Clock A loses 4 minutes every hour, clock B always shows the correct
time and clock C gains 3 minutes every hour. On a Monday, all the
three clocks showed the same time, 8 PM. On the following Wednesday,
when the clock C shows 2 PM, what time will clock A show?
- 7:20 am
- 8:40 am
- 9:20 am
- 10:40 am
Kindly suggest how to approach this problem.
My approach
There is a lapse of 42 hours from 8 pm of Monday to 2 pm of Wednesday. As clock C gains 3 minutes every hour, the actual lapse should be 42 hours – (42×3) minutes. Further clock A gains loses 4 minutes every hour, so the lapse of time in clock A should be 42 hours – ((42×3)-(42×4)) minutes.
I couldn't proceed , also I am not sure if it's a right approach or if there's a better way to do this.
Kindly help, thanks in advance.
Best Answer
We have three "times" we can observe, one for each clock. If we knew the time on clock B, we could work out what time clocks A and C would show, but instead we're told the time on clock C and need to work out what time clock A shows.
As you note, if clock C reads 2pm then that means it is claiming that 42 hours have passed. So how many hours have actually passed?
If 1 true hour passed, then C will show 1 hour 3 minutes as having passed.
If 2 true hours passed, then C will show 2 hours 6 minutes as having passed.
If $t$ true hours passed, then C will show $t$ hours and $3t$ minutes having passed. Or in other words, C will show $t \times 1 \frac{3}{60}$ hours passing.
Then if C showed 42 hours passing, then that means $t \times 1 \frac{3}{60} = 42$. Can you take this and rearrange it to find what $t$ is equal to?
Once you've done so, you can apply the same logic to finding the time on A - every hour that passed, A claims that only 56 minutes have passed. So if you know that $t$ hours have passed, A should show a time that is $56t$ minutes later.