In a party of 150 persons, 75 persons take tea, 60 persons take coffee and 50 persons take milk. 15 of them take <strong>BOTH</strong> tea and coffee, but <strong>NONE</strong> taking milk takes tea. If each person in the party takes <strong>AT LEAST</strong> one drink, then what is the number of persons taking milk <strong>ONLY</strong>?
- A. 50
- B. 40
- C. 30 ✓
- D. 20
Correct Answer: C. 30
Explanation
Let n(T)=75, n(C)=60, n(M)=50. Given n(T \cap C)=15, n(M \cap T)=0, so n(T \cap C \cap M)=0. Using n(T \cup C \cup M) = 150, we find 150 = 75+60+50-15-n(C \cap M)-0+0 \implies n(C \cap M) = 20. Milk only is n(M) - n(M \cap C) = 50 - 20 = 30.
Related questions on Algebra
- If p + q + r = 0, then what is z^{\frac{p^2}{qr}} \times z^{\frac{q^2}{rp}} \times z^{\frac{r^2}{pq}} equal to ?
- What is the value of k for which (k^2 - 5k + 4)x^2 + (k^2 - 3k - 4)x + (k^2 - 4k) = 0 is an identity ?
- If \frac{a^2}{b^2 + c^2} = \frac{b^2}{c^2 + a^2} = \frac{c^2}{a^2 + b^2}, then what is the value of a^4 + b^4 + c^4 equal to ?
- If \frac{1}{x} = \frac{1}{p} + \frac{1}{q}, then what is \frac{pq}{p^2 - q^2}\left(\frac{x + p}{x - p} - \frac{x + q}{x - q}\right) equa...
- If (x - 5) is the HCF of x^2 - x - p and x^2 - qx - 10, then what is the value of (p + q) ?