Who is older, Joe or Smoe?

Two friends, Joe and Smoe, were born in May, one in 1932, the other a year later. Each had an antique grandfather clock of which he was extremely proud. Both of the clocks worked fairly well considering their age, but one clock gained ten seconds per hour while the other one lost ten seconds per hour. 

On a day in January, the two friends set both clocks correctly at 12:00 noon. "Do you realize," asked Joe, "that the next time both of our clocks will show exactly the same time will be on your 47th birthday?" Smoe agreed. 

Who is older, Joe or Smoe?

Know who is older in the case! 

"Smoe is older than Joe"

What was the puzzle?

Since one of the clock looses and other gains 10 seconds per hour, that means one looses 240 seconds (4 minutes) & other gains 240 seconds (4 minutes) in a day.

Both the clocks are set at 12:00 PM correctly. One has to gain 6 hours (360 minutes) and other has to loose 6 hours (360 minutes) to show the same time again. At the speed of 4 minutes per day the would need 360/4 = 90 days to show the same time again. 

On 90th day, they will come together to show 6:00. Exactly at 12 noon on 90th day one clock must be showing 6:00 PM and other must be showing 6:00 AM, if they have feature of showing AM/PM.

Now as per Joe it would be 47th birthday of Smoe on the day on which the clocks will show the same time. That means, the clocks are set correctly on the noon of 90 days prior to Smoe's birthday which is 1 May for sure but year yet to be known. 

If the year is leap year then 90th day before 1st May will be on 1st February and if it's not a leap year then it would be on January 31. Since, they have set their clocks correctly at 12:00 on some day in January, the year must not be a leap year. 

But if Smoe had been born in 1933, his 47th birthday would have been on May 1, 1980 which is leap year. Hence, Smoe must have born in 1932 and Joe in 1933.

Therefore, Smoe is older than Joe.

The story must be of 1979!

Walking Up An Ascending Escalator

My wife and I walk up an ascending escalator. I climb 20 steps and reach the top in 60 seconds. My wife climbs 16 steps and reaches the top in 72 seconds. If the escalator broke tomorrow, how many steps would we have to climb?

Here is way to find the total number of steps! 

Total Steps on Broken Escalator

What was the question?

Climbing 16 steps makes you to reach at the top in 72 seconds but if you climb 20 steps then it requires 60 seconds only.

That means, climbing 4 steps extra pushes you at the top saving 12 seconds. This is the speed of the escalator which is 4 steps per 12 seconds.

That is escalator speed is 1 step per 3 seconds and 20 steps per 60 seconds. But in 60 seconds I climb 20 steps more hence total steps on escalator must be 40.

This is how escalator pushes me 20 steps + I climb 20 steps = 40 steps in 60 seconds.

On the other hand my wife climb 16 steps + escalator pushes her (40-16) i.e. 24 steps = 40 steps in 72 seconds.  


MATHEMATICAL APPROACH :

Let's suppose there are 'x' steps on escalator. If M is my speed , W is my wife's speed and E is speed of the escalator in terms of steps per second then,

M = 20/60 = 1/3 and W = 16/72 = 2/9.

In my case, for relative speed (steps per second) x/60, we have,

M - E = x/60

1/3 - E = x/60    ...........(1)

And in my wife's case, for relative speed (steps per second) x/72, we have, 
 
W - E = x/72

2/9 - E = x/72  ..............(2)

Subtracting (2) from (1),

(1/3) - (2/9) = (x/60) - (x/72)

(1/9) = x / 360

X = 40

So there are 40 steps on the escalator. 

The Missing Number?

99 unique numbers between 1 and 100 are listed one by one, with 5 seconds pause between every two consecutive numbers. If you are not allowed to take any notes, what is the best way to figure out which is the missing number? 

This is how to correctly guess the missing number!

Guessing The Missing Number!

What was the challenge given?

Just keep up adding the given numbers and remember only the last two digits of the sum.

The sum of all numbers from 1 to 100 is 5050, so if you know the sum of all the listed numbers, you will know the missing number as well. 

At the end, if the result is less than 50, subtract it from 50. If the result is larger than 50, subtract it from 150.

Lighting Up The Candles

In a group of 200 people, everybody has a non burning candle. On person has a match at lights at some moment his candle. With this candle he walks to somebody else and lights a new candle. Then everybody with a burning candle will look for somebody without a burning candle, and if found they will light it. This will continue until all candles are lit. Suppose that from the moment a candle is lit it takes exactly 30 seconds to find a person with a non burning candle and light that candle.

From the moment the first candle is lit, how long does it take before all candles are lit?

ESCAPE to answer! 

Time Calculation For Lighting Up The Candles

What is the exact situation?

From a moment from first candle is lit, 30 seconds later there would be total 2 candles lit. In next 30 seconds, each of these 2 candle holders will find 1 candle to lit. So there are now 4 candles lit after 60 seconds. In next 30 seconds, these 4 candles would lit another 4 candles making total 8 candles lit. 

In short, for every 30 seconds, the number of candles lit are doubled. So after 7 sets of 30 seconds, 2^7 = 128 candles would be lit. At 8th set of 30 seconds, 256 candles can be lit. But we have only 200 candles. Still 72 of 128 candles would lit another 72 in 8th set of 30 seconds. 

To conclude, 8 X 30 = 240 seconds = 4 minutes required to lit all 200 candles.