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If 30 machines, each working at the same constant rate, together can produce n/2 units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?
- a)30
- b)40
- c)45
- d)50
- e)60
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If 30 machines, each working at the same constant rate, together can p...
Given:
- Let the production rate of one machine = r units per day
- Number of machines working = 30
- Number of items produced by 30 machines = n/2 units
- Time taken by 30 machines to produce n/2 items = 15 days
To Find: Number of machines needed to produce 2n units of the item in 45 days
Approach:
- Let the number of machines needed be x
- Production rate of one machine = r units per day
- Production rate of x machines = rx units per day
- We know that Work = Rate * Time
- So, 2n = r * 45 * x
-
- For finding the value of x, we need to either find the values of n and r, or the ratio n/r
-
- As we are given the time taken by 30 machines to produce n/2 items, we can use this information to find the value of n/r.
Working out:
5. So, it will take 40 machines to produce 2n units of the item in 45 days
Answer : B
Most Upvoted Answer
If 30 machines, each working at the same constant rate, together can p...
Understanding the Problem
- 30 machines can produce n/2 units of an item in 15 days at a constant rate.
- We need to find out how many machines will be needed to produce 2n units of the item in 45 days.
Calculating the Rate of Production
- Let's first calculate the rate of production of one machine in terms of units per day.
- 30 machines produce n/2 units in 15 days, so 30 machines produce n/2 units / 15 days = n/30 units per day.
- Therefore, one machine produces (n/30) / 30 = n/900 units per day.
Calculating the Number of Machines Required
- To produce 2n units in 45 days, we need to find out how many machines are required.
- Let x be the number of machines needed.
- x machines produce 2n units in 45 days, so x machines produce 2n units / 45 days = 2n/45 units per day.
- Since one machine produces n/900 units per day, x machines produce x * (n/900) units per day.
- Equating the rate of production of x machines to the required rate, we get x * (n/900) = 2n/45.
- Solving for x, we get x = (2n/45) * (900/n) = 40 machines.
Conclusion
- Therefore, 40 machines will be needed to produce 2n units of the item in 45 days.
- 30 machines can produce n/2 units of an item in 15 days at a constant rate.
- We need to find out how many machines will be needed to produce 2n units of the item in 45 days.
Calculating the Rate of Production
- Let's first calculate the rate of production of one machine in terms of units per day.
- 30 machines produce n/2 units in 15 days, so 30 machines produce n/2 units / 15 days = n/30 units per day.
- Therefore, one machine produces (n/30) / 30 = n/900 units per day.
Calculating the Number of Machines Required
- To produce 2n units in 45 days, we need to find out how many machines are required.
- Let x be the number of machines needed.
- x machines produce 2n units in 45 days, so x machines produce 2n units / 45 days = 2n/45 units per day.
- Since one machine produces n/900 units per day, x machines produce x * (n/900) units per day.
- Equating the rate of production of x machines to the required rate, we get x * (n/900) = 2n/45.
- Solving for x, we get x = (2n/45) * (900/n) = 40 machines.
Conclusion
- Therefore, 40 machines will be needed to produce 2n units of the item in 45 days.
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If 30 machines, each working at the same constant rate, together can produce n/2 units of an item in 15 days, how many machines will be needed to produce 2n units of the item in 45 days?a)30b)40c)45d)50e)60Correct answer is option 'B'. Can you explain this answer?
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