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A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.
  • a)
    32 minutes
  • b)
    20 minutes
  • c)
    25 minutes
  • d)
    40 minutes
  • e)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A factory produces nuts and bolts. A machine in it produces only nuts ...
2000 nuts are produced in 14 minutes (10 minutes break and 500 nuts per minutes so 4 minutes to produce 2000 nuts ), for next 2000 nuts it will take 14 minutes more, and for more two thousand it will take 4 minutes more, so total time = 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes
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Most Upvoted Answer
A factory produces nuts and bolts. A machine in it produces only nuts ...
To find the minimum time required to produce 6000 pairs of bolts and nuts, we need to calculate the time taken by each machine to produce the required quantity and then take the maximum of those times.

1. Calculate the time taken by the machine producing nuts:
- The machine produces 500 nuts per minute.
- After producing 2000 nuts, it needs to be cleared for 10 minutes.
- So, the time taken to produce 2000 nuts is (2000 / 500) + 10 = 14 minutes.

2. Calculate the time taken by the machine producing bolts:
- The machine produces 600 bolts per minute.
- After producing 3000 bolts, it needs to be cleared for 15 minutes.
- So, the time taken to produce 3000 bolts is (3000 / 600) + 15 = 20 minutes.

3. Since the machines are operated simultaneously, the time taken by both machines will be the same.
- Let's assume the time taken to produce 6000 pairs of bolts and nuts is 't' minutes.

4. The number of nuts produced in 't' minutes by the machine producing nuts is:
- (t / 14) * 500

5. The number of bolts produced in 't' minutes by the machine producing bolts is:
- (t / 20) * 600

6. Since we need to produce 6000 pairs of nuts and bolts:
- (t / 14) * 500 = (t / 20) * 600

7. Solve the above equation to find 't':
- (t / 14) * 500 = (t / 20) * 600
- 500t = 600t / 20 * 14
- 500t = 600t / 280
- 500t * 280 = 600t
- 140000t = 600t
- 140000 = 600t - 500t
- 140000 = 100t
- t = 140000 / 100
- t = 1400

Therefore, the minimum time required to produce 6000 pairs of bolts and nuts is 1400 minutes. However, this is not one of the answer choices provided.

Let's recheck our calculations:

- (1400 / 14) * 500 = (1400 / 20) * 600
- 1000 * 500 = 70 * 600
- 500000 = 42000

It seems we made a calculation error. Let's reevaluate the problem.

The correct calculation is as follows:

6. Since we need to produce 6000 pairs of nuts and bolts:
- (t / 14) * 500 = (t / 20) * 600

7. Solve the above equation to find 't':
- 500t / 14 = 600t / 20
- 500t * 20 = 600t * 14
- 10000t = 8400t
- 8400t - 10000t = 0
- -1600t = 0
- t = 0

Therefore, the minimum time required to produce 6000 pairs of bolts and nuts is 0 minutes.

However, this does not make sense as it is not possible to produce the
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Community Answer
A factory produces nuts and bolts. A machine in it produces only nuts ...
2000 nuts are produced in 14 minutes (10 minutes break and 500 nuts per minutes so 4 minutes to produce 2000 nuts ), for next 2000 nuts it will take 14 minutes more, and for more two thousand it will take 4 minutes more, so total time = 32 minutes
similarly, 6000 bolts are produced in 20 + 5 = 25 minutes
so minimum time required is 32 minutes
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A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.a)32 minutesb)20 minutesc)25 minutesd)40 minutese)None of theseCorrect answer is option 'A'. Can you explain this answer?
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A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.a)32 minutesb)20 minutesc)25 minutesd)40 minutese)None of theseCorrect answer is option 'A'. Can you explain this answer? for Quant 2024 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.a)32 minutesb)20 minutesc)25 minutesd)40 minutese)None of theseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A factory produces nuts and bolts. A machine in it produces only nuts while another produces only bolts. The machine producing only nuts produces 500 nuts per minute and need to be cleared for 10 minutes after production of 2000 nuts. The machine producing only bolts produces 600 bolts per minute and needs to be cleared for 15 minutes after production of 3000 bolts. Find the minimum time required to produce 6000 pairs of bolts and nuts if both machines are operated simultaneously.a)32 minutesb)20 minutesc)25 minutesd)40 minutese)None of theseCorrect answer is option 'A'. Can you explain this answer?.
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