Aptitude Discussion

Q. |
In Nuts And Bolts factory, one machine produces only nuts at the rate of 100 nuts per minute and needs to be cleaned for 5 minutes after production of every 1000 nuts. Another machine produces only bolts at the rate of 75 bolts per minute and needs to cleaned for10 minutes after production of every 1500 bolts. If both the machines start production at the same time, what is the minimum duration required for producing 9000 pairs of nuts and bolts? |

✖ A. |
130 minutes |

✖ B. |
135 minutes |

✔ C. |
170 minutes |

✖ D. |
180 minutes |

**Solution:**

Option(**C**) is correct

**Machine I:**

Number of nuts produced in one minute = 100

To produce 1000 nuts time required = 10 min

Cleaning time for nuts = 5 min

Over all time to produce 1000 nuts = 15 min.

Over all time to produce 9000 = 135 min − 5 min = 130 min -----(1)

**Machine II:**

To produce 75 bolts time required = 1min

To produce 1500 bolts time required = 20 min

Cleaning time for bolts = 10 min.

Effective time to produce 1500 bolts = 30 min

Effective time to produce 9000 bolts = 30×6 − 10 = 170 min ------ (2)

From (1) and (2),

Minimum time = **170 minutes**

**Edit:** Thank you **Najaf** for pointing out the typo in the solution, modified solution and in part A, time has been changed to 130 min from 133 min.

**Devansh Singh**

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see you need to understand that we do not go for the 9000 mark directly for eg, 1500 in 30 min. (20min + 10 min) so 9000 bolts in 180 minutes. This would be wrong because we are considering the extra 10 minutes at the end as the 9000 bolts would already be completed at the end of 170 minutes and thus extra 10 min. for machine cleaning would not be needed.

If you still don't understand please let me know , i'll try to explain it in a more easy language.

**Additi**

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Minimum time should be 130 because part A is producing 9000 pairs in 130 min whereas part B is producing 9000 pairs in 170 minute, if i am wrong correct me ?

it was asked to find the time for production of NUTS AND BOLTS. Hence 170 min.

**Shubh**

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why 5 cycles and not 6?

**Najaf**

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To produce 9,000 nuts:

(Production Time of 1,000 nuts x 9) + Cleaning Time for 8 cycles

$ \Rightarrow (9 \times 10 \text{ mins}) + (5 \times 8 \text{ mins}) = 130\text{ mins}$

To produce 9,000 bolts:

(Production Time of 1,500 bolts x 6) + Cleaning Time for 5 cycles

$ \Rightarrow (6 \times 20 \text{ mins}) + (5 \times 10 \text{ mins}) = 170 \text{ mins}$

So according to my calculation, part A (nut production) is done wrong.

Thank you, modified the solution accordingly.

In the solution why are 5min and 10 min being reduced from the total time of production of 9000 nuts and 9000 bolts respectively?