Welcome to your CAT Averages & Ages

1.The average of n numbers is 32. If three-fourth of the numbers are increased by 4 and the remaining are decreased by 6, what is the new average? ______

2.Six boys and six girls went to a hotel to have lunch. Each boy paid an equal amount, and it is Rs.20 more than what each girl paid. The bill amount was Rs.1380. Half of the girls as well as half of the boys left after paying their share of the bill. Find the average amount (in Rs) paid by the others. ______

3.The daily average temperatures in Chennai for the 7 days of a week were recorded. The average temperatures on Sunday, Monday and Tuesday were 20°C, 38°C and 23°C, respectively. The average temperatures on Thursday, Friday and Saturday were 29°C, 22°C and 30°C, respectively. If the average of average temperatures on the first three days of the week beginning with Sunday equals that of the last four days, find the temperature on Wednesday.

4.The average age of a couple when they got married was 30 years. Three years after their marriage, a child was born to them. The present average age of the couple and the child is 34 years. Find the present age of the child

5.Nine years ago, the sum of the ages of the members of a family of seven is 209 years. Three years later, one member died at the age of 52 years and a child was born. After two more years, one more member died again at 52 and yet another child was born. The current average age of all the members of the family is nearest to.

6.In a company there are 252 employees, in which the ratio of the number of men and women is 2: 1. Some more women are employed and the ratio of men and women becomes 1: 1. The average age of all the employees is now 22 years and the average age of the women is 2 years less than the average age of the men. Find the average age (in years) of men and women.

7.In a class, the average height of the boys lies between 100 cm and 120 cm. The average height of the girls lies between 80 cm and 100 cm. If there are 90 boys and 60 girls in the class, the average height of the class (in cm) definitely lies in which of the following ranges?

8.Find the average of all the four-digit numbers whose units digit is twice the thousand’s digit. ______

9. I was born 30 years after my father was born. My sister was born 25 years after my mother was born. The average age of my family is 26.25 years right now. My sister will get married 4 years from now and will leave the family. Then, the average age of the family will be 107/3 years. What is the age of my father?

10.10 students are shifted from each of the sections A and C to section B and then 10 students each are shifted from section B to each of the sections A and Section C. Now, what is the ratio of the maximum possible average of section A and section C?

11. Sachin Tendulkar has a certain batting average of N (a whole number) in his career of 86 innings. In the 87th inning, he gets out after scoring 270 runs which increases his batting average by a whole number. The batting average is calculated by dividing the total number of runs scored by the total number of innings played by the player. How many values of his new average is/are possible?

12. If the average marks of 17 students in a class is A. The marks of the students when arranged in either an ascending or a descending order were found to be in arithmetic progression. The class teacher found that the students who were ranked 3rd, 7th, 9th, 11th, and 15th had copied in the exam and hence, got all of them rusticated. The average of the remainder of the class

13.The average weight of a class of 25 students is 30 kg. The average weight of the girls is 5 kg more than that of the boys. If the class teacher’s weight, which is between 64 kg and 106 kg, is included, the average weight of the male members of the class equals that of the female members. If the average weight of the boys (in kg) is an integer, then what is the number of girls in the class?

14.The average weight of 12 oil drums is 60 kg, which is equal to the difference between the weights of the two heaviest drums. If the average weight of the remaining 10 drums is half the total average weight, then find the weight of the heaviest drum.

15.In the hotel Park Plaza, the rooms are numbered from 221 to 250 on the first floor, 446 to 460 on the second floor, and 661 to 700 on the third floor. There are three types of room charges as follows; Rs. 1000, Rs. 600 and Rs. 300. The room charges are the same for all the rooms on a particular floor. In the month of December 2003, the rooms not occupied were 50% on the first floor, 60% on the second floor and 40% on the third floor. Find the maximum average charges per room for the month of December 2003.