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A certain number of trucks were required to transport 60 tons of steel wire from TISCO factory.however,it was found that since each truck could take 0.5 tons of cargo less,another 4 trucks were needed.how many trucks were initially planned to be used? It's ans is 20.can youexplain why?
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A certain number of trucks were required to transport 60 tons of steel...
Let no. of trucks = t
Then , according to question....

60/t - 0.5 = 60/(t+4)

Solving this equation....

t = 20 
Community Answer
A certain number of trucks were required to transport 60 tons of steel...
Solution:

Let's assume that initially, x trucks were planned to transport 60 tons of steel wire from TISCO factory.

Then, the capacity of each truck = 60/x tons

Now, it is given that each truck could take 0.5 tons of cargo less. So, the new capacity of each truck = (60/x) - 0.5 tons

It is also given that with this reduced capacity, 4 more trucks were needed to transport the same amount of steel wire.

So, the new number of trucks required = x + 4

Now, we can form an equation based on the above information:

60 = (x + 4) * [(60/x) - 0.5]

Simplifying this equation, we get:

60 = 60 - 2x + 120/x - 2

2x - 120/x = 2

Multiplying both sides by x, we get:

2x^2 - 2x * 60 + 120 = 0

x^2 - 30x + 60 = 0

Solving this quadratic equation using the quadratic formula, we get:

x = (30 ± sqrt(900 - 4*60))/2

x = (30 ± sqrt(720))/2

x = 15 ± 6sqrt(5)

Since x represents the initial number of trucks, it must be a positive integer. Therefore, the only possible value of x is 20, which satisfies all the given conditions.

Hence, the initial number of trucks planned to transport 60 tons of steel wire was 20.
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In a certain training institute which had exactly 200 students, each student was given exactly one question from one among the following categories: Reasoning, Mathematics, Grammar, Interpretation and Comprehension.Chart 1 gives the distribution of questions among the students.However, since the students were not happy with the type of questions each one had received, they exchanged their questions with other students in such a way that none of them had a question of the same category as they had earlier.Chart 2 shows the distribution of number of students who initially had questions from Reasoning category and exchanged their questions across students of various categories.Further, exactly 8 students who originally had questions on Interpretation now have questions on Reasoning with them. Also 8 students who initially had questions on comprehension now have questions on Interpretation category.Also out of the students who initially had questions on Grammar, 3 students now have questions on Reasoning and 16 have questions on Mathematics category.Q.If out of the students who initially had questions on Mathematics, the number of students who now have questions on Reasoning is twice the number of students now having questions on Grammar, then at least how many students now have questions on Comprehension with them who initially had questions on Mathematics with them? Correct answer is '20'. Can you explain this answer?

Answer the following question based on the information given below.In a certain training institute which had exactly 200 students, each student was given exactly one question from one among the following categories: Reasoning, Mathematics, Grammar, Interpretation and Comprehension.Chart 1 gives the distribution of questions among the students.However, since the students were not happy with the type of questions each one had received, they exchanged their questions with other students in such a way that none of them had a question of the same category as they had earlier.Chart 2 shows the distribution of number of students who initially had questions from Reasoning category and exchanged their questions across students of various categories.Further, exactly 8 students who originally had questions on Interpretation now have questions on Reasoning with them. Also 8 students who initially had questions on comprehension now have questions on Interpretation category.Also out of the students who initially had questions on Grammar, 3 students now have questions on Reasoning and 16 have questions on Mathematics category.Q.Out of the students who initially had questions on Interpretation,if the number of students who now have questions on Mathematics and Grammar is the same, then at least how many of the students who now have questions on Mathematics initially had questions on Comprehension? Correct answer is '10'. Can you explain this answer?

In a certain training institute which had exactly 200 students, each student was given exactly one question from one among the following categories: Reasoning, Mathematics, Grammar, Interpretation and Comprehension.Chart 1 gives the distribution of questions among the students.However, since the students were not happy with the type of questions each one had received, they exchanged their questions with other students in such a way that none of them had a question of the same category as they had earlier.Chart 2 shows the distribution of number of students who initially had questions from Reasoning category and exchanged their questions across students of various categories.Further, exactly 8 students who originally had questions on Interpretation now have questions on Reasoning with them. Also 8 students who initially had questions on comprehension now have questions on Interpretation category.Also out of the students who initially had questions on Grammar, 3 students now have questions on Reasoning and 16 have questions on Mathematics category.If out of the students who initially had questions on Mathematics with them, the number of students who now have questions on Comprehension is the maximum possible; then out of the students who now have questions on Grammar category what is the maximum possible number of students who initially had questions on Comprehension category? Correct answer is '16'. Can you explain this answer?

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A certain number of trucks were required to transport 60 tons of steel wire from TISCO factory.however,it was found that since each truck could take 0.5 tons of cargo less,another 4 trucks were needed.how many trucks were initially planned to be used? It's ans is 20.can youexplain why?
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