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It was planned to send 60 tons of relief material to a flood-affected area through a certain number of helicopters. However, due to technical reasons, each helicopter could take 0.5 ton less of relief material than was initially planned. In order to supply all the material, four additional helicopters were required. How many helicopters were initially planned to be used?
- a)10
- b)12
- c)16
- d)20
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
It was planned to send 60 tons of relief material to a flood-affected...
Let the initial no. of helicopters be x and relief material per helicopter be y.
Then xy = 60 and also xy = (x + 4)(y - 0.5)
4y - 0.5x = 2
Using xy = 60 & so y = 60/x
240/x = 0.5x = 2
We get a quadratic equation, x2 + 4x - 480 = 0
Solving it we get x = -24 or 20.
The value of x must be positive & so x = 20
Hence, there were 20 helicopters which were initially planned.
Hence, the correct option is (d).
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Community Answer
It was planned to send 60 tons of relief material to a flood-affected...
Given:
- The relief material planned to be sent to a flood-affected area is 60 tons.
- Due to technical reasons, each helicopter could take 0.5 ton less of relief material than initially planned.
- Four additional helicopters were required to supply all the material.
To find:
- The number of helicopters initially planned to be used.
Assumption:
- The number of helicopters initially planned is represented by 'x'.
Approach:
1. Calculate the total relief material that can be carried by 'x' helicopters initially.
2. Calculate the total relief material that can be carried by 'x + 4' helicopters after the technical issues.
3. Set up an equation using the given information and solve for 'x'.
Solution:
1. Calculate the total relief material that can be carried by 'x' helicopters initially:
- Each helicopter can carry 0.5 tons less than initially planned.
- So, the relief material carried by each helicopter = (initial planned relief material - 0.5)
- The total relief material carried by 'x' helicopters initially = x * (initial planned relief material - 0.5)
- Given that the total relief material sent is 60 tons, we can write the equation as:
x * (initial planned relief material - 0.5) = 60
2. Calculate the total relief material that can be carried by 'x + 4' helicopters after the technical issues:
- Each helicopter can carry 0.5 tons less than initially planned.
- So, the relief material carried by each helicopter = (initial planned relief material - 0.5)
- The total relief material carried by 'x + 4' helicopters after the technical issues = (x + 4) * (initial planned relief material - 0.5)
- Given that the total relief material sent is 60 tons, we can write the equation as:
(x + 4) * (initial planned relief material - 0.5) = 60
3. Set up an equation using the given information and solve for 'x':
- Equating the two equations derived above, we have:
x * (initial planned relief material - 0.5) = (x + 4) * (initial planned relief material - 0.5)
- Simplifying the equation, we get:
x = x + 4
- Subtracting 'x' from both sides, we get:
0 = 4
- This is not possible, so there must be an error in the question or the options provided.
Conclusion:
- The given question does not have a valid solution based on the provided information.
- The relief material planned to be sent to a flood-affected area is 60 tons.
- Due to technical reasons, each helicopter could take 0.5 ton less of relief material than initially planned.
- Four additional helicopters were required to supply all the material.
To find:
- The number of helicopters initially planned to be used.
Assumption:
- The number of helicopters initially planned is represented by 'x'.
Approach:
1. Calculate the total relief material that can be carried by 'x' helicopters initially.
2. Calculate the total relief material that can be carried by 'x + 4' helicopters after the technical issues.
3. Set up an equation using the given information and solve for 'x'.
Solution:
1. Calculate the total relief material that can be carried by 'x' helicopters initially:
- Each helicopter can carry 0.5 tons less than initially planned.
- So, the relief material carried by each helicopter = (initial planned relief material - 0.5)
- The total relief material carried by 'x' helicopters initially = x * (initial planned relief material - 0.5)
- Given that the total relief material sent is 60 tons, we can write the equation as:
x * (initial planned relief material - 0.5) = 60
2. Calculate the total relief material that can be carried by 'x + 4' helicopters after the technical issues:
- Each helicopter can carry 0.5 tons less than initially planned.
- So, the relief material carried by each helicopter = (initial planned relief material - 0.5)
- The total relief material carried by 'x + 4' helicopters after the technical issues = (x + 4) * (initial planned relief material - 0.5)
- Given that the total relief material sent is 60 tons, we can write the equation as:
(x + 4) * (initial planned relief material - 0.5) = 60
3. Set up an equation using the given information and solve for 'x':
- Equating the two equations derived above, we have:
x * (initial planned relief material - 0.5) = (x + 4) * (initial planned relief material - 0.5)
- Simplifying the equation, we get:
x = x + 4
- Subtracting 'x' from both sides, we get:
0 = 4
- This is not possible, so there must be an error in the question or the options provided.
Conclusion:
- The given question does not have a valid solution based on the provided information.
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It was planned to send 60 tons of relief material to a flood-affected area through a certain number of helicopters. However, due to technical reasons, each helicopter could take 0.5 ton less of relief material than was initially planned. In order to supply all the material, four additional helicopters were required. How many helicopters were initially planned to be used?a)10b)12c)16d)20Correct answer is option 'D'. Can you explain this answer?
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