Question

A soap factory makes 600 units in 9 days with
help of 20 machines. How many units can be
made in 12 days with the help of 18
machines?​

Answer 1

Answer:

The number of units increases with the number of machines. On the other hand as the number of machines increases, the number of days required decreases. Thus the number of machines is directly proportional to the number of units and inversely proportional to the number of days. The first information gives

20=k×600×1920=k×600×19.

This gives the constant of proportionality

k=20×9600k=20×9600

Let xx be the number of units which can be manufactured using 1818 machines in 1212 days. Using the same reasoning, we obtain

18=k×x×11218=k×x×112.

Thus we obtain

x=18×12k=18×12×60020×9=720x=18×12k=18×12×60020×9=720.

Hence 720720 units can be manufactured using 1818 machines for 1212 days.