Each-of-the-students-in-the-class-was-in-the-theater-exactly-two-times-during-the-winter-holidays-while-performances-A-B-and-C-were-seen-by-25-12-and-23-students-respectively-How-many-students-are-

Question Number 105851 by 1549442205PVT last updated on 01/Aug/20

$$\mathrm{Each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{class}\:\mathrm{was} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{theater}\:\mathrm{exactly}\:\mathrm{two}\:\mathrm{times}\:\mathrm{during}\: \\ $$$$\:\mathrm{the}\:\mathrm{winter}\:\mathrm{holidays},\mathrm{while} \\ $$$$\mathrm{performances}\:\mathrm{A},\mathrm{B}\:\mathrm{and}\:\mathrm{C}\:\mathrm{were}\:\mathrm{seen}\:\mathrm{by} \\ $$$$\mathrm{25},\mathrm{12}\:\mathrm{and}\:\mathrm{23}\:\mathrm{students},\mathrm{respectively} \\ $$$$.\mathrm{How}\:\mathrm{many}\:\mathrm{students}\:\mathrm{are}\:\mathrm{there}\:\mathrm{in}\:\mathrm{the}\: \\ $$$$\mathrm{class}?\mathrm{How}\:\mathrm{many}\:\mathrm{of}\:\mathrm{them}\:\mathrm{saw}\:\mathrm{performances} \\ $$$$\:\mathrm{A}\:\mathrm{and}\:\mathrm{B},\mathrm{B}\:\mathrm{and}\:\mathrm{C},\mathrm{C}\:\mathrm{and}\:\mathrm{A}? \\ $$

Answered by mr W last updated on 01/Aug/20

$${N}_{{A},{B}} +{N}_{{A},{C}} =\mathrm{25}\:\:\:…\left({i}\right) \\ $$$${N}_{{A},{B}} +{N}_{{B},{C}} =\mathrm{12}\:\:\:…\left({ii}\right) \\ $$$${N}_{{A},{C}} +{N}_{{B},{C}} =\mathrm{23}\:\:\:…\left({iii}\right) \\ $$$$\Sigma: \\ $$$$\mathrm{2}\left({N}_{{A},{B}} +{N}_{{B},{C}} +{N}_{{A},{C}} \right)=\mathrm{25}+\mathrm{12}+\mathrm{23}=\mathrm{60} \\ $$$${N}_{{A},{B}} +{N}_{{B},{C}} +{N}_{{A},{C}} =\mathrm{30}\:\:\:\:…\left({iv}\right) \\ $$$$\left({iv}\right)−\left({iii}\right): \\ $$$${N}_{{A},{B}} =\mathrm{7} \\ $$$$\left({iv}\right)−\left({i}\right): \\ $$$${N}_{{B},{C}} =\mathrm{5} \\ $$$$\left({iv}\right)−\left({ii}\right): \\ $$$${N}_{{A},{C}} =\mathrm{18} \\ $$$$\Rightarrow{totally}\:\mathrm{30}\:{students},\:\mathrm{7}\:{saw}\:{A}\:\&{B}, \\ $$$$\mathrm{5}\:{saw}\:{B}\:\&\:{C},\:\mathrm{18}\:{saw}\:{A}\:\&\:{C}. \\ $$

Commented by 1549442205PVT last updated on 01/Aug/20

$$\mathrm{Thank}\:\mathrm{Sir}. \\ $$

Commented by PRITHWISH SEN 2 last updated on 01/Aug/20

$$\mathrm{Is}\:\mathrm{the}\:\mathrm{answer}\:\mathrm{of}\:\mathrm{Q105791}\:\mathrm{correct}? \\ $$

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