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SAT Exam  >  SAT Questions  >  A piece of cloth costs Rs. 35. If the piece w... Start Learning for Free
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?
A. 10 m
B. 14 m
C. 12 m
D. 8 m
  • a)
    B
  • b)
    D
  • c)
    C
  • d)
    A
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each m...
To solve this problem, let's assume the length of the piece of cloth is "x" meters.

Given that the cost of the cloth is Rs. 35, we can write the equation:
35 = x * 1

Now, let's consider the second scenario where the piece of cloth is 4 meters longer and each meter costs Rs. 1 less. In this case, the new length of the cloth would be (x + 4) meters and the cost per meter would be (1 - 1) = 0 Rs.

The total cost in this scenario would remain unchanged, so we can write the equation:
35 = (x + 4) * 0

Simplifying this equation, we get:
35 = 0

However, this equation is not possible since we cannot multiply any number by 0 to get a non-zero result. Therefore, the second scenario is not valid.

Since the second scenario is not possible, we can conclude that the length of the piece of cloth must be "x" meters and the cost per meter must be 1 Rs.

Now, let's substitute the values back into the original equation:
35 = x * 1

Simplifying this equation, we find:
x = 35

Therefore, the length of the piece of cloth is 35 meters.

However, none of the given options match this length, so none of the options are correct.

In conclusion, there seems to be an error in the question or the options provided. The correct length of the piece of cloth cannot be determined based on the given information.
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Community Answer
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each m...
Let, length of the piece of cloth = x m
Cost of cloth = Rs. 35
∴ Cost of 1 m cloth = Rs. 35/x
According to the question,
⇒ (x + 4) (35/x - 1) = 35
⇒ 35 - x + 140/x - 4 = 35
⇒ 35x - x2 + 140 - 4x = 35x
⇒ x2 + 4x - 140 = 0
⇒ x2 + 14x - 10x - 140 = 0
⇒ x(x + 14) - 10(x + 14) = 0
⇒ (x + 14) (x - 10) = 0
⇒ x = - 14 or 10
∴ The piece of cloth is 10 m long
Alternate Method:
We can tabulate the given data according to the following table:

As the total remains constant at Rs.35, we get:
xy = 35     
⇒ x = 35/y      ----(i)
Also, (x – 1) × (y + 4) = 35      ----(ii)
On substituting the value of x from equation (i) into equation (ii), we get:
[(35/y) – 1] × (y + 4) = 35 
On solving, we get:
y = -14 and 10
∴ The piece of cloth is 10 m long
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A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?A. 10 mB. 14 mC. 12 mD. 8 ma)Bb)Dc)Cd)ACorrect answer is option 'A'. Can you explain this answer?
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A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?A. 10 mB. 14 mC. 12 mD. 8 ma)Bb)Dc)Cd)ACorrect answer is option 'A'. Can you explain this answer? for SAT 2025 is part of SAT preparation. The Question and answers have been prepared according to the SAT exam syllabus. Information about A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?A. 10 mB. 14 mC. 12 mD. 8 ma)Bb)Dc)Cd)ACorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for SAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter was to cost Rs. 1 lesser, then the total cost would remain unchanged. How long is the piece of cloth?A. 10 mB. 14 mC. 12 mD. 8 ma)Bb)Dc)Cd)ACorrect answer is option 'A'. Can you explain this answer?.
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