Solution:

Let us assume that there are 100 customers
Then there will be 40 percent people who will want to purchase items i.e. 40 people.
Now, fifteen percent of them wants to purchase mobile phones which means that 0.15*40 = 6 people want to purchase mobile phones which is 6 percent of the total customers.

Thus 6 % of people want to purchase mobile phones.

Solution:

Radius =3 cm

Volume of given ice cream = (pie)*6^2*15 = 540(pie)

If we divide to 10 children, the volume that will be given to each child will be 54(pie)

Let r be radius and h be the height of the cone

Then,
(Pie) r^2h/3 + 2(pie) r^3/3 = 54(pie)

Also given h = 4r

4r^3/3 +2r^3/3 = 54

2r^3 = 54

r^3 = 27

r = 3

Thus the radius of the ice cream cone is 3 cm.

Solution:

The next two numbers will be 42 and 47.
If you look closely, you will see that the following numbers are either a multiple of 7 or the next digit with a 7 in it.

Solution:

If you pick '2 2 2' or any combination of '1 2 3' then the sum will add up to 6.

Now the probability that you will get '2 2 2' is 5/16 (5 2s out of 16) times 4/15 (4 2s left out of 15) times 3/14 (3 2s left out of 14).
Thus the total probability is 5/16 * 4/15 * 3/14 = 1/56.

The probability of getting any combination of '1 2 3' is equal to 6/16 (6 1s in the list) times 5/15 (5 2s out of 15 numbers left) times 5/14 (5 3s out of 14 numbers left) times the number of different combinations of '1 2 3' which is 6.
Thus the total probability is 6/16 * 5/15 * 5/14 * 6 = 15/56.

1/56 + 15/56 = 16/56 or 2/7 or 28.6%.

Thus the probability of choosing the numbers which sums up to 6 is 29 percent (approx.)

Solution:

What we will do first is we will subtract the driving time of twenty minutes from the 2 hours 30 minutes difference and we are left with 2 hours 10 minutes.

Now Tia left in morning, thus for the mirror effect, the hands must be pointing up and down i.e. at 6 o'clock. (It could have been at 12 o'clock as well as the hands are straight up but we know she left in the morning).

Now we have to divide 2 hours and 10 minutes by 2 in order to find a center point that will be 65 minutes in this case for compensating for the mirror.

Now if we add 65 minutes to 6 o'clock, we get the time when she left the home which will be 7:05 and the time which she saw in the mirror was 4:55.

Now if we add the 20 minutes we had subtracted previously again to the time she left her home, we will get the time she reached at the party which will be 7:25.

Thus the time when she reached the party was 7:25.

Solution:

These types of problems are known as linear relation problems. If you know how to solve, they re pretty easy.

Bruce takes 11s to run y yards
Thus he will cover 1 yard in 11/y seconds

Now 1 yard = 11/y seconds
Multiplying both sides with x
We get, x yards = 11x/y seconds

Thus Bruce will take 11x/y seconds to cover the distance x.

Solution:

The first two digits are fixed.
You are left with eight digits (since one digit can be used just once).
Also you have only 4 more digits left to frame a phone number.

Thus the possibilities = 8P4 = 1680.

Solution:

Let the present ages of the Peter Parker and Mary Jane be 4x and 3x

As per the question, after four years the ratio of ages will be 9/7
Thus (4x + 4) / (3x + 4) = 9/7

x=8

Thus their present ages are 32 and 24 respectively

Now assume that they were married X years ago,

Then as per the question
(32 - X) / (24 - X) = 5/3

2X = 24
X = 12

Thus Peter and Mary married twelve years ago.

Solution:

Distance = d
Speed = s
Time = t
Now, d = s*t

When t1 = (3/4)t
Then,
d = s1*t1

Applying t1 value,
s*t = s1*(3/4)t
Then
s1/s = 4/3

Therefore, increase in speed = (s1/s - 1)
=4/3 - 1
=1/3
=33.33%

Solution:

Let the four nos. in A.P. are (a-d), (a), (a + d) and (a + 2d).
Now as per the given conditions
4a + 2d = 28
2a+d=14

Also a*(a + 2d) / ((a + d)*(a - d)) = 8/15
15a^2 + 30ad = 8a^2 - 8d^2
7a^2 + 30ad + 8d^2 = 0

Or (a + 4d) (7a + 2d) = 0
a + 4d = 0 or 7a + 2d = 0
Solving a + 4d = 0 and 2a + d = 0 we obtain a = 8 and d = (-2)

Thus the numbers are
4, 6, 8 and 10.