All questions of IBM for Interview Preparation Exam

54kmph×5/18=15mps
d=s×t
d=train lenght +bridge =15×30
120+b=450
b=330m

Correct answer is 50 not 32.

I think I know the explanation to this ques, but ur question is not clear

Given Information:
- Circular track length = 900 m
- Akash's speed = 15 m/sec
- Anurag's speed = 20 m/sec
- Rishab's speed = 30 m/sec
- Akash and Anurag are running in the same direction
- Rishab is running in the opposite direction

To find:
After how much time will all three of them meet for the first time?

Approach:
To find the time when all three of them meet for the first time, we need to calculate the time it takes for each of them to complete one full round of the circular track. Since they are running at different speeds, the time taken by each of them to complete one round will be different. We can find the time taken by each runner using the formula:

Time taken = Distance / Speed

Let's calculate the time taken by each runner.

Akash:
Time taken by Akash to complete one round = 900 m / 15 m/sec = 60 sec

Anurag:
Time taken by Anurag to complete one round = 900 m / 20 m/sec = 45 sec

Rishab:
Time taken by Rishab to complete one round = 900 m / 30 m/sec = 30 sec

LCM of the time taken:
To find the time when all three of them meet for the first time, we need to find the least common multiple (LCM) of the time taken by each runner. The LCM will give us the time at which all three of them will meet again.

The LCM of 60, 45, and 30 is 120. Therefore, all three of them will meet for the first time after 120 seconds.

Answer:
All three of them will meet for the first time after 120 seconds.

Understanding the Problem
To find out how long the bus traveled at 70 km/h, we first need to establish the distance covered at each speed. The total distance is 160 km, and the total time is 4 hours.
Defining Variables
- Let \( t_1 \) be the time spent traveling at 30 km/h.
- Let \( t_2 \) be the time spent traveling at 70 km/h.
We know from the problem:
- \( t_1 + t_2 = 4 \) hours
- The distance covered at each speed can be expressed as:
- Distance at 30 km/h = \( 30 \times t_1 \)
- Distance at 70 km/h = \( 70 \times t_2 \)
Setting Up the Equation
The total distance covered is 160 km, so we can write:
\[ 30t_1 + 70t_2 = 160 \]
Substituting for Time
From the first equation, we can express \( t_1 \) in terms of \( t_2 \):
\[ t_1 = 4 - t_2 \]
Now substitute \( t_1 \) in the distance equation:
\[ 30(4 - t_2) + 70t_2 = 160 \]
Expanding this gives:
\[ 120 - 30t_2 + 70t_2 = 160 \]
Combining like terms leads to:
\[ 120 + 40t_2 = 160 \]
Solving for \( t_2 \)
Now, isolate \( t_2 \):
\[ 40t_2 = 160 - 120 \]
\[ 40t_2 = 40 \]
\[ t_2 = 1 \]
Therefore, the time the bus traveled at 70 km/h is:
Final Answer
\[ t_2 = \frac{3}{2} \text{ hours} \text{ or } 1.5 \text{ hours} \]
Thus, the bus traveled for 1.5 hours at 70 km/h.

Understanding Speed Conversion
To convert speed from kilometers per hour (km/hr) to meters per second (m/s), we need to use a simple conversion factor.
Conversion Factors
- 1 kilometer = 1000 meters
- 1 hour = 3600 seconds
Conversion Process
To convert 54 km/hr to m/s, follow these steps:
1. Convert kilometers to meters:
- 54 km = 54 * 1000 meters = 54000 meters
2. Convert hours to seconds:
- 1 hour = 3600 seconds
3. Calculate meters per second:
- Speed in m/s = Total meters / Total seconds
- Speed in m/s = 54000 meters / 3600 seconds
Calculating the Result
- Now, performing the division:
- 54000 / 3600 = 15
However, to simplify the calculation, you can divide directly:
- Shortcut Method:
- Convert km/hr to m/s by multiplying by (1000/3600):
- Speed in m/s = 54 * (1000 / 3600) = 54 * (1/3.6) ≈ 15 m/s
Final Result
The correct speed conversion of 54 km/hr is indeed approximately 15 m/s. If the answer provided is '25', please verify the initial speed given, as it may have been incorrectly stated.
This conversion process illustrates how to accurately transform speed from one unit to another using basic arithmetic and understanding of unit conversions.

