Arun Sharma Solutions for Exercise 2: Level of Difficulty

A bakery sells three kinds of pastries- pineapple, chocolate, and black forest. On a particular day, the bakery owner sold the following number of pastries: $90$ Pineapples, $120$Chocolate, and $150$ Black forests. If none of the customers bought more than two pastries of each type, what is the minimum number of customers that must have visited the bakery that day?

Gauri Apartment housing society organised annual games, consisting of three games: snooker, badminton and tennis. In all, $510$ people were members in the apartments' society and they were invited to participate in the games. Each person participating in as many games as he/she feels like. While viewing the statistics of the performance, Mr Capoor realised the following facts. The number of people who participated in at least two games was $52\%$ more than those who participated in exactly one game.

The number of people participating in $11, 22$ or $33$ games respectively was at least equal to $11$.

Being a numerically inclined person, he further noticed an interesting thing: The number of people who did not participate in any of the three games was the minimum possible integral value with these conditions.

What was the maximum number of people who participated in exactly three games?

A school has $180$students in its senior section where foreign languages are offered to students as part of their syllabus. The foreign languages offered are: French, German and Chinese and the numbers of people studying each of these subjects are $80,90 \text{and} 100$ respectively. The number of students who study more than one of the three subjects is $50\%$ more than the number of students who study all the three subjects. There are no students in the school who study none of the three subjects. Then how many students study all three foreign languages?

In a class of $42$ students, each play at least one of the three games-cricket, hockey or football.It is found that $14$ play cricket, $20$ play hockey and $24$ play football. Three play both cricket and football, two play both hockey and football and none play all the three games. Find the number of students who play cricket but not hockey.

Answer the following question based on the given information:

In the ancient town of Mohenjodaro, a survey founds that students were fond of three kinds of cold drinks(Pepsi, Coke, and Thumps up). It was also found that there were three kinds of beverages that they like (Tea, Coffee, and Cold Coffee).
The population of these towns was found to be $400000$ people in all and the survey was conducted on $10\%$ of the population. Mr. Yadav, a data analyst observed the following things about the survey-

(i) The number of people in the survey who like exactly two cold drinks is five times the number of the people who like all three cold drinks.
(ii) The sum of the number of people in the survey who like Pepsi and $42\%$ of those who like coke but not Pepsi is equal to the number of people who like tea.
(iii) The number of people in the survey who like Coffee is equal to the sum of $\frac{3}{8}$ of those who like Coke and $\frac{1}{2}$of those who like Thumps up. This number is also equal to the number who like Cold Coffee.
(iv) $18500$ people like Pepsi, $15000$ like all the beverages, and $3500$ like all the cold drinks
(v) $14000$ do not like Pepsi but likes Thumps up. 
(vi) $11000$ like Pepsi and exactly one more drink.
(v) $6000$like only Coke and the same number of people Like Pepsi and Thumps up but not Coke.

Find the number of the people in the survey who do like at least one of the three cold drinks?
  

What is the maximum number of people in the survey who like none of the three beverages?

Answer the following question based on the given information:

In the ancient town of Mohenjodaro, a survey founds that students were fond of three kinds of cold drinks(Pepsi, Coke, and Thumps up). It was also found that there were three kinds of beverages that they like (Tea, Coffee, and Cold Coffee).
The population of these towns was found to be $400000$ people in all and the survey was conducted on $10\%$ of the population. Mr. Yadav, a data analyst observed the following things about the survey-

(i) The number of people in the survey who like exactly two cold drinks is five times the number of the people who like all three cold drinks.
(ii) The sum of the number of people in the survey who like Pepsi and $42\%$ of those who like coke but not Pepsi is equal to the number of people who like tea.
(iii) The number of people in the survey who like Coffee is equal to the sum of $\frac{3}{8}$ of those who like Coke and $\frac{1}{2}$of those who like Thumps up. This number is also equal to the number who like Cold Coffee.
(iv) $18500$ people like Pepsi, $15000$ like all the beverages, and $3500$ like all the cold drinks
(v) $14000$ do not like Pepsi but likes Thumps up. 
(vi) $11000$ like Pepsi and exactly one more drink.
(v) $6000$like only Coke and the same number of people Like Pepsi and Thumps up but not Coke.

Find the maximum number of the people in the survey who do like at least one of the three beverages?
  

In a certain class of students, the number of students who drink only tea, only coffee, both tea and coffee, and neither tea nor coffee are $x, 2x, \frac{57}{x}, \& \frac{57}{3x}$ respectively. The number of people who drink coffee can be _____.