Nishit K Sinha Solutions for Chapter: Miscellaneous, Exercise 1: Practice Exercises

In a party, $70\%$ of the people drank coffee, $65\%$ drank soft drinks, $27\%$ did not drink anything, whereas $248$people drank both. What is the number of people who attended the party?

In a survey conducted in Patna, it was found that $\frac{3}{4}$ th of the town owns colour TV,$85\%$ of the people own refrigerator, and every $4$ in $5$ in the town owns music system. What is the minimum percentage of people who have all the three?

If class with $\mathrm{n}$ students is organized into four groups keeping the following conditions:

•  Each student belongs to exactly two groups and
•  Each pair of groups has exactly one student in common.

What is the value of $\mathrm{n}$ ?

In Ranchi, only two newspapers The Hindustan and The Indian Express are published. It is known that $25\%$ of the city population reads The Hindustan and $20\%$ reads The Indian Express, whereas $8\%$ read both newspapers. It is also known that $30\%$ of those who read The Hindustan but not The Indian Express look into advertisements, whereas $50\%$ of those who read both The Hindustan and The Indian Express look into advertisement. What percentage of the population looks into advertisement?

In a certain examination of $3$subjects, $^\{, 35\}$ students failed in Maths, $40$in Physics, and $40$in Chemistry. Twenty failed in Maths and Physics, $17$in Physics and Chemistry, and $15$in Maths and Chemistry. If $132$students did not fail in any subject, then what is the maximum number of students who have appeared for the examination?

A club has $256$members of whom $144$can play football, $123$ can play tennis, and $132$can play cricket. Moreover, $58$members can play both football and tennis, $25$can play both cricket and tennis, while $63$can play both football and cricket. If every member can play at least one game, then the number of members who can play only tennis is

Each of $74$students in a class studies at least one of the three subjects $\mathrm{H}$, $\mathrm{E}$ and $\mathrm{P}$. Ten students study all three subjects, while twenty study $\mathrm{H}$ and $\mathrm{E}$, but not $\mathrm{P}$. Every student who studies $\mathrm{P}$ also studies $\mathrm{H}$ or $\mathrm{E}$ or both. If the number of students studying $\mathrm{H}$ equals that studying $\mathrm{E}$, then the number of students studying $\mathrm{H}$ is_____

$290$students of MBA (International Business) in a reputed Business School have to study foreign language in Trimesters $\mathrm{IV}$and $\mathrm{V}$. Suppose the following information are given

$\mathrm{i}$. $120$students study Spanish

$\mathrm{ii}$. $100$students study Mandarin

$\mathrm{iii}$. At least $80$students, who study a foreign language, study neither Spanish nor Mandarin Then the number of students who study Spanish but not Mandarin could be any number from