Out of $500$ car owners investigated, $400$ owned car $\mathrm{A}$ and $200$ owned car $\mathrm{B} , 50$ owned both $\mathrm{A}$ and $\mathrm{B}$ cars. Is this data correct?
Out of $500$ car owners investigated, $400$ owned car $\mathrm{A}$ and $200$ owned car $\mathrm{B} , 50$ owned both $\mathrm{A}$ and $\mathrm{B}$ cars. Is this data correct?
Let $U$ be the set of car owners investigated, $M$ be the set of persons who owned car $A$ and $S$ be the set of persons who owned car $B.$
Given that $\quad n( U )=500, n( M )=400, n( S )=200$ and $n( S \cap M )=50$
Then $\quad n( S \cup M )=n( S )+n( M )-n( S \cap M )=200+400-50=550$
But $S \cup M \subset U$ implies $n( S \cup M ) \leq n( U )$
This is a contradiction. So, the given data is incorrect.
Similar Questions
In a survey of $60$ people, it was found that $25$ people read newspaper $H , 26$ read newspaper $T, 26$ read newspaper $I, 9$ read both $H$ and $I, 11$ read both $H$ and $T,$ $8$ read both $T$ and $1,3$ read all three newspapers. Find:
the number of people who read exactly one newspaper.
In a survey of $60$ people, it was found that $25$ people read newspaper $H , 26$ read newspaper $T, 26$ read newspaper $I, 9$ read both $H$ and $I, 11$ read both $H$ and $T,$ $8$ read both $T$ and $1,3$ read all three newspapers. Find:
the number of people who read exactly one newspaper.
In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2: 3$. If further $44$ girls leave the class, then class the ratio of boys to girls is $5: 2$. How many more boys should leave the class so that the number of boys equals that of girls?
In a classroom, one-fifth of the boys leave the class and the ratio of the remaining boys to girls is $2: 3$. If further $44$ girls leave the class, then class the ratio of boys to girls is $5: 2$. How many more boys should leave the class so that the number of boys equals that of girls?
- [KVPY 2017]
A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?
A college awarded $38$ medals in football, $15$ in basketball and $20$ in cricket. If these medals went to a total of $58$ men and only three men got medals in all the three sports, how many received medals in exactly two of the three sports?
In a school there are $20$ teachers who teach mathematics or physics. Of these, $12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics ?
In a school there are $20$ teachers who teach mathematics or physics. Of these, $12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics ?
In a city $20$ percent of the population travels by car, $50$ percent travels by bus and $10$ percent travels by both car and bus. Then persons travelling by car or bus is......$\%$
In a city $20$ percent of the population travels by car, $50$ percent travels by bus and $10$ percent travels by both car and bus. Then persons travelling by car or bus is......$\%$