Find minimum number of customers that must have visited the bakery that day? A bakery sells three kinds of pastries -pineapple,
  choclate and black forest. On a particular day,
  the bakery owner sold the following number of 
  pastries : $90$ pineapple , $120$ chocolate and
  $150$ black forest. If none of the customers bought
   more than $2$ pastries of each type, what is the 
  minimum number of customers that must have 
  visited the bakery that day ?


$a.)\ 80 \\
\color{green}{b.)\ 75} \\
c.)\ 60 \\
d.)\ 90 $

I have drawn the venn diagram and concluded that the visitors are $210$.

But that is not in options.



I look for a short and a simple way.

I have studied maths up to $12$th grade.
You haven’t enough information to fill in the Venn diagram. (And what you’ve done is inconsistent with the data, since you have $120$ pineapple pastries.)

To get the smallest possible number of customers, you want each customer to buy as many pastries as possible consistent with the totals given. $150$ black forest pastries were bought; if each customer bought $2$, there would have been at least $\frac{150}2=75$ customers, and there can’t possibly be any fewer customers than that. Is $75$ customers enough to account for the other sales? Yes: for instance, it could be that $60$ of the customers also bought $2$ chocolate pastries each, and $45$ of them also bought $2$ pineapple pastries each. (Many other arrangements are also possible.) 

It’s the black forest pastries that determine the lower bound on the number of customers, simply because more black forest pastries were sold than any other type.
As $~90~$ is min.   

So $~\frac{90}{2}=45~$ should be ans. 

But it is not in options.

If we consider $~60~$ single pastries out of $~90~$ pastries are bought by $~60~$ customers and remaining $~30~$ pastries  are bought by $~15~$  customers each $~2~$. i.e.  $~(15*2=30)~$.

Min customers $~60+15=75~$.