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Shalaj and Associates, a shoe-manufacturing company, has three machines producing shoes. If machine X produces l/4th as many as machine Y produces in the same time, and machine Y produces twice as many as machine Z produces in the same time, then during a fixed time, what fraction of the total number of shoes is produced by machine Z?
  • a)
    1/14
  • b)
    1/3
  • c)
    2/7
  • d)
    none of these
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Shalaj and Associates, a shoe-manufacturing company, has three machine...
Assume that Y produces 4P units in unit time. Then X and Z produce P and 2P units in the same time. So, Total shoes produced = 7P, Fraction of the total number of shoes produced by machine Z = 2/7
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Shalaj and Associates, a shoe-manufacturing company, has three machine...
Solution:

Let's assume that machine Z produces x number of shoes in a fixed time.

Given:
- Machine Y produces twice as many shoes as machine Z in the same time.
- Machine X produces 1/4th as many shoes as machine Y in the same time.

From the given information, we can deduce the following relationships:
- Machine Y produces 2x shoes in a fixed time.
- Machine X produces (1/4)*(2x) = x/2 shoes in a fixed time.

Now, let's find the total number of shoes produced by all three machines in a fixed time.

Total shoes produced = shoes produced by machine X + shoes produced by machine Y + shoes produced by machine Z

Total shoes produced = (x/2) + 2x + x

Total shoes produced = 5x/2 + x

Total shoes produced = 7x/2

To find the fraction of the total number of shoes produced by machine Z, we need to find the ratio of shoes produced by machine Z to the total number of shoes produced.

Fraction of shoes produced by machine Z = (shoes produced by machine Z) / (total shoes produced)

Fraction of shoes produced by machine Z = x / (7x/2)

Fraction of shoes produced by machine Z = x * (2/7x)

Fraction of shoes produced by machine Z = 2/7

Therefore, the fraction of the total number of shoes produced by machine Z is 2/7.

Hence, the correct answer is option C) 2/7.
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Shalaj and Associates, a shoe-manufacturing company, has three machines producing shoes. If machine X produces l/4th as many as machine Y produces in the same time, and machine Y produces twice as many as machine Z produces in the same time, then during a fixed time, what fraction of the total number of shoes is produced by machine Z?a)1/14b)1/3c)2/7d)none of theseCorrect answer is option 'C'. Can you explain this answer?
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