In a class of 100 students, 55 students have passed in Mathematics and 67 students have passed in Ph

English

Gujarati

Hindi

1.Set Theory

easy

In a class of $100$ students, $55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is

A

$22$

B

$33$

C

$10$

D

$45$

Solution

(d) $n\,(M) = 55,n\,(P) = 67,n\,(M \cup P) = 100$

Now, $n\,(M \cup P) = n\,(M) + n\,(P) – n\,(M \cap P)$

$100 = 55 + 67 – n\,(M \cap P)$

$\therefore n\,(M \cap P) = 122 – 100 = 22$

Now $n$ ($P$ only) =$n\,(P) – n(M \cap P)$$ = 67 – 22 = 45$.

Standard 11

Mathematics

Share

Similar Questions

In a group of $65$ people, $40$ like cricket, $10$ like both cricket and tennis. How many like tennis only and not cricket? How many like tennis?

medium

In a survey of $400$ students in a school, $100$ were listed as taking apple juice, $150$ as taking orange juice and $75$ were listed as taking both apple as well as orange juice. Find how many students were taking neither apple juice nor orange juice.

easy

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 at least one of the newspapers.

medium

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.

medium

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?

hard

(KVPY-2017)