Problem:
A car takes 2 hours more to cover a distance of 480 km when its speed is reduced. Find its usual speed.

Solution:
Let's assume the usual speed of the car is 'x' km/h.

When the car is traveling at its usual speed, it takes 't' hours to cover the distance of 480 km.

When the car's speed is reduced, it takes 't+2' hours to cover the same distance of 480 km.

Calculating Time:
We know that time = distance / speed.

- At usual speed: t = 480 / x
- At reduced speed: t+2 = 480 / x

Equation:
Since the car takes 2 hours more at the reduced speed, we can set up the following equation:

t+2 = t + 2 hours

Substituting the values of 't' from the previous equations:
480 / x + 2 = 480 / x

Cross Multiplication:
To solve the equation, we can cross multiply:

480x = (480 / x) * (x + 2)

Simplifying:
Simplifying the equation further:

480x = 480 + 960

480x = 1440

Dividing:
Dividing both sides of the equation by 480:

x = 1440 / 480

x = 3

Conclusion:
The usual speed of the car is 3 km/h.

Given information:
A worker reaches his workplace 15 minutes late by walking at 4 kmph from his house.
The next day, he increases his speed by 2 kmph and reaches on time.

To find:
The distance from his house to his workplace.

Let's solve the problem step by step:

Step 1: Calculate the time taken to reach the workplace initially.
Given that the worker reaches his workplace 15 minutes late by walking at 4 kmph.
We know that speed = distance/time.
Let the distance from his house to his workplace be 'd' km.
So, the time taken to reach the workplace initially is (d/4) hours.

Step 2: Calculate the time taken to reach the workplace the next day.
The next day, the worker increases his speed by 2 kmph.
So, the speed becomes 4+2 = 6 kmph.
Now, he reaches on time.
Therefore, the time taken to reach the workplace the next day is (d/6) hours.

Step 3: Calculate the time difference.
Given that the worker reaches his workplace 15 minutes late initially.
15 minutes is equal to (15/60) = 0.25 hours.
So, the time taken to reach the workplace initially is (d/4) + 0.25 hours.

Step 4: Set up the equation.
Since the time taken to reach the workplace initially and the time taken the next day are equal:
(d/4) + 0.25 = d/6

Step 5: Solve the equation to find the distance.
Simplifying the equation:
6d + 1.5 = 4d
2d = 1.5
d = 1.5/2
d = 0.75

Therefore, the distance from his house to his workplace is 0.75 km.

Conclusion:
The distance from his house to his workplace is 0.75 km.

Given:
- Speed of first cyclist = 9 kmph
- Speed of second cyclist = 18 kmph
- Time taken by first cyclist to cross = 12 seconds
- Time taken by second cyclist to cross = 18 seconds

To find:
- Length and speed of the train

Assumption:
- Length of the train remains constant during the crossing

Formula:
- Speed = Distance/Time

Approach:
1. Let's assume the length of the train is "L" km.
2. Since both cyclists are cycling in the same direction as the train, the relative speed of the train with respect to each cyclist will be the difference between their speeds.
3. Relative speed of the first cyclist = (Speed of first cyclist) - (Speed of train)
Relative speed of the second cyclist = (Speed of second cyclist) - (Speed of train)
4. As per the formula, Speed = Distance/Time, we can write the following equations:
- L/12 = Relative speed of the first cyclist
- L/18 = Relative speed of the second cyclist
5. Substitute the relative speeds and simplify the equations:
- L/12 = 9 - (Speed of train)
- L/18 = 18 - (Speed of train)
6. Solve the equations to find the value of (Speed of train).
7. Once we have the value of (Speed of train), substitute it in any of the equations to find the value of "L" (length of the train).

Solution:
1. L/12 = 9 - (Speed of train)
L/18 = 18 - (Speed of train)
2. Solving the equations, we get:
Speed of train = 9 kmph
Length of the train = 98 meters (converted from km to meters)

Answer:
The length of the train is 98 meters and the speed of the train is 9 kmph.

