What has hands, but can’t clap?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Manish has to secure 40% marks to pass his B.tech final exams.
He got just 40 marks and failed by 40-marks.

What is the maximum marks?

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

What makes this number unique: 8,549,176,320?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

One day Jenifer meets the Lion and the Tiger in the Forest of Forgetfulness. She knows that the Lion lies on Mondays, Tuesdays, and Wednesdays, and tells the truth on the other days of the week. The Tiger, on the other hand, lies on Thursdays, Fridays, and Saturdays, but tells the truth on the other days of the week. Now they make the following statements to Jenifer:

Lion: Yesterday was one of my lying days.

Tiger: Yesterday was one of my lying days too.

What day is it?

If 21x = 79x, what is the value of x?

Can anyone tell me a word in the English dictionary which has a silent 'z'?