Maths Puzzles

74658

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

We know that both of them were lying in all their statements. Thus we can assume the opposite of what they said:

Priyanka: I am definitely over 30.
Rubina: I am not 28 and you are at most 4 years older to me.
Priyanka: You are at most 28.

Now we can conclude from the first statement that Priyanka is 31 years old at least. From the second and third statement, we can conclude that Rubina is at most 28 years old. Therefore, the possible ages of Priyanka and Rubina can be:

Priyanka: 31, 32, 33, 34, 35, 36...
Rubina: 22, 23, 24, 25, 26, 27...

If we look at the second statement again, we know the difference between their ages is a maximum of 4 years.
Therefore, Priyanka age is 31 years while Rubina age is 27.

If we assume that Rihana and Peeta pay the same amount, they can decide with "rock, paper, scissor" to determine who will pay the extra dollar. Any other method may be used as well. Suppose that Rihana pays $1 extra.

In this manner, Rihana pays $5, Peeta pays $4 and Logan pays $2.

If the pizza would have cost $11, this method will then prove to be great because both Rihana and Peeta will pay $5 each and Logan will pay $1. This will keep the offset same as previous. Rihana is paying 6% more, Peeta is paying 15% more and Logan is paying 27% more.

Suppose that the number of boys be "b" and number of girls be "g".

Now, each boy has equal number of brothers and sisters:
(b - 1) = g
=> (b - g) = 1 ------ (1)

In addition, each girl has twice as many brothers as sisters:
2 (g-1) = b
=> (2g - b) = 2 ------- (2)

From (1) and (2)
g = 3 and b = 4

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

3 3/4 hours

Assume that the initial amount of petrol in each of the petrol tanks be P.
Now, let us assume that they drove for H hours.

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

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

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

18

More hours => more burgers.
More boys => more burgers.

The time become twice (3 hours / 1.5 hours).
Boys become six times (9 / 1.5).

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

S = 60 * 60 * 24 seconds = 86, 400 seconds.
H = (8 * 365 *24) + (2 * 366 *24) hours = 87, 648 hours

Clearly, H is greater than S even though not by much.

The required integer is -1.

For an example, let us subtract 7 from -1.

-1 - 7 = -8

Now the successor of 7 is 8 and (-8) is exactly divisible by 8.

You can try that for any number and it will hold true.

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

As per the condition

5.50 = 5 + c + c
2c = 0.5
C = 0.25

Thus the cost of the cap is 25 Paise

60

The patient will be able to take all the tablets in an hour. This is because the first tablet will start the time.
1st tablet = 0 min
2nd tablet = 15 min
3rd tablet = 30 min
4th tablet = 45 min
5th tablet = 60 min