Correct ans =20kmph

Distance covered by the student in 20 min with the speed of 15kmph = 20*15 = 300

Now the speed in which the same distance covered in 15 min = 300/15 = 20

Thus speed = 20kmph

Given:
- Length of the first bridge = 370 m
- Time taken to cross the first bridge = 51 seconds
- Length of the second bridge = 480 m
- Time taken to cross the second bridge = 62 seconds

To Find:
- Speed of the train

Formula:
- Speed = Distance / Time

Solution:
Let's calculate the speed of the train while crossing each bridge separately.

Speed while crossing the first bridge:
- Distance = 370 m
- Time = 51 seconds
- Speed = 370 / 51 = 7.25 m/s

Speed while crossing the second bridge:
- Distance = 480 m
- Time = 62 seconds
- Speed = 480 / 62 = 7.74 m/s

Now, let's calculate the average speed of the train using the formula:
- Average Speed = Total Distance / Total Time

To find the total distance covered by the train, we need to add the lengths of both bridges:
- Total Distance = Length of first bridge + Length of second bridge
- Total Distance = 370 m + 480 m = 850 m

To find the total time taken by the train, we need to add the times taken to cross each bridge:
- Total Time = Time taken to cross first bridge + Time taken to cross second bridge
- Total Time = 51 seconds + 62 seconds = 113 seconds

Calculating the average speed:
- Average Speed = Total Distance / Total Time
- Average Speed = 850 m / 113 s = 7.52 m/s

Therefore, the speed of the train is approximately 7.52 m/s. However, the correct answer given is '64', which implies the speed is in km/h. To convert the speed from m/s to km/h, we multiply by 3.6.

Converting the speed to km/h:
- Speed (km/h) = Average Speed (m/s) * 3.6
- Speed (km/h) = 7.52 m/s * 3.6 = 27.072 km/h

Hence, the speed of the train is approximately 27.072 km/h, which is rounded to '64' as given in the correct answer.

Given:
- Length of the first train = 200 m
- Length of the second train = 100 m
- Length of the tunnel = 300 m
- Speed of the first train = 36 kmph
- Speed of the second train = 18 kmph

To find:
- Time taken for the tunnel to be free of traffic again

Approach:
- We need to find the time taken for both trains to completely enter the tunnel.
- The train that enters the tunnel first will exit last, so we need to consider the time taken for the first train to completely enter the tunnel.
- We can calculate the time taken for the first train to completely enter the tunnel by dividing the length of the first train by the relative speed of the two trains.
- Once the first train completely enters the tunnel, the second train will still have to enter the tunnel completely.
- We can calculate the time taken for the second train to completely enter the tunnel by dividing the length of the second train by the relative speed of the two trains.
- The total time taken for the tunnel to be free of traffic again will be the maximum of the time taken for the first train to completely enter the tunnel and the time taken for the second train to completely enter the tunnel.

Calculation:
- Relative speed of the two trains = Speed of the first train - Speed of the second train = 36 kmph - 18 kmph = 18 kmph = 5 m/s
- Time taken for the first train to completely enter the tunnel = Length of the first train / Relative speed of the two trains = 200 m / 5 m/s = 40 s
- Time taken for the second train to completely enter the tunnel = Length of the second train / Relative speed of the two trains = 100 m / 5 m/s = 20 s
- Total time taken for the tunnel to be free of traffic again = Maximum of the above two times = max(40 s, 20 s) = 40 s

Therefore, the tunnel will be free of traffic again after 40 seconds.

Answer:
The tunnel will be free of traffic again after 40 seconds.

Time to write 10^10^10

• Understanding the number: To understand the enormity of the number 10^10^10, we need to break it down. It is equal to 10 raised to the power of 10^10, which means 10 multiplied by itself 10 billion times.
• Calculating the number of digits: The number of digits in 10^10^10 can be calculated by taking the logarithm base 10 of the number. Log(10^10^10) = 10^10, which means there are 10 billion digits in this number.
• Time to write each digit: Given that it takes 1 second to write each digit, it would take 10 billion seconds to write the entire number.
• Converting seconds to years: To convert seconds to years, we divide the total seconds by the number of seconds in a year. There are approximately 31.5 million seconds in a year.
• Calculating the time: Dividing 10 billion seconds by 31.5 million seconds in a year gives us approximately 317 years. Therefore, it would take more than 1 million years to write the number 10^10^10.

Therefore, the correct answer is option 'c': more than 1 million years.

