70 patients in a hospital consume 1350 litres of milk in 30 days. At the same rate, how many patients will consume 1710 litres in 28 days?

The correct answer is: 28 days.

Let the number of patients be represented as x, the volume of milk be represented as y and the number of days be represented as z. Now, more patients will mean more milk is required so x and y will have a directly proportional relationship i.e
x  y
Now if more patients are present in the hospital, milk will be consumed in a fewer number of days 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 70 patients consume 1350 litres of milk in 30 days. So,  x = 70, y = 1350 and z = 30. Putting the values in equation (1)
70 = k
k =  = 
Step 2 of 2:
Now we are asked to find the number of patients that will consume 1710 litres in 28 days. Let the number of patients be “p”. So, x = p, y = 1710 and z = 28. Putting the values in equation (1)
p = k
Now, put the value of k =
p = 
p = 95 patients
Final Answer:
Hence, 95 patients will consume 1710 litres in 28 days.