A group of 123 workers went to a canteen for cold drinks, ice-cream and tea, 42 workers took ice-cream, 36 tea and 30 cold drinks. 15 workers purchased ice-cream and tea, 10 ice-cream and cold drinks, and 4 cold drinks and tea but not ice-cream, 11 took ice-cream and tea but not cold drinks. Determine how many workers did not purchase anything?

Answer

44

Explanation

c + f + g + e = 42 … (i)
b + d + g + e = 36 … (ii)
a + f + d + g = 30 … (iii)
g + e = 15 … (iv)
f + g = 10 … (v)
d = 4 … (vi)
e = 11 … (vii)

From (iv) and (vii), g + 11 = 15 implies g = 4 ... (viii)
From (v) and (viii), f + 4 = 10 implies f = 6 ... (ix)
From (i), c + 6 + 4 + 11 = 42 implies c = 21 ... (x)
From (ii), b + 4 + 4 + 11 = 36 implies b = 17 ... (xi)
From (iii), a + 6 + 4 + 4 = 30 implies a = 16 ... (xii)
Number of required persons
`= 123 - (16+17+21+4+11+6+4)`
= 123 - 79
= 44