Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Management
  • 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

View full answer

Similar Questions

Trending Articles/News

anam-khan

CAT 2024 answer key out at iimcat.ac.in; objection facility till December 5
anam-khan

CAT 2024 Answer Key (OUT) Live: Response sheet, answer key PDF at iimcat.ac.in; challenge window opens at 6 pm
anam-khan

CAT answer key 2024 tomorrow; how are scores normalised?

Latest Question