There are 100 children in a primary school. The number of children who like blue and red is 30. The number of children who like yellow and blue is 20. The number of children who like only one color is 45. No child likes only yellow and red. How many children like all three colours?

Option 1 : 5

Given:

Total no. of children = 100

No. of children who like blue and red = 30

No. of children who like yellow and blue = 20.

No. of children who like only one colour = 45.

The Venn diagram representation of the given information is as follows:

[ alt="F1 Shraddha Archana 07.02.2022 D33" src="//storage.googleapis.com/tb-img/production/22/02/F1_Shraddha_Archana_07.02.2022_D33.png" style="width: 188px; height: 213px;">

• No. of children who like only red or only yellow or only blue = 45
• Here, X likes only yellow; Y likes only red
• So, no. of children who like only blue = 45 - (X + Y) = 45 - X - Y 

• Children who like all three colours = 100 - 45 - 20 - 30 = 100 - 95 = 5
• Thus, 5 children like all three colours.

Hence, "option 1" is the correct answer.