Solution:

There are 3 fruits (1 grapes, 1 apples, and 1 oranges).

Solution:

28 =>1+2+4+7+14

cannot be 1 (as number cannot be included)

Solution:

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

Solution:

Never

Explanation:
In the question, the distance of x miles is given at a particular moment. The middle car is running at that time at 50 MPH. The distance will keep increasing with time as three are running at different speeds. It will increase by x miles every hour till a certain point of time and then it will start decreasing till the fastest car meets the slowest again.

As per question, all the cars stop then. Thus, the distance will never be x miles again.

Solution:

60 minutes

Explanation:
Roy will be able to consume all the five tablets in an hour.

Tablet 1 will be taken in 0 min.
Tablet 2 will be taken in 15 min.
Tablet 3 will be taken in 30 min.
Tablet 4 will be taken in 45 min.
Tablet 5 will be taken in 60 min.

Solution:

Let us solve this problem with variables to find the general nature. Let us assume that there are x black chocolates and y white chocolates. Three things can happen when you take out two chocolates.
1) You take out two black chocolates.
Then, you will be replacing one black chocolate and so the jar will have x+1 black chocolates and y-2 white chocolates.
2) You take out two white chocolates.
Then, you will be replacing 1 black chocolate and so the jar will have x-1 black chocolates and y white chocolates.
3) You take out 1 black chocolate and 1 white chocolate. Then, you will be replacing a white chocolate and so the jar will have x-1 black chocolates and y white chocolates.
Thus at every step, you are wither removing a black chocolate or replacing two white chocolates by one black chocolate irreversibly till there is just one chocolate left. Therefore each white chocolate is equivalent to two black chocolates.

This, if the number of white chocolates are odd in number, the last one remaining will be white chocolate and if the number of white chocolates are even in number, the last one remaining will be black chocolate.

Solution:

She has misplaced 119 pens in total.

Solution:

Little Johny have Rupees 99.98 in his wallet when he entered the store.

Solution:

24 13 11 5
----------
24 0 0 0
11 13 0 0
6 13 0 5
6 2 11 5
8 0 11 5
8 5 11 0
8 13 3 0
8 8 3 5
8 8 8 0

Solution:

Man1 is carrying 5 bags and the Man2 is carrying 7 bags.

Let's assume that the Man1 was carrying M1 bags and the Man2 was carrying M2 bags.
M2 + 1 = 2 * (X-1)
M2 + 1 = 2M1 - 2
M2 = 2M1 - 3

Also,
M2 - 1 = M1 + 1
M2 = M1 + 2

=>
2M1 - 3 = M1 + 2
M1 = 5

=>
M2 = 7