Four 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 ?

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Q: 71 (IAS/2009)
Four 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 ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,3,1,0,3,0,1

keywords: 

{'lengths': [0, 0, 1, 0], 'metal rods': [0, 0, 1, 0], 'equal length': [2, 0, 1, 2], 'maximum number': [1, 0, 1, 2], 'pieces': [0, 2, 1, 2], 'parts': [6, 2, 8, 19], 'part': [12, 1, 5, 10], 'cm': [2, 0, 7, 20]}

To find the maximum number of pieces that can be cut from the given metal rods, we need to determine the length of the equal parts that will be cut from each rod.

The maximum length of the equal parts that can be cut is equal to the greatest common divisor (GCD) of the lengths of the rods.

Let`s calculate the GCD of the given rod lengths:

GCD(78, 104) = 26

GCD(26, 117) = 13

GCD(13, 169) = 13

The GCD of all the rod lengths is 13 cm. Therefore, we can cut each rod into parts of length 13 cm.

Now, to find the maximum number of pieces that can be cut, we need to divide the length of each rod by the length of the equal parts.

For the rod of length 78 cm:

Number of pieces = 78 cm / 13 cm = 6 pieces

For the rod of length 104 cm:

Number of pieces = 104 cm / 13 cm = 8 pieces

For the rod of length 117 cm:

Number of pieces = 117 cm / 13 cm = 9 pieces

For the rod of length 169 cm:

Number of pieces = 169 cm / 13 cm = 13 pieces

To find the total number of pieces, we sum up the number of pieces from each rod:

Total number of pieces = 6 + 8 + 9 + 13 = 36 pieces

Therefore, the correct option is Option 2: 36.

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