A baker observed that 58% of his customers like mango pastries whereas 84% like chocolate pastries. If x% of his customers like both mango and chocolate pastries then what is the possible range of x?
OPTIONS
A) 48 ≤ x ≤ 60
B) 38 ≤ x ≤ 54
C) 42 ≤ x ≤ 58
D) 42 ≤ x ≤ 52
Answers
Answer:
option C is the correct answer.
Step-by-step explanation:
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Given : A baker observed that 58% of his customers like mango pastries whereas 84% like chocolate pastries.
x% of his customers like both mango and chocolate pastries then what is the possible range of x
To Find : possible range of x
Solution:
n(M) = 58 %
n(C) = 84 %
n(M ∩ C) = x %
n(M ∩ C) ≤ n(M) , n(C)
Hence x % ≤ 58 % , 84 %
=> x ≤ 58
n(M U C) = n(M) + n(C) - n(M ∩ C)
=> n(M U C) = 58 % + 84 % - x %
=> n(M U C) = 142 % - x %
n(M) m , n(C) ≤ n(M U C) ≤ 100 %
84 % ≤ n(M U C) ≤ 100 %
=> 84 % ≤ 142 % - x % ≤ 100 %
=> 84 - 142 ≤ -x ≤ 100 - 142
=> -58 ≤ -x ≤ - 42
=> 58 ≥ x ≥ 42
Hence 42 ≤ x ≤ 58 is the correct option
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