Question

In NutsAndBolts 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 be cleaned for 10 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

Hint:

For problems involving multiple machines, calculate the individual time for each and then find the minimum.

Answer 1

The Correct Option is C

- Nuts machine produces 100 nuts/minute, and for 1000 nuts, it needs 5 minutes of cleaning, so 1000 nuts take 15 minutes (100 minutes for nuts + 5 minutes cleaning). - Bolts machine produces 75 bolts/minute, and for 1500 bolts, it needs 10 minutes of cleaning, so 1500 bolts take 20 minutes (100 minutes for bolts + 10 minutes cleaning). To produce 9000 pairs of nuts and bolts, the minimum time is calculated as: \[ \text{Total time} = 170 \quad \text{minutes.} \] \[ \boxed{170} \]