A shop has only red, green blue carpets 60% of the carpets have red colour, 30% have green colour - Maths - Sets

Question

A shop has only red, green blue carpets 60% of the carpets have
red colour, 30% have green colour 50% have blue colour If no carpet
has all the 3 colours, then what %age of the carpets have only 1
colour?

Ajanta Trivedi · Accepted Answer

let the total number of carpets = 100

let n(R) , n(B) and n(G) represents the number of carpets of red color, blue color and green color respectively.

thus $n (R) = 60; n (B) = 50 a n d n (G) = 30$

$n (R \cup B \cup G) = 100$

since no carpet has all the three colors. therefore $n (R \cap B \cap G) = 0$

$n (R \cup B \cup G) = n (R) + n (B) + n (G) - n (R \cap B) - n (B \cap G) - n (G \cap R) 100 = 60 + 50 + 30 - [n (R \cap B) + n (B \cap G) + n (G \cap R)] n (R \cap B) + n (B \cap G) + n (G \cap R) = 60 + 50 + 30 - 100 = 140 - 100 = 40$

thus the number of carpets which have only one color.

$n (R \cup B \cup G) - n (R \cap B) - n (B \cap G) - n (G \cap R) = 100 - 40 = 60$

thus the 60 % carpet have only one color.

hope this helps you.

cheers!!

A shop has only red, green blue carpets. 60% of the carpets have red colour, 30% have green colour 50% have blue colour. If no carpet has all the 3 colours, then what %age of the carpets have only 1 colour?