Directions: Consider the following Venn diagram, where X, Y and Z are three sets. Let the number of elements in Z be denoted by n(Z). which is equal to 90.
If the number of elements in Y and Z are in the ratio 4 : 5, then what is the value of b?
21
Calculation:
Given: n(Z) = 90 and the number of elements in Y and Z are in the ratio 4 : 5
To find: b = ?
n(Y) = 16 + 18 + 17 + b
n(Z) = 12 + 18 + 17 + c = 90
\(\rm \frac{n(y)}{n(z)}=\frac{16+18+17+b}{12+18+17+c}=\frac{4}{5}\\ \Rightarrow \frac{51+b}{90}=\frac{4}{5}\\ \Rightarrow (51+b)\times 5=360 \\\Rightarrow255+5b=360\\ \Rightarrow5b=105\\ \Rightarrow b=21\)
Hence, option (3) is correct.
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List I
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