Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

A man has to get a fox, a chicken, and a sack of corn across a river.

He has a rowboat, and it can only carry him and one other thing.
If the fox and the chicken are left together, the fox will eat the chicken.
If the chicken and the corn are left together, the chicken will eat the corn.

How does the man do it?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

Can you replace the X (both small and big x) with the numbers between 1 to 19 such that all the rows of 3 numbers between X (big x) sum to 23?

I am a type of vehicle that has two wheels and is powered by humans. What am I?
Hint 1: You can ride me for exercise.
Hint 2: I am environment-friendly.

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?

If a wheel has 54 spokes, how many spaces are there between the spokes?

What is the Surname of Barbie Doll?

A mathematics teacher took exams for his students. Out of the total students, 25% passed both the tests included in the exam. However, only 42% were able to clear the first test.

Can you find out the percentage of those students who passed the first test and also passed the second test?