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Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?
- a)27
- b)36
- c)43
- d)400
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are ...
Since each Iron rod must be cut into parts of equal length and
each part must be as long as possible, so HCF should be
taken.
HCF of 78, 104, 117 and 169 = 13.
No. of parts from 78cm. rod = 78 /13=6
No. of parts from 104 cm. rod =104/13=8
No. of parts from 117 cm. rod =117/ 13=9
No. of parts from 169 cm. rod =169 /13=13
Maximum no. of pieces = 6 + 8 + 9 + 13 = 36
each part must be as long as possible, so HCF should be
taken.
HCF of 78, 104, 117 and 169 = 13.
No. of parts from 78cm. rod = 78 /13=6
No. of parts from 104 cm. rod =104/13=8
No. of parts from 117 cm. rod =117/ 13=9
No. of parts from 169 cm. rod =169 /13=13
Maximum no. of pieces = 6 + 8 + 9 + 13 = 36
Most Upvoted Answer
Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are ...
To find the maximum number of pieces that can be cut from the given iron metal rods, we need to find the greatest common divisor (GCD) of the lengths of the rods and divide each length by this common divisor.
Finding the GCD:
- The GCD of 78 cm and 104 cm can be found by dividing the larger number by the smaller number and taking the remainder.
104 cm ÷ 78 cm = 1 remainder 26 cm
- The GCD of 78 cm and 26 cm can be found by dividing the larger number by the smaller number and taking the remainder.
78 cm ÷ 26 cm = 3 remainder 0 cm
Since the remainder is 0, the GCD of 78 cm and 26 cm is 26 cm.
Now, we need to find the GCD of 26 cm and 117 cm:
- 117 cm ÷ 26 cm = 4 remainder 13 cm
- 26 cm ÷ 13 cm = 2 remainder 0 cm
The GCD of 26 cm and 13 cm is 13 cm.
Finally, we need to find the GCD of 13 cm and 169 cm:
- 169 cm ÷ 13 cm = 13 remainder 0 cm
The GCD of 13 cm and 169 cm is 13 cm.
Therefore, the common divisor for all the lengths is 13 cm.
Finding the maximum number of pieces:
To find the maximum number of pieces, we divide each length by the common divisor and sum up the results.
- For the rod of length 78 cm: 78 cm ÷ 13 cm = 6 pieces
- For the rod of length 104 cm: 104 cm ÷ 13 cm = 8 pieces
- For the rod of length 117 cm: 117 cm ÷ 13 cm = 9 pieces
- For the rod of length 169 cm: 169 cm ÷ 13 cm = 13 pieces
The total number of pieces that can be cut is 6 + 8 + 9 + 13 = 36.
Therefore, the maximum number of pieces that can be cut is 36. Hence, option (B) is the correct answer.
Finding the GCD:
- The GCD of 78 cm and 104 cm can be found by dividing the larger number by the smaller number and taking the remainder.
104 cm ÷ 78 cm = 1 remainder 26 cm
- The GCD of 78 cm and 26 cm can be found by dividing the larger number by the smaller number and taking the remainder.
78 cm ÷ 26 cm = 3 remainder 0 cm
Since the remainder is 0, the GCD of 78 cm and 26 cm is 26 cm.
Now, we need to find the GCD of 26 cm and 117 cm:
- 117 cm ÷ 26 cm = 4 remainder 13 cm
- 26 cm ÷ 13 cm = 2 remainder 0 cm
The GCD of 26 cm and 13 cm is 13 cm.
Finally, we need to find the GCD of 13 cm and 169 cm:
- 169 cm ÷ 13 cm = 13 remainder 0 cm
The GCD of 13 cm and 169 cm is 13 cm.
Therefore, the common divisor for all the lengths is 13 cm.
Finding the maximum number of pieces:
To find the maximum number of pieces, we divide each length by the common divisor and sum up the results.
- For the rod of length 78 cm: 78 cm ÷ 13 cm = 6 pieces
- For the rod of length 104 cm: 104 cm ÷ 13 cm = 8 pieces
- For the rod of length 117 cm: 117 cm ÷ 13 cm = 9 pieces
- For the rod of length 169 cm: 169 cm ÷ 13 cm = 13 pieces
The total number of pieces that can be cut is 6 + 8 + 9 + 13 = 36.
Therefore, the maximum number of pieces that can be cut is 36. Hence, option (B) is the correct answer.
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Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer?
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Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer?.
Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer? for Teaching 2024 is part of Teaching preparation. The Question and answers have been prepared according to the Teaching exam syllabus. Information about Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Teaching 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer?.
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Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Four Iron metal rods of lengths 78 cm, 104 cm, 117 cm, and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?a)27b)36c)43d)400Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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