Question

A stationary shop orders a batch of pens from a factory. The factory could make the batch of pens in 20 days using 12 machines. Due to a fault, only 3 machines were used for the first 8 days. All 12 machines were used from day 9 onwards. How many days did it take to make the batch of pens?

Answer 1

It took a total of 26 days to make the batch of pens, with only 3 machines running for the first 8 days and all 12 machines running for the remaining 18 days.

Step-by-step explanation:

The student has asked how many days it took to make a batch of pens when 12 machines could complete the task in 20 days, but only 3 machines were used for the first 8 days and all 12 machines from day 9 onwards.

First, we find the work rate per machine by dividing the total work (1 batch of pens) by the total number of machine-days that would have been required if all 12 machines were used for 20 days: 1 batch / (12 machines × 20 days) = 1/240 batch per machine-day.

For the first 8 days, only 3 machines were working, which means 3 machines × 8 days = 24 machine-days. The work done in these days is 24 machine-days × 1/240 batch per machine-day = 1/10 of the batch.

We subtract the completed fraction of the work from the whole to find the remaining work: 1 - 1/10 = 9/10 of the batch. To finish this remaining work with all 12 machines, we take the remaining fraction of work and divide it by the work rate with all 12 machines: (9/10 batch) / (12 machines × 1/240 batch per machine-day) = 18 days.

Therefore, the total time taken is the initial 8 days plus the additional 18 days, which equals 26 days to complete the batch of pens.