How to solve clock, calendar and age problems
Clocks, calendars, ages: one relation, then arithmetic
Three word-problem staples with one shared method: translate the wording into a single exact relation, evaluate it, then answer precisely what was asked.
Updated
Clock angles, day-of-week spans, and age riddles look like three topics but reward one habit: the reasoning is in SETTING UP the relation, and the arithmetic afterwards is easy. Most points lost in this family are lost after the maths is done — to answering a slightly different question than the one asked.
Clocks: two hands, two speeds
The minute hand moves 6° per minute. The hour hand moves 30° per hour PLUS 0.5° for every minute — it drifts off the hour mark continuously. Compute both positions from 12, take the difference, and give the SMALLER angle (if the gap exceeds 180°, answer 360° minus it). The classic error is leaving the hour hand parked on the hour; the second classic is reporting the reflex angle.
Calendars: divide by 7
Count the exact days between the two dates — month lengths, carefully — then keep only the remainder after dividing by 7. Step that many weekdays forward from the known day. Counting day by day is where the errors live; the remainder step is where the answer lives.
Ages: name the unknown, write both facts
'A is 4 times as old as B; in 6 years A will be twice as old' is two equations in one unknown. Write them, solve, then CHECK by pushing both ages forward — the check takes five seconds and catches everything. Then answer the person asked, TODAY: the option list carries the other person's age and both future ages.
The strategy
- Spot which of the three forms it is.
- Write the relation before touching numbers.
- Evaluate; sanity-check against the wording.
- Re-read the question: smaller angle? which person? which date?
Common traps
- The hour hand treated as parked on the hour mark.
- The reflex angle reported instead of the smaller one.
- A 30-day month counted as 31 inside the span.
- The right equations solved for the wrong person — or the right person at the wrong time.
Speed · ~60s/item: Roughly 30–110 seconds across the three forms. The set-up deserves two-thirds of the time; rushed set-up is where this family bleeds points.
Try it yourself: 4 practice questions
Pick an answer, then reveal it. Nothing is recorded, there is no clock, and none of these questions is ever used in a test.
Dana is 4 times as old as Kofi. In 6 years' time, Dana will be 2 times as old as Kofi. How old is Dana now?
Reveal the answer
The answer is D — 12.
Show why — the worked reasoning
Dana is 4 times as old as Mara. In 8 years' time, Dana will be 3 times as old as Mara. How old is Dana now?
Reveal the answer
The answer is D — 64.
Show why — the worked reasoning
In 2032, 24 February falls on a Tuesday. What day of the week is 11 March 2032?
Reveal the answer
The answer is B — Thursday.
Show why — the worked reasoning
In 2029, 12 November falls on a Monday. What day of the week is 29 November 2029?
Reveal the answer
The answer is C — Thursday.
Show why — the worked reasoning
Try questions like this
The free test has 20 questions across abstract, numerical, verbal and spatial reasoning. It takes 12 minutes, needs no sign-up, and explains every answer.
A free account opens every lesson, practice drills and a study plan built from your results.
Questions people ask
Will clocks, calendars and ages questions be on the free test?
Maybe. The free test gives numerical reasoning 5 of its 20 questions, spread across 13 different question types, so any one test may or may not include this kind.