Question

A factory requires 42 machines to produce a given number of articles in 63 days. How many machines would be required to produce the same number of articles in 54 days ?

Answer 1

Hint: To get the number of machines required to produce the same number of articles in 54 days. We will first find the ratio of number of machines required in both the cases and then we will find the ratio of number of days and at last equate both the results such that we will get the number of machines required.

Complete step-by-step answer:
In this question it is given that the number of articles produced by 42 machines in 63 days is equal to number of articles produced in 54 days by some x machines.
If the articles are to be produced in a lesser number of days, more machines are required.
Hence, the number of machines and number of articles are in inverse proportion.
Let the number of machines required to make the same number of articles in 54 days be x
Then,
 \[x = 49\] inverse ratio of \[63:54\]
\[ \Rightarrow 42:x = 54:63\]
Applying the rule, product of extremes = product of means
\[42 \times 63 = x \times 54\]
\[x = \dfrac{{42 \times 63}}{{54}}\]
\[x = 49\]
Hence, 49 machines are required to make the same number of articles in 54 days.

Note: We can solve this question and find the number of days to produce the same number of articles by unitary method also where we find the articles produced per day and then multiply to the number of days asked.