Question

In a locality with 120 residents, 90 like to have mango shake, 65 like to have banana shake and 75 like to have strawberry shake. 30 like only one of the three shakes and 55 like only two of the three shakes. 5 residents do not like any of the three shakes. How many residents like all the three shakes?
A. 25
B. 30
C. 35
D. Cannot be determined​

Answer 1

Answer:

Answer- B:10

Step-by-step explanation:

115 = 90+65+75-20-55-x

x=30

Answer 2

Given,

The total number of residents$\[ = 120\]$

The number of persons that like mango shake$\[ = 90\]$

The number of persons that like to have banana shake$\[ = 65\]$

The number of persons that like to have strawberry shake$\[ = 75\]$

The number of persons that like to have only one of the three shakes$\[ = 30\]$

The number of persons that like only two of the three shakes$\[ = 55\]$

The number of persons that do not like any of the three shakes$\[ = 5\]$

Solution,

Assume that the number of persons that like all the three shakes are x.

The number of persons that like shakes

$\[\begin{array}{l} = 120 - 5\\ = 115\end{array}\]$

Therefore,

$\[\begin{array}{l} \Rightarrow 115 = 90 + 65 + 75 - 20 - 55 - x\\ \Rightarrow 115 = 230 - 75 - x\\ \Rightarrow x = 230 - 75 - 115\\ \Rightarrow x = 40\end{array}\]$

Hence, the correct option is (b) i.e. $\[30\].$