Solution:

Watermelon

Explanation:
- Something their friend Howard can eat: watermelon
- Something their neighbor penny can drink: juice of watermelon
- Something their friend Raj's cow can eat: Watermelon rinds
- Something his girlfriend Amy can plant in her garden: the seeds of a watermelon

Solution:

Solution can be verified from the picture below.

Solution:

833 pears

Explanation:
Step one: First you want to make 3 trips of 1,000 pears 333 kilometers. You will be left with 2,001 pears and 667 kilometers to go.

Step two: Next, you want to take 2 trips of 1,000 pears 500 kilometers. You will be left with 1,000 pears and 167 kilometers to go (you have to leave a pear behind).

Step three: Finally, you travel the last 167 kilometers with one load of 1,000 pears and are left with 833 pears in Cherryville

Solution:

   9567
+ 1085
======
 10652

Solution:

All Digits [0-9] follow the following pattern: There is one occurrence of all digits in every 10 numbers Example. Digit-9 occurred one time between 10 and 19 in 9, between 20 and 29 in 29
However, for tens(91,92,93...99) and hundreds (900,901.... 999), the occurrence is much more. Since we have included 1000, Therefor 1 is the most occurred digit.
Note: Despite three '0s' in 1000, 0 is not most occurred digit as they don't have tens and hundreds like other digits.

Solution:

As shown below, we can make equation as 6 = 6 = 6.

Solution:

Maths Teacher

Explanation:
How can she give grades on the 1st day of the college?

Solution:

When he is rowing the boat in the river, the boat is floating with watermelons in it and, therefore, all the watermelons have already displaced the water equal to their volume. Hence, there won't be any change in the water level, whether the farmer eats it or throws them away.

Solution:

Both will rotate at Same speed.

Explanation:
Gears of the same size will always rotate at constant speeds despite any smaller or larger gears in between them.

Solution:

We just added four matchsticks as shown in below picture.