Solution:

74658

* 8 + 6 =14
* 5 - 4 = 1
* 7 = 2*4 - 1
* 4 + 6 = 10
* 7+4+6+5+8 = 30

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:

Since Jasmine and Thibault ate equal amount, they should pay the same amount. But since that's not possible, they can decide with 'rock, paper, scissor' or an equivalent measure to determine who will pay the extra dollar. Now, let's assume tha Jasmine pays $1 extra after losing

Jasmine will pay $5, Thibault will pay $4 and Noah will pay $2.

If the pizza's cost was $11, we can simply keep the same offset and divide. Jasmine is paying 6% more, Thibault is paying 15% more and Noah is paying 27% more.
Keeping the offset same both Jasmine and Thibault will pay $5 each and Noah will pay $1.

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.

Solution:

3 3/4 hours

Explanation:
Suppose that the amount of petrol in each of the cars in the beginning was M.
Now, suppose that they drove for X hours.

In that case, the amount of petrol used by one car in X hours will be = M*X /4
The amount of petrol used by the other car will be = M*X/5

Therefore, the petrol left in one car = M - M*X / 4
Petrol left in the other car = M - M*X / 5

Now, according to the question,
M - M*X / 5 = 4 (M - M*X / 4)
=> X = 15 / 4 = 3 3/4 hours.

Therefore Murphy and Cooper drove for 3 3/4 hours.

Solution:

18

Explanation:
More minutes implies more tea.
More women implies more tea.

The time become twice (3 minutes / 1.5 minutes).
women become six times (9 / 1.5).

Number of tea = 2 * 6 * Original(1.5)
= 18

Solution:

Q>P

Explanation:
P = 60 * 60 * 24 seconds = 86, 400 seconds.
Q = (8 * 365 *24) + (2 * 366 *24) hours = 87, 648 hours

Therefore, Q is greater than P. If the leap years were not counted, results would have been different.

Solution:

The integer with the special property is -1.

To test the property, let us subtract any digit from it, let's say 5.

-1 - 5 = -6

The succeeding digit of 5 is 6.

When (-6) is divided by 6, it is completely divided.

For all other numbers as well, this stands true.

Solution:

Let the cost of cap = m
Cost of pen = (5 + m)

As per the condition

5.50 = 5 + m + m
2m = 0.5
m = 0.25

Hence, the cap costs 25 Paise.

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.