Solution:

The solution is provided in the image below.

Solution:

1/3

Explanation
Assuming T1 is the Toy for brother1, T2 is the toy for brother2 and T3 is the toy for brother3.

Following are the possible cases for toys distribution:

Boy1 Boy2 Boy3
T1 T2 T3
T1 T3 T2
T2 T1 T3
T2 T3 T1 .... (A)
T3 T1 T2 .... (B)
T3 T2 T1

In both steps (A) & (B), no one gets the correct toy.
Therefore probability that none brother can get the own toy is 2/6 = 1/3

Solution:

Yes, by adding 'G' to 'One'
G + One => Gone

Solution:

-3 -1 1

Explanation:
-3 * 1 * -1 = 3(prime)
-1 - (-3) = 1 -(-1) = 2

Solution:

As we have been informed that the prices are a full dollar increment, this eases out the situation.

If we look at the price of pineapple and capsicum, we can easily make out that both of them are priced $1.
This is because the price has to be at least $1 and since both of them costs $2 together, they must cost $1 separately.

Solving the rest of the question is child’s play. You have to use simple mathematics.

For an instance:
Jalapeno + Pineapple = $5
Now, we know that pineapple costs $1. Thus,
Jalapeno + $1 = $5
Jalapeno = $4

You can find out the price for each one of the toppings in a similar fashion.
Capsicum $1
Pineapple $1
Mushrooms $3
Corn $2
Jalapeno $4
Red Pepper $2
Black Pepper $3
Olives $4

Solution:

5 questions

Explanation:
This question can be solved using a simple trick. If all the questions were answered correctly, the student would have 200 chocolates.
For every wrong answer, he will lose 5 chocolates and he will also lose 10 chocolates that he would have gained if he would have answered correctly. Thus, for every wrong answer, you have to deduct 15 chocolates from 200.
200 - 125 = 75
15 * 5 = 75
Hence, he gave wrong answer for 5 questions.

Solution:

45

1/5 of 45 = 9
9 + 45 = 54

Solution:

7 Races.

Solution:

Since both of them lied in all three statements, this means that the opposite is true. So the changed statements will be:

Poornima: I am surely over 30.
Riya: I am not 28 and you are at most 4 years older to me.
Poornima: You are at most 28.

Poornima is 31 years old at least as can be concluded from the first statement. Combining the second and the third statement, we can accomplish that Riya is at most 28 years old. Hence, the possible ages of Poornima and Riya can be:

Poornima: 31, 32, 33, 34, 35, 36...
Riya: 22, 23, 24, 25, 26, 27...

Now, reading the second statement again, we can conclude that the difference between the ages of Poornima and Riya is at max 4 years.
This brings us the result that Poornima is 31 years old whereas Riya is 27 years old.

Solution:

Let us denote the number of boys as 'p' and the number of girls as 'q'.

The first statement says that each boy has equal numbers of brothers and sisters
(p - 1) = q
=> p - q = 1 ------- (a)

The second statement says that every girl has twice as many brothers as that of sisters
2 (q - 1) = p
=> 2q - p = 2 ------- (b)

By solving (a) and (b)
We get q as 3 and p as 4.

Therefore, there are 4 boys and 3 girls in the family.