Shiv want to lay a track 200 m long and 6 m wide using a team of 60 boys in 2 days. After 1 day, Shiv finds 75 m x 6 m track has been laid. How many men should shiv hire additionally if 2 men do the job of 5 boys?

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Shiv wants to build a track that’s 200 meters long and 6 meters wide. He’s got a team of 60 boys to do it in 2 days. But after the first day, they’ve only managed to lay 75 meters by 6 meters. How many more men does Shiv need to hire if 2 men can do the work of 5 boys?

Shiv want to lay a track 200 m long and 6 m wide using a team of 60 boys in 2 days. After 1 day, Shiv finds 75 m x 6 m track has been laid. How many men should shiv hire additionally if 2 men do the job of 5 boys?

Shiv should hire 30 additional men to lay the remaining track on time.

Given:

• 60 boys lay a 200 m track in 2 days.
• After 1 day, 75 m of track is already laid.

From the given information, we know that:

• 60 boys lay 200 m of track in 2 days.
• Therefore, in 1 day, they lay 100 m of track.
• So, the work rate of 1 boy per day is (100 m / 60 boys) = 5/3 meters.

Now, after 1 day, 75 m of track is already laid. Therefore, the remaining track to be laid is 200 m – 75 m = 125 m.

To find the number of boys required to lay the remaining 125 m of track:

Number of boys = (125 m×3) / 5 = 75

Number of boys = 75.

Now, since 2 men do the job of 5 boys, we convert the number of boys required to men:

Number of men = 75 boys /5 × 2 = 30 men.

So, Shiv should hire 30 additional men to lay the remaining track on time.

Work and Time in Mathematics

Work and time problems in mathematics typically involve determining how long it takes for a certain task to be completed based on the rate at which work is being done. These problems can involve individuals working together to complete a task, or they may involve scenarios where a single person works at different rates over time.

Here are the key concepts and formulas used in work and time problems:

1. Rate of Work (or Efficiency): This refers to the amount of work done per unit of time. It’s usually measured in terms of work done per hour, per day, etc.

2. Work Formula: The basic formula used is:

   Work = Rate of Work × Time

   This formula states that the amount of work done is equal to the rate of work multiplied by the time taken.

3. Combined Work: When multiple individuals are working together, their individual rates of work are added together.

4. Time Formula: If you know the total amount of work to be done and the combined rate of work, you can find the time it takes to complete the task using the formula:

   Time = Total Work / Combined Rate of Work

Let’s illustrate these concepts with an example:

Example: If it takes Alice 6 hours to complete a task and it takes Bob 8 hours to complete the same task, how long will it take them if they work together?

Solution:

1. Find the rates of work for Alice and Bob:

   • Alice’s rate = 1 task / 6 hours = 1/6 tasks per hour
   • Bob’s rate = 1 task / 8 hours = 1/8 tasks per hour

2. Calculate the combined rate of work: Combined rate = Alice’s rate + Bob’s rate = 1/6 + 1/8 = 4/24 + 3/24 = 7/24 tasks per hour

3. Determine the time it takes for them to complete the task together: Total work = 1 task (since they’re completing one task) Time = Total Work / Combined Rate of Work = 1 / (7/24) = 24/7 hours

   So, it will take them approximately 247724​ hours to complete the task together.

This is the basic approach to solving work and time problems in mathematics. Depending on the specific problem, you may need to adjust the approach slightly, but these concepts and formulas should provide a good foundation for solving such problems.

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