correct answer is: c) 160 items

Explanation

Let, the number of items is ‘x’ .

People        Days        Hours        Items
10                10               5              10
40                20              10              x

Since, if People increase the number of Items also increase.
\therefore People and Items are Direct proportion =10:40
If Days increase the number of Items also increase.
\therefore Days and Items are Direct proportion =10:20
If Hours increase the number of Items also increase.
\therefore Hours and Items are Direct proportion =5:10
According to the question,

or, \large\frac{10}{40}\times\frac{10}{20}\times\frac{5}{10}=\frac{10}{x}
or, \large\frac{1}{16}=\frac{10}{x}
or, x=160 _{[cross multiply]}
\therefore The number of items is 160 .
Ans: 40 people make 160 items in 20 days, working for 10 hours per day.

These particular questions can also be asked in the following ways:
1. Calculate the total number of items that 40 people can produce in 20 days when working for 10 hours each day, given that 10 people make 10 items in 10 days while working for 5 hours per day.
2. Determine the production output of 40 people over 20 days with 10 hours of work each day, using the information that 10 people produce 10 items in 10 days with 5 hours of work per day.
3. What is the total number of items that 40 individuals can manufacture in 20 days if they work for 10 hours daily, considering the scenario where 10 people produce 10 items in 10 days with 5 hours of work each day?