The one that doesn’t work is best as it will always be correct twice a day.
but
The one that loses a minute a day takes 12×60=720 days to show the right time again. i.e. it shows the right time once in 720 days

The answer is 301

EXPLANATION-

Condition 1 – When she put the eggs in groups of two, three, four, five, and six  there was one egg left over
Since there was one egg left when packed in 2,3,4,5,6, we need to find the LCM (lowest common multiple) of 2,3,4,5,6 and add one to get the least possible answer, THat is 60+1=61.
Moreover, we can easily figure  that 60x+1 will always satisfy the first 5 conditions, where x is a positive integer.

Condition 2- when she put them in groups of seven  they ended up in complete groups with no eggs left over
To satisfy this condition, we have to find the least  value of X such that 60x+1 is divisible by 7.

That is,
(60x+1)%7 = 0   Where % is mod

When,
x=1  —–> 61 % 7 = 5
x=2  —–>121 % 7 = 2
x=3  —–>181 % 7 = 6
x=4  —–>241 % 7 = 3
x=5  —–>301 % 7 = 0    —- SATISFIED

Hence, 301 eggs is the Minimum Number of eggs.

NOTE-
While there are many possible answers satisfies this equation (60x+1)%7 = 0
Answers – 301,  721, 1141,  1561, 1981 …………

A is Salman and time is afternoon

EXPLANATION-
Now here in this question let us suppose A is Ranveer ,
so now he is saying (A) that ” B (i.e. the other guy) is Ranveer ” , since he is himself Ranveer , he is lying . So , the time is afternoon and the person is Salman a/c to this scenario.

Now , suppose A is salman , now he is saying that the other guy is Ranveer , so he is saying the truth so it must be Afternoon and A is Salman as we assumed.

So , in both scenarios A is Salman and time is afternoon hence it is the answer

There were only three people.
Son, his father and his grandfather.

Here 2 persons have their sons

First,
Dr.Willam will wear both of the gloves, one above the other.
He operate the first person.After finishing he remove the outer pair of gloves as inside out and place it in a tray.
Then operate the second person.

Now he will wear the first gloves as inside out above the second gloves.

Operate the third person.
At last he remove the gloves and dispose them.

Round manhole covers can never fall into their own hole

Square manholes can be turned in such a way as to fall into the hole.
A circle always have the same diameter no matter which way you turn it.

Today and Tomorrow 😛

Suicide

Suicidal attempt is criminal activity and is punishable,
but after suicide no one can be punished.

The next number in sequence is 1113213211.

EXPLANATION-
The sequence goes like
You need to spell the no of digits.

e.g. take the no 1,11,21
Take 1. it spells as one 1 so we get the no 11,
take 11 we spell it as two ones‘ and we get 21

.so take the last given no in the sequence 13112221 so we spell it as one 1  one 3 two 1 three 2’s one 1.
So the next no in sequence is 1113213211.