CAT Problems on Ages

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CAT Problems on Ages:

Question 1:

Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to

a) 23 years
b) 22 years
c) 21 years
d) 25 years
e) 24 years

Question 2:

A college has raised 75% of the amount it needs for a new building by receiving an average donation of Rs. 600 from the people already solicited. The people already solicited represent 60% of the people the college will ask for donations. If the college is to raise exactly the amount needed for the new building, what should be the average donation from the remaining people to be solicited?

a) Rs. 300
b) Rs. 250
c) Rs. 400
d) Rs. 500

Question 3:

Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is:

a) n
b) n + 1
c) kn, where k is a function of n
d) n + (2/7)

Question 4:

The average marks of a student in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If his highest score is 92, find the lowest.

a) 55
b) 60
c) 62
d) Cannot be determined

Question 5:

Total expenses of a boarding house are partly fixed and partly varying linearly with tile number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?

a) 550
b) 580
c) 540
d) 560

Answers and Solutions for CAT Problems on Ages:

Solutions:

Ten years ago, the total age of the family is 231 years.
Seven years ago, (Just before the death of the first person), the total age of the family would have been 231+8*3 = 231+24 = 255.
After the death of one member and the birth of a child, the total age is 195 years.
Four years ago, after the death of one member and birth of another child, the total age of the family is 195+24-60 = 159 years.
The current total age of the family is = 8×4 + 159 = 191 years
The average age is 191/8 = 23.875 years = 24 years (approx)

Let there be total 100 people whom the college will ask for donation. Out of these 60 people have already given average donation of 600 Rs. Thus total amount generated by 60 people is 36000. This is 75% of total amount required . so the amount remaining is 12000 which should be generated from remaining 40 people. So average amount needed is 12000/40 = 300

The first five numbers could be n-2, n-1, n, n+1, n+2. The next two number would then be, n+3 and n+4, in which case, the average of all the 7 numbers would be $$\frac{(5n+2n+7)}{7}$$ = n+1

Total marks = 80 x 10 = 800
Total marks except highest and lowest marks = 81 x 8 = 648
So Summation of highest marks and lowest marks will be = 800 – 648 = 152
When highest marks is 92, lowest marks will be = 152-92 = 60

Average expense = $$\frac{55000}{100}$$ = Rs.550.