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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 all the three dishes is 80, then what is the minimum possible number of families who like only Misal Pao ?

 

Option: 1

120


Option: 2

100


Option: 3

80


Option: 4

60


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) … r = 80

Substituting the value of r in (4) in equations (1), (2) and (3), we get

(5) … a + (x + y) = 80

(6) … b + (x + z) = 60

(7) … (a +b + c) + (x + y + z) = 220

Equation (7) says :

(a +b + c) + (x + y + z) = 220

or, {a + (x + y)} + {b + z} + c = 220

or, 80 + (60 – x) + c = 220 [Substituting values from (5) and (6)]

or, c = 80 + x … (8)

xMin can be 0,

which implies that the minimum value of c can be (80 + 0) = 80.

Hence, the minimum possible number of families who like only Misal Pao = 80

Posted by

shivangi.bhatnagar

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