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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

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 exactly one dish is 180, then what is the maximum possible number of families who like Misal Pao ?

 

Option: 1

240


Option: 2

180


Option: 3

120


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) … (a + b + c) = 180 [a, b and c are families who like exactly one dish]

Subtracting (4) from (3), we get

(5) … (x + y + z) + r = 300 – 180 = 120

From (5), maximum possible value of r, that is rMax = 120

Hence minimum possible value of (x + y + z), that is (x + y + z)Min = 120 – 120 = 0

Since x, y and z have to be whole numbers, and (x + y + z)Min = 0 when r is maximum,

Hence xMin = yMin = zMin = 0 when r is maximum.

Therefore, aMin = 160 – (0+120+0) = 40 [from (1)]

and bMin = 140 – (0+120+0) = 20 [from (2)]

(6) … Hence, minimum value of (a + b) + x = (40+20)+0 = 60

Hence, the maximum possible number of families who like Misal Pao

= maximum value of c + (y + z) + r 

= 300 – 60 [Subtracting (6) from (3)]

= 240

Posted by

Divya Prakash Singh

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