From a cloth store, 15 customers bought orange dress, 15 bought red dress, 20 bought blue dress, 2 bought all the three 7 colours and 8 bought at least two of these. How many bought at least one dress from the store?

Correct option is D

Given:

15 customers bought orange dress, 15 bought red dress, 20 bought blue dress, 2 bought all the three colours and 8 bought at least two of these colours.  

Solution:

The shaded portion represent customer who bought atleast two dresses.

=> Customers who bought exactly 2 dresses

= 8 - (2 × 2) = 8 - 4 = 4

Thus we have,

n (O) = 15, n (R) = 15, n (B) = 20

n (O ∩ R ∩ B) = 2

n (O ∩ R) = n (R ∩ B) = n (B ∩ O) = 4

∴ n (O ∪ R ∪ B) = n (O) + n (R) + n (B) - n (O ∩ R) - n (R ∩ B) - n (B ∩ O) + n(O ∩ R ∩ B)

= 15 + 15 + 20 - 4 - 4 - 4 + 2

= 50 - 10 = 40 

Alternate Solution:
Total customers who bought more than at least two colors
=> 8 + 2 = 10
Customers bought clothes of at least one color from the store
=> (15 + 15 +20) - 10
=> 50 - 10 = 40
∴ 40 Customers bought clothes of at least one color from the store.