How to Solve Faulty Clock (Gaining/Losing Time) Problems
Solve faulty clock aptitude problems using a clock-time-to-true-time rate ratio, with worked examples for gaining and losing clocks.
Expected Interview Answer
A faulty clock problem is solved by comparing the clock’s own elapsed time to the true elapsed time between two known-correct checkpoints, forming a ratio, and scaling that ratio to answer whatever gain, loss, or future-time question is asked.
If a clock shows a correct time at one instant and again shows a correct-looking time later, the true elapsed time and the clock’s displayed elapsed time between those two checkpoints let you compute the rate at which the faulty clock runs: rate = (clock’s elapsed time) / (true elapsed time). Any future prediction — what the faulty clock will show after N true hours, or how much true time has passed when the faulty clock shows a given duration — is then found by multiplying or dividing by that same rate. The standard “gains/loses X minutes every Y hours” phrasing directly gives the rate as (Y ± X/60)/Y hours of clock time per hour of true time. Always keep clear which direction the ratio goes: converting true time to clock time multiplies by the rate, while converting clock time back to true time divides by it.
- One rate ratio handles both gaining and losing clock problems
- The same technique answers “what will it show” and “how much true time passed” questions
- Explicit true-time vs clock-time direction avoids the most common sign error
AI Mentor Explanation
A stopwatch that runs slightly fast, timing a bowler’s run-up as 6.1 seconds when the real run-up took 6 seconds, has a fixed rate of 6.1/6 clock-seconds per true-second. Using that same ratio, you can predict what the faulty stopwatch will read for any other true duration, or reverse it to find the true duration behind any faulty reading — exactly the ratio technique used to solve faulty clock problems.
Worked example
Rate
- 1450 clock-min / 1440 true-min
True elapsed
- 72 hours = 4320 true-min
Clock elapsed
- 4320 × 1450/1440 = 4350 min = 72.5h
Step-by-Step Explanation
Step 1
Identify two correct checkpoints
Find the true elapsed time and the clock’s displayed elapsed time between them.
Step 2
Form the rate ratio
Rate = clock time elapsed ÷ true time elapsed.
Step 3
Decide the conversion direction
True → clock time multiplies by the rate; clock → true time divides by it.
Step 4
Scale to the asked duration
Apply the rate to the specific true or clock duration the question asks about.
What Interviewer Expects
- Correct rate ratio derived from two checkpoints or a stated gain/loss rate
- Correct direction of conversion (true-to-clock vs clock-to-true)
- Careful unit consistency (minutes vs hours) throughout the calculation
- Sanity check that a gaining clock always shows more elapsed time than true time
Common Mistakes
- Inverting the rate ratio, converting the wrong direction
- Mixing minutes and hours without converting to a common unit
- Assuming the clock resets to correct at every checkpoint instead of drifting continuously
- Forgetting that “gains X minutes” means clock time exceeds true time, not the reverse
Best Answer (HR Friendly)
“I find two points where the clock was known to be correct, compare the true time between them to the time the clock itself displayed, and that gives me a fixed rate — clock time over true time. From there, any question about the future is just scaling: multiply true time by that rate to predict the clock’s reading, or divide a clock reading by the rate to recover true elapsed time. Keeping straight which direction I am converting is the part I am most careful about.”
Follow-up Questions
- How would you solve this if the clock’s rate itself changes partway through the day?
- How do you handle a clock that stops completely for part of the interval?
- How would you find when two faulty clocks, drifting at different rates, next show the same time?
- How does this rate-ratio method relate to the general concept of relative speed?
MCQ Practice
1. A clock loses 15 minutes every 24 true hours. What is its clock-time-to-true-time rate?
Losing 15 minutes means the clock shows only 1425 minutes of clock time per 1440 true minutes, giving a rate of 1425/1440.
2. A watch gains 5 minutes every 12 true hours. After 36 true hours, how many minutes has it gained?
36 true hours is 3 lots of 12 hours, so the gain is 3 × 5 = 15 minutes.
3. A faulty clock shows exactly 6 hours of elapsed clock time when the true elapsed time was 5.9 hours. Is the clock gaining or losing, and by what factor is clock time multiplied to get true time?
Clock time (6h) exceeds true time (5.9h), so the clock is gaining; to convert clock time back to true time, multiply by true/clock = 5.9/6.
Flash Cards
Core faulty clock rate formula? — Rate = clock time elapsed ÷ true time elapsed.
How to convert true time to clock time? — Multiply true time by the rate.
How to convert clock time back to true time? — Divide clock time by the rate.
"Gains X minutes every Y hours" means? — Clock time exceeds true time; rate = (Y + X/60)/Y.