days

✏️ Worked example — "counting both days"

How many days from 10 February to 20 March 2026, counting both days?

2026 is not a leap year, so February has 28 days.
February: 10 to 28 inclusive = 28 − 10 + 1 = 19 days.
March: 1 to 20 = 20 days.
Total = 19 + 20 = 39 days. (If you are told not to count the first day, it is 38.)

💡 Shortcut — the "+1" rule

From day 5 to day 12 of a month: 12 − 5 = 7 days after, but 8 days if you count both ends. Picture fence posts: 5, 6, 7, 8, 9, 10, 11, 12 — that's 8 posts.

Which of these years is NOT a leap year?

2000
2024
2100
2016

2100 is a century year. 2100 ÷ 400 is not exact, so it is not a leap year (even though 2100 ÷ 4 works). 2000 ÷ 400 = 5, so 2000 was a leap year.

9Finding the day of a date

Days of the week repeat every 7 days. So after 7, 14, 21, 28 … days it is the same weekday again. Only the extra days (the remainder when you divide by 7) move the weekday forward. These extra days are called odd days.

Days in the month	Odd days (÷ 7 remainder)	Same date next month moves
31	3	3 days forward
30	2	2 days forward
29 (leap Feb)	1	1 day forward
28 (Feb)	0	same day!
365-day year	1	same date next year: 1 day forward
366-day year (29 Feb in between)	2	2 days forward

✏️ Worked example — next month

5 September 2026 is a Saturday. What day is 5 October 2026?

September has 30 days → 30 = 4 weeks + 2 odd days.
Saturday + 2 days → Sunday, Monday.

✏️ Worked example — a few weeks later

2 October 2026 (Gandhi Jayanti) is a Friday. What day is 14 November 2026 (Children's Day)?

Days left in October after the 2nd: 31 − 2 = 29. Add 14 days of November: 29 + 14 = 43 days later.
43 ÷ 7 = 6 weeks, remainder 1.
Friday + 1 = Saturday.

✏️ Worked example — next year

15 August 2026 is a Saturday. What day is 15 August 2027?

Between them there is no 29 February (2027 is not a leap year), so 365 days pass = 52 weeks + 1 day.
Saturday + 1 = Sunday.

September 2026 has 30 days = 4 weeks + 2 days. So the first two weekdays of the month — Tuesday and Wednesday — appear 5 times; every other weekday appears 4 times.

💡 Shortcut — how many Mondays?

Every month has 4 full weeks (28 days). The extra days (0, 1, 2 or 3) are the weekdays that appear a 5th time — they are the weekdays of the 1st, 2nd and 3rd of the month. So in a 31-day month starting on Friday, Friday, Saturday and Sunday each occur 5 times.

⚠️ Olympiad trap — counting forward from the wrong day

If 3rd is Monday, then 10th, 17th, 24th and 31st are also Mondays (add 7 each time). Many students write 9th because they count the 3rd as "one". Adding 7 to the date is safest.

10 May is a Wednesday. What day of the week is 10 June of the same year?

Saturday
Friday
Wednesday
Sunday

May has 31 days = 4 weeks + 3 odd days. Wednesday + 3 = Saturday.

Explore

10Quick recap

1 km = 1000 m, 1 m = 100 cm, 1 cm = 10 mm; 1 kg = 1000 g; 1 L = 1000 mL.
Big → small unit: multiply. Small → big unit: divide.
Metres in a km, grams in a kg, mL in a L take 3 places: 3 km 45 m = 3045 m.
Carry 1 big unit when small units reach 1000 (or 100 for cm); borrow 1 big unit = 1000 small units.
Ruler not starting at 0? Length = end mark − start mark.
Hour hand = short; minute hand = long. The hour hand moves between numbers as minutes pass.
a.m. = midnight to noon; p.m. = noon to midnight.
24-hour clock: p.m. hours add 12 (3:15 p.m. = 15:15); 12:30 a.m. = 00:30; 12:30 p.m. = 12:30.
1 h = 60 min, 1 day = 24 h, 1 week = 7 days. Time is not decimal: 2.5 h = 2 h 30 min.
Elapsed time: bridge to the next hour, jump hours, add leftover minutes.
31-day months: Jan, Mar, May, Jul, Aug, Oct, Dec. 30-day: Apr, Jun, Sep, Nov. Feb: 28/29.
Leap year: divisible by 4; century years must be divisible by 400 (2000 yes, 1900 no).
Odd days: 31-day month → +3, 30 → +2, 28 → 0; next year → +1 (or +2 across 29 Feb).
"Counting both days" means end − start + 1.

Flip cards

Question2 kg 50 g = ? g

Answer2050 g

Question3750 mL = ? L ? mL

Answer3 L 750 mL (= 3.75 L)

Question9:25 p.m. in 24-hour time?

Answer21:25

Question00:15 in 12-hour time?

Answer12:15 a.m. (15 minutes after midnight)

Question150 minutes = ?

Answer2 h 30 min

Question8:40 a.m. to 1:05 p.m. = ?

Answer20 min + 4 h + 5 min = 4 h 25 min

QuestionIs 1800 a leap year?

AnswerNo — century year not divisible by 400.

Question1 April is Monday. What day is 1 May?

AnswerApril has 30 days → +2 → Wednesday.