To solve this problem, we can use the formula for the number of handshakes in a group of people.

Let's assume that there are 'n' people at the party. Each person shakes hands with 'n-1' other people (excluding themselves).

So, the total number of handshakes can be calculated using the formula:

Total number of handshakes = (n * (n-1)) / 2

Given that there were 66 handshakes, we can set up the equation:

66 = (n * (n-1)) / 2

To solve this equation, we can multiply both sides by 2 to get rid of the fraction:

132 = n * (n-1)

Next, we can rearrange the equation to get a quadratic equation:

n^2 - n - 132 = 0

Now, we can factorize the quadratic equation:

(n - 12)(n + 11) = 0

Setting each factor equal to zero, we get two possible solutions:

n - 12 = 0 or n + 11 = 0

Solving for 'n', we find:

n = 12 or n = -11

Since the number of people cannot be negative, we discard the solution n = -11.

Therefore, the number of people at the party is 12.

So, the correct answer is B) 12 people.

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To solve this problem, we need to determine the number of days it takes for the snail to reach the top of the pit.

Each day, the snail climbs 5 meters upwards. However, at night it slides 4 meters back downwards. Therefore, the snail makes a net progress of 1 meter each day (5 meters climbed - 4 meters slid back).

To reach the top of the pit, the snail needs to climb a total of 20 meters. Since it makes a net progress of 1 meter each day, it will take the snail 20 days to reach the top of the pit.

Let's go through each option to determine the correct answer:

Option A) 12 days - This option is incorrect because it is less than the total number of days required for the snail to reach the top of the pit.

Option B) 9 days - This option is incorrect because it is less than the total number of days required for the snail to reach the top of the pit.

Option C) 16 days - This option is correct because it is equal to the total number of days required for the snail to reach the top of the pit.

Option D) 2 days - This option is incorrect because it is less than the total number of days required for the snail to reach the top of the pit.

The correct answer is C) 16 days. This option is correct because it represents the total number of days required for the snail to reach the top of the pit.

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To solve this problem, let's assume the age of the youngest child as "x" years.

According to the given information, the ages of the 5 children are x, x+3, x+6, x+9, and x+12 years.

The sum of their ages is given as 50 years:

x + (x+3) + (x+6) + (x+9) + (x+12) = 50

Simplifying the equation:

5x + 30 = 50

Subtracting 30 from both sides:

5x = 20

Dividing both sides by 5:

x = 4

Therefore, the age of the youngest child is 4 years.

The correct answer is A) 4 years.

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To answer this question, let's analyze the given information:

1. Shahrukh speaks truth only in the morning and lies in the afternoon.
2. Salman speaks truth only in the afternoon.

According to the given information, A says that B is Shahrukh. Based on this statement, we need to determine the time of day and the identity of A.

Let's evaluate each option:

Option A) Afternoon. A is Shahrukh - This option is incorrect because Shahrukh lies in the afternoon, and A says that B is Shahrukh. Therefore, A must be lying, which contradicts the given information that Shahrukh only speaks truth in the morning.

Option B) Afternoon. B is Salman - This option is incorrect because it does not provide any information about A's identity or the time of day.

Option C) Morning. A is Salman - This option is incorrect because it contradicts the given information that Salman only speaks truth in the afternoon.

Option D) Afternoon. A is Salman - This option is correct because it aligns with the given information. Salman speaks truth only in the afternoon, and A says that B is Shahrukh. Since A is telling the truth, it implies that B is indeed Shahrukh. Therefore, the correct answer is option D.

In conclusion, the correct answer is option D. The time of day is afternoon, and A is Salman.

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To find the total number of seats unoccupied, we need to determine the number of passengers on the bus.

If the total fare is shared equally among the passengers, we can calculate the fare per passenger by dividing the total fare by the number of passengers.

Let's assume the number of passengers on the bus is "x".

The fare per passenger = Total fare / Number of passengers = 80.67 / x

Since the fare is shared equally among all passengers, the fare per passenger should be a whole number.

Now, let's consider the given information: the fare per passenger is 80.67 / x and the total number of seats on the bus is 40.

To find the number of passengers, we can set up an equation:

Number of passengers * Fare per passenger = Total fare

x * (80.67 / x) = 80.67

Simplifying the equation, we have:

80.67 = 80.67

This equation is true for any value of x. Therefore, the number of passengers can be any number.

To find the number of seats unoccupied, we subtract the number of passengers from the total number of seats:

Number of seats unoccupied = Total number of seats - Number of passengers = 40 - x

Since the number of passengers can be any number, the number of seats unoccupied can also be any number between 0 and 40.

Therefore, there is not enough information given to determine the exact number of seats unoccupied. The correct answer cannot be determined with the given information.

None of the options (A, B, C, or D) provided is correct.

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To solve this question, we need to understand the relationship between the given words "VXUPLVH" and "SURMISE" and apply the same relationship to the word "SHDVD".

In the given words "VXUPLVH" and "SURMISE", each letter in the first word is moved four positions backward in the alphabet to form the corresponding letter in the second word.

Applying the same rule to the letters in "SHDVD", we need to move each letter four positions backward in the alphabet:

S -> O H -> D V -> R D -> Z D -> Z

Therefore, the word "SHDVD" would be transformed into "ODRZZ".

None of the given options match the transformed word "ODRZZ". Hence, none of the options A, B, C, and D are correct.

Therefore, the correct answer is not provided in the given options.

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To determine whether the merchant made a profit or loss overall, we need to calculate the cost price and selling price of each lamp.

Let's assume the cost price of the first lamp is x.

Given that the merchant made a 25% gain on the first lamp, the selling price of the first lamp can be calculated as:

Selling price = Cost price + Gain Selling price = x + (25/100)x Selling price = x + 0.25x Selling price = 1.25x

Similarly, let's assume the cost price of the second lamp is y.

Given that the merchant experienced a 20% loss on the second lamp, the selling price of the second lamp can be calculated as:

Selling price = Cost price - Loss Selling price = y - (20/100)y Selling price = y - 0.2y Selling price = 0.8y

Now, we are given that the merchant sold the two lamps for a total price of Rs. 12. Therefore, we can write the equation:

Selling price of the first lamp + Selling price of the second lamp = Rs. 12 1.25x + 0.8y = 12

We need to solve this equation to find the values of x and y.

However, we can also analyze the answer options to determine if the merchant made a profit or loss overall.

Option A) 60 Paise gain - This option is incorrect because it suggests a gain, while the correct answer is a loss.

Option B) 60 paise Loss - This option is correct because it suggests a loss, which is the correct answer.

Option C) 80 Paise loss - This option is incorrect because it suggests a greater loss than the correct answer.

Option D) 72 Paise - This option is incorrect as it does not indicate whether it is a gain or a loss.

Therefore, the correct answer is option B) 60 paise Loss. The merchant experienced a loss overall.

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To answer this question, we need to consider the placement of the trees and the condition that they must be equal distances from each other.

Option A) Square vertices - If we place the trees at the vertices of a square, then the distances between the trees will not be equal. The distance between adjacent trees will be equal to the length of a side of the square, but the distance between non-adjacent trees will be greater.

Option B) Equilateral triangle vertices and centroid - If we place the trees at the vertices of an equilateral triangle, then the distances between the trees will also not be equal. The distance between adjacent trees will be equal to the length of a side of the triangle, but the distance between non-adjacent trees will be greater.

Therefore, neither option A nor option B satisfies the condition that all 4 trees must be equal distances from each other.

Since none of the given options meet the requirements, the correct answer is D) None of the above.

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