Hi,
In the question it is given that in a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade.
Maximum number of students who like all three drinks can be 52. ( because 52 number of students can have coffee, tea & lemonade at the same time)
If it is 53 then one student will not have lemonade ( as only 52 students had lemonade)
For Minimum number of students who had all three drinks we have two equations
n+s+d+t = 100   - Equation 1
d+2t-n = 105   - Equation 2
For minimum value of t in equation 2, n has to be equal to zero, otherwise as value of n increases t will increase.
s+d+t = 100
d+2t = 105
Here d can have maximum value = 100 so using hit and trial
let t= 3 then d= 99, s= -2 ( not possible)
let t=4 then d = 97, s= -1 ( not possible)
At t=5, d= 95 & s= 0 ( It is possible & valid case)
Therefore minimum value of t=5.
Hope this helps!