If 7 workers can build 7 cars in 7 days, then how many days would it

An interesting thing in such questions is 7 workers and 7 cars. Makes me think of each worker working on his own single car and finishing it in 7 days. So 1 worker finishes 1 car in 7 days.
5 workers working on their own individual 5 cars will also take 7 days. 210 workers working on 210 cars will take 7 days too.
210 workers working on 420 cars will take 14 days (each worker makes 1 car in 7 days and then another in another 7 days)
and so on... Sometimes you can just reason it out too.




Actually, both are using the same concept of variation. You can do it one step at a time or all together, whatever suits you. Just different ways of looking at the same thing.

Let me tell you how I think of the all together method.

7 workers - 7 cars - 7 days
5 workers - 5 cars - a days

No of days needed = 7 * (5/7) * (7/5)
You get this expression by thinking in the following way: Initially, you needed 7 days so that is the quantity that has to change so write "No of days needed = 7 *"

Just consider cars now. When you need to make only 5 cars (i.e. less cars) as compared to 7 cars, do you need more days or less? Less ofcourse so you multiply above by (5/7) (it is smaller than 1 so will decrease whatever it multiplies)
Now you have: "No of days needed = 7 * (5/7)"

Now just consider workers. If you have fewer workers (5 instead of 7), will you need more days to finish the work or less? More ofcourse so multiply by (7/5) (which is greater than 1)
Now you have: "No of days needed = 7 * (5/7) * (7/5) = 7 days"

On the same lines, try this:
4 people make 28 baskets in 4 days working 8 hrs every day. How many days will 8 people take to make 14 baskets working 2 hrs a day?