A Strange Clock

Express everything in minutes starting in 0 at midday. Since every 60 minutes are displayed as 70, and 10:23 is 623 minutes after midday, we get $\frac{60}{70}=\frac{x}{623},$ where $x$ is the actual time. This gives $x=534$ minutes after midday, that is, 8 hours and 54 minutes.

Clock adds 10 mins /hour, which means it adds 1min/6mins.

suppose, the actual time is 9 pm, then the clock must be showing (9 * 10 = 90 mins) more. it should shoe the time 10.30pm. but it shows 10.23pm. it means the actual time is near to 9pm but not accurate 9pm.

At 6 the clock shows 7. Hence at 8 the clock shows 9:20 and at 9 it shows 10:30. hence the answer has to be either 8:54 or 8:23. As the clock gains 10 mins per 60 mins it actually shows (7/6)mins for 1 min. So for 54 mins, it will show 54*(7/6)=63 mins. This 63 mins added to 9:20 gives 10:23 hence the time is 8:54!

clock gains 10 mins every hours which means 10 mins every 60 mins which means 1/6 min for every minute let time passed from midday is 10:23 which means 623 minutes from midday let time on clock is Y and the actual time is X Y=X+X 1/6 623=X 7/6 so X=623*6/7=534 which is 534/60=8.9 which is 8:54

First of all, let us express everything in minutes. The clock gains 10 mins every hour, so it gains 10 mins every 60 minutes or 1 minute every 6 minutes.

To express it algebraically, let's say $x$ minutes have passed after the clock was set correctly. During this time, the clock gains $\frac{x}{6}$ minutes. So even though only $x$ minutes have passed, the clock shows $x + \frac{x}{6}$ minutes have passed.

In this case, the clock shows 10:23, which means 623 minutes have passed after the clock was set correctly. We suppose that $x$ minutes have passed in reality. So,

$x + \frac{x}{6} = 623$

$\frac{7x}{6} = 623$

$x = 534$

Converting this back into hours, we get 8 hours and 54 minutes. So, 8:54 is the correct time.

The clock shows 60 min more after 7 hours. So using unitary method, in (7 * 60) min it shows 60 min more So, in (3 * 60+23=203) min its shows (60 * 203)/(7 * 60)= 29 min more.

But at 6 the clock was showing 7, so clock was one hour fast beforehand. So in total, at 10:23 the clock is showing 1hr and 29 min more than it actually is. So, at 10:23 actual time is 8:54

At 6 it shows 7.So, at 8 it shows 9:20.At 9 it shows 10:30. Actually 7/6 mins for 1 min.For 54 mins it shows 54*(6/7) min=63 mins.Now,if 63 mins is added to 9:20 its 10:23.thus the time is 8:54.

                                         [SOLVED]

6 --> 7; 7 --> 8:10; 8 --> 9:20; 9 --> 10:30;

actual clock display = 10:23, hence time should be just little less than 9:00.

Brute Force applied. SORRY ALGEBRA

for every 60 min. clock shows 70 min.

ratio=6:7

now clock is 10.23==10x60+23=623 min.

6:7=x:623

x=534min

534 min=8hr+54min.

Since clock goes 10 mts slow each hr,From &.07 PM to to 10.23 PM in the clock it is 3 hrs and 23 mts later. but at 7 Pm it was actually 06:00 PM, therefore calculating 10 mts slow/hr ,it will be 08.54 Ans

K.K.GARG,INDIA

x/623=6/7 x=534 8:54