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  • Directions for question : In a group of 300 families in a colony of Dharavi, each family likes at least one dish among Pao Bhaji, Vada Pao and Misal Pao. 160 familie

Directions for question :

In a group of 300 families in a colony of Dharavi, each family likes at least one dish among Pao Bhaji, Vada Pao and Misal Pao. 160 families like Pao Bhaji and 140 families like Vada Pao.

Question:

If the number of families who like Misal Pao is 180, then what is the maximum possible number of families who like only Pao Bhaji ?

 

 

Option: 1

180


Option: 2

120


Option: 3

60


Option: 4

30


Answers (1)

best_answer

 

Let PB, VP and MP in the Venn diagram stand for families who like Pao Bhaji, Vada Pao and Misal Pao respectively.

Since each family likes at least one dish among Pao Bhaji, Vada Pao and Misal Pao, therefore n = 0

It is given that :

(1) … a + (x + y) + r = 160

(2) … b + (x + z) + r = 140

(3) … (a +b + c) + (x + y + z) + r = 300

(4) … c + (y + z) + r = 180

Subtracting (4) from (3), we get

(5) … (a + b) + x = 300 – 180 = 120

To maximize the value of a (which is what has been asked from us), we need to minimize the value of both b and x.

bMin can be 0

xMin can also be 0

Hence, the maximum possible number of families who like only Pao Bhaji

= maximum possible value of a

= 120 – (0 + 0) [Subtracting (bMin + xMin) from (5)]

= 120

Posted by

manish

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