If 18 binders can bind 900 books in 10 days, how many binders will be required to bind 660 books in 12 days?

The correct answer is: 12 days.

Let the number of binders be represented as x, the number of books be represented as y and the number of days be represented as z. Now, more books will mean we will require more binders so x and y will have a directly proportional relationship i.e
x  y
Now if more days are given, fewer binders will be required which means x and z have an inversely proportional relationship i.e
x  
So, we can say that
x  
x = k …….(1)
Where k is a proportionality constant
Step 1 of 2:
It is given that 18 binders can bind 900 books in 10 days. So,  x = 18, y = 900 and z = 10. Putting the values in equation (1)
18 = k
k =  = 
Step 2 of 2:
Now we are asked to find the number of binders that will be required to bind 660 books in 12 days. Let the number of binders be “b”. So, x = b, y = 660 and z = 12. Putting the values in equation (1)
b = k
Now, put the value of k =
d =  
d = 11 binders
Final Answer:
Hence, 11 binders will be required to bind 660 books in 12 days.