7 machines take 7 min to make 7 identical toys. At the same rate how many minutes would it take for 100 machines to make 100 toys?
(A) 1 (B) 7
(C) 100 (D) 700
My trial: Given that
7 machines:7minutes:7 toys
1 machine:1minute:1 toy
100 machines:100 minutes:100 toys
therefore it would 100 minutes for 100 machines to make 100 toys.
But my book suggests that answer must be 7 minutes I don't know where I am wrong. I think there should be a correct method to solve such problems. Please give correct solution to this problem.
thanks
Best Answer
7 machines make 7 toys in - 7 minutes.
So, 7 machines make 100 toys in - $\frac {7} {7}.100 $ minutes = 100 minutes
Or, 100 machines make 100 toys in - $ 100. \frac {7}{100} = 7 $ minutes
The general way to proceed is to keep all quantities constant, except one, and see how it varies with the quantity you require. Now the explanation is that same number of machines would take more time to make more toys, hence it is directly proportional. However, more machines would take less time to make same number of times,i.e, it is inversely proportional.