Question

A company produces 12 defective bulbs out of 1,000 bulbs. In the warehouse, bulbs are packaged in groups, each having identical numbers of bulbs. Find the maximum bulbs in each group such that no defective bulb is packaged with working bulbs, given that there is only one lot of manufactured bulbs.

Answer 1

Total number of bulbs $=1,000$
Number of defective bulbs $=12$
$\therefore$ Number of working bulbs $=1000-12=988$

Each package should contain an equal number of bulbs.
Also, no package should contain both defective and working bulbs.

$\therefore$ There exists a common factor of both $988$ and $12.$

The largest common factor will result in the largest package size, i.e., GCD of $988$ and $12.$

Using long division method,
GCD $=4$

$\therefore$ The largest package size is $4.$

Hence, There would be 3 packages of defective bulbs and 247 packages of working bulbs.