Tag: math & puzzles

Questions Related to math & puzzles

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member?

general knowledge math & puzzles

  1. 44

  2. 40

  3. 24

  4. 80

Show answer
Correct Option: B

AI Explanation

To find the age difference of the new member, we need to compare the average age of the committee before and after the replacement.

Let's assume the average age of the committee members before the replacement is 'x'.

Since the average age remains the same after the replacement, the sum of the ages of the committee members before and after the replacement must be the same.

The total age before the replacement is 10x (since there are 10 members).

After the replacement, the total age will be the sum of the ages of the old members plus the age of the new member.

Since one old member has been replaced by a young member, the sum of the ages of the old members will be 10x - y, where 'y' represents the age difference between the old and new member.

Therefore, the total age after the replacement is (10x - y) + (x - y), which simplifies to 11x - 2y.

Since the total age remains the same, we can equate the expressions for the total age before and after the replacement:

10x = 11x - 2y

Now let's solve for 'y', which represents the age difference between the old and new member:

10x - 11x = -2y

-y = -x

y = x

This means that the age difference between the old and new member is 'x'.

Since we want to find how much younger the new member is, we need to find the value of 'x'.

Since the average age of the committee before the replacement is the same as it was 4 years ago, we can write the equation:

x = x - 4

Simplifying this equation, we get:

4 = 0

This equation has no solution, which means there is a contradiction in the given information. It is not possible for the average age of the committee to remain the same after replacing an old member with a younger member.

Therefore, the question is flawed and does not have a valid solution.

If x=y=2z and xyz=256 then what is the value of x?

general knowledge math & puzzles

  1. 12

  2. 6

  3. 8

  4. 16

Show answer
Correct Option: C
Explanation:

To find the value of x, we can use the given information.

We are given that x = y = 2z and xyz = 256.

Since x = y, we can substitute x with y in the second equation:

xy * z = 256

(x * x) * z = 256

x^2 * z = 256

Now, we know that x = 2z, so we can substitute x in terms of z:

(2z)^2 * z = 256

4z^2 * z = 256

4z^3 = 256

To solve for z, we can divide both sides of the equation by 4:

z^3 = 64

Taking the cube root of both sides gives us:

z = 4

Now that we know the value of z, we can substitute it back into the equation x = y = 2z:

x = y = 2 * 4

x = y = 8

Therefore, the value of x is 8.

The answer is: C. 8

If one-seventh of a number exceeds its eleventh part by 100 then the number is.......
general knowledge math & puzzles

  1. 1100

  2. 1925

  3. 1875

  4. 7700

Show answer
Correct Option: B

The ratio of Rita's age to her mother's age is 8:3. The difference of their ages is 35 years. The ratio of their ages after 4 years will be?
general knowledge math & puzzles

  1. 12:5

  2. 17:8

  3. 32:17

  4. 14:7

Show answer
Correct Option: A

A man can row 5 kmph in still water. If the river is running at 1kmph, it takes him 75 minutes to row to a place and back. How far is the place?

general knowledge math & puzzles

  1. 3

  2. 6

  3. 9

  4. 12

Show answer
Correct Option: A

Susan can type 10 pages in 5 minutes. Mary can type 5 pages in 10 minutes. Working together, how many pages can they type in 30 minutes?

general knowledge math & puzzles

  1. 15

  2. 75

  3. 25

  4. 65

Show answer
Correct Option: B

AI Explanation

To solve this problem, we can find the individual typing rates for Susan and Mary, and then add them together to find their combined typing rate.

Susan can type 10 pages in 5 minutes, which means she types at a rate of 10/5 = 2 pages per minute. Mary can type 5 pages in 10 minutes, which means she types at a rate of 5/10 = 0.5 pages per minute.

To find their combined typing rate, we add their individual rates: Combined typing rate = Susan's typing rate + Mary's typing rate Combined typing rate = 2 + 0.5 Combined typing rate = 2.5 pages per minute

Now, we can use the combined typing rate to find the number of pages they can type in 30 minutes: Number of pages = Combined typing rate * Time Number of pages = 2.5 * 30 Number of pages = 75

Therefore, Susan and Mary can type 75 pages in 30 minutes.

The correct answer is B) 75.

A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?

general knowledge math & puzzles

  1. 2 hours 30 minutes

  2. 2 hours 20 minutes

  3. 3 hours 20 minutes

  4. 3 hours 30 minutes

Show answer
Correct Option: C

AI Explanation

To solve this problem, let's assume the person's usual time is represented by "x" minutes.

According to the given information, the person is walking at 5/6 of his usual rate. This means he is walking at a speed of (5/6)x minutes per minute.

We are also given that the person is 40 minutes late. This means the actual time taken by the person is (x + 40) minutes.

We can set up an equation based on the given information:

(x + 40) = (5/6)x

To solve for x, we can multiply both sides of the equation by 6 to eliminate the fraction:

6(x + 40) = 5x

Expanding the equation:

6x + 240 = 5x

Now, we can subtract 5x from both sides:

x + 240 = 0

x = -240

Since time cannot be negative, we can discard the negative solution.

Therefore, the person's usual time is 240 minutes, which is equivalent to 4 hours.

Converting 240 minutes to hours and minutes:

240 minutes = 4 hours

So, the person's usual time is 4 hours.

The correct answer is C) 3 hours 20 minutes.

Which of the following is least like the others?

general knowledge math & puzzles

  1. cube

  2. sphere

  3. pyramid

  4. circle

Show answer
Correct Option: D
Explanation:

To solve this question, the user needs to understand the characteristics of each shape and identify which one is different from the others.

Explanation of each option:

A. cube: A cube is a three-dimensional shape that has six square faces, eight vertices, and 12 edges.

B. sphere: A sphere is a three-dimensional shape that is perfectly round in shape, like a ball. It has no edges or vertices and has a curved surface.

C. pyramid: A pyramid is a three-dimensional shape that has a polygonal base and triangular faces that meet at a single vertex.

D. circle: A circle is a two-dimensional shape with a curved boundary and every point on the boundary is an equal distance from the center point.

Option D is least like the others because it is the only two-dimensional shape. The other three options are three-dimensional shapes. Therefore, the answer is:

The Answer is: D

One of the following is my secret word:AIM DUE MOD OAT TIE.With the list in front of you, if I were to tell you any one of my secret word, then you would be able to tell me the number of vowels in my secret word.Which is my secret word?

general knowledge math & puzzles

  1. TIE

  2. AIM

  3. OAT

  4. DUE

Show answer
Correct Option: A

AI Explanation

To determine the number of vowels in the secret word, let's analyze each option:

Option A) TIE - This option has 2 vowels (I and E). Option B) AIM - This option has 2 vowels (A and I). Option C) OAT - This option has 2 vowels (O and A). Option D) DUE - This option has 2 vowels (U and E).

Based on the given information, we can see that every option has 2 vowels. Therefore, it is not possible to determine the secret word based on the number of vowels alone.

Hence, it is not possible to determine the secret word with the given information.

In june a baseball team that played 60 games had won 30% of its game played. After a phenomenal winning streak this team raised its average to 50% .How many games must the team have won in a row to attain this average?

general knowledge math & puzzles

  1. 12

  2. 20

  3. 24

  4. 30

Show answer
Correct Option: C