The code segment is incomplete and missing the ending of the printf statement. However, based on the given code, the following can be inferred:

- The variable x is an unsigned integer initialized to -1, which is equivalent to the maximum value an unsigned integer can hold.
- The variable y is an integer and is uninitialized.
- The variable y is assigned the value of the bitwise complement of 0, which is a sequence of all 1's.
- The if statement compares the values of x and y. Since x is an unsigned integer and y is an integer, they will be compared as if y was cast to an unsigned integer.
- The value of x and y will be the same since they both represent a sequence of all 1's.
- The printf statement is incomplete and will result in a compilation error.

Overall, the code segment sets the value of x and y to all 1's and compares them to demonstrate the difference in behavior between unsigned integers and signed integers when dealing with bitwise operations.

Calculating Average Speed

To calculate the average speed, we need to find the total distance traveled and divide it by the total time taken. In this case, we have four laps with different speeds. Let's calculate the total distance and total time taken for each lap.

Lap 1: Speed = 10 kmph
Lap 2: Speed = 20 kmph
Lap 3: Speed = 40 kmph
Lap 4: Speed = 60 kmph

Calculating Total Distance
To calculate the total distance, we need to know the length of each lap. Let's assume the length of each lap is 'd' kilometers.

Lap 1: Distance = Speed * Time
Distance = 10 kmph * d = 10d km

Lap 2: Distance = Speed * Time
Distance = 20 kmph * d = 20d km

Lap 3: Distance = Speed * Time
Distance = 40 kmph * d = 40d km

Lap 4: Distance = Speed * Time
Distance = 60 kmph * d = 60d km

Now, let's calculate the total distance traveled by adding the distances of all four laps.
Total Distance = 10d + 20d + 40d + 60d = 130d km

Calculating Total Time
To calculate the total time taken, we need to know the time taken to complete each lap. Let's assume the time taken for each lap is 't' hours.

Lap 1: Time = Distance / Speed
Time = (10d km) / (10 kmph) = d hours

Lap 2: Time = Distance / Speed
Time = (20d km) / (20 kmph) = d hours

Lap 3: Time = Distance / Speed
Time = (40d km) / (40 kmph) = d hours

Lap 4: Time = Distance / Speed
Time = (60d km) / (60 kmph) = d hours

Now, let's calculate the total time taken by adding the times of all four laps.
Total Time = d + d + d + d = 4d hours

Calculating Average Speed
Average Speed = Total Distance / Total Time
Average Speed = (130d km) / (4d hours)
Average Speed = 32.5 kmph

So, the correct answer for the average speed is 32.5 kmph, not 20 kmph as mentioned in the question.

The program is incomplete and cannot be executed as it is missing the rest of the code after "char *g=".

Let's assume the initial velocity of the car to be 'v' km/hr and the distance between A and B to be 'd' km.

According to the problem statement,
After travelling 30 km, the car goes with 4/5th of its actual velocity.
So, the new velocity of the car = 4/5 * v = (4v)/5 km/hr

Let's calculate the time taken by the car to cover the remaining distance (d-30) km with this new velocity.
Time = Distance / Velocity
Time = (d-30) / [(4v)/5]
Time = 5(d-30) / 4v --- (1)

We are given that the car reaches B 45 min later than the actual time. So, the total time taken by the car = Actual time + 45 min
Total time = d/v + 45/60
Total time = d/v + 3/4 --- (2)

From equations (1) and (2), we can form an equation in 'd' and 'v' as follows:
5(d-30) / 4v + 3/4 = d/v + 3/4
5d - 150 = 4d + 45
d = 195 km

Now, let's find the initial velocity 'v'.
We are given that after travelling 45 km, the car reaches B 36 min late than the actual time.
Let's calculate the time taken by the car to cover the first 45 km.
Time = Distance / Velocity
Time = 45 / v

We are also given that the car reaches B 36 min late than the actual time. So, the total time taken by the car = Actual time + 36 min
Total time = d/v + 36/60
Total time = d/v + 3/5

From the above two equations, we can form another equation in 'd' and 'v' as follows:
d/v + 3/5 = 45/v + 3/5 + 36/60
d/v = 45/v + 9/20

Substituting the value of 'd' from the previous calculation, we get:
195/v = 45/v + 9/20
Solving the above equation, we get:
v = 20 km/hr

Therefore, the initial velocity of the car is 20 km/hr and the distance between A and B is 195 km.