11
The average age of a group of persons going for picnic is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age becomes 15.5 years. The number of persons initially going for picnic is
A.
B.
C.
D.
Answer & Solution
Let the initial number of persons be
x
Now, 16x + 20
×15 = 15.5(x+20)
Or, 16x –
15.5x = 310 - 300
Or, 0.5x =
10
Or, x = 20
12
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, at the age of 60, and a child was born during the same year The current average of this eight-member joint family is nearest to
A.
B.
C.
D.
Answer & Solution
10 years ago, sum of ages of all 8 members =
231 years
7 years ago:
Total age = (231 + 8 × 3 - 60) = 195 years
4 years ago:
Total age = (195 + 8 × 3 - 60) = 159 years
Present sum of ages:
(159 + 8 × 4) = 191 years
Current average age:
191 / 8 = 23.8 ≈ 24 years
13
Mr. Joe's family consists of six people-himself, his wife and their four children. It is known that the average age of the family immediately after the birth of the first, second, third and fourth child was 16, 15, 16 and 15 years respectively. Find the age of Mr. Joe's eldest son if the present average age of the entire family is 16 years.
A.
B.
C.
D.
Answer & Solution
Given that:
Family: Mr.
Joe, his wife, and 4 children (total 6 members)
Average ages
at different points:
- After
1st child: 16 years → Total age = 16 × 3 = 48
- After 2nd child: 15 years → Total age = 15 × 4 = 60
- After 3rd child: 16 years → Total age = 16 × 5 = 80
- After 4th child: 15 years → Total age = 15 × 6 = 90
- Present
average age: 16 years → Total age = 16 × 6 = 96
Now,
Time passed
= 1 year
Age of
eldest child when the fourth child was born = 10 years
Now, after 1
year: 10 + 1 = 12 years.
14
Total expenses of a boarding house are partly fixed and partly varying linearly with the number of boarders. The average expense per boarder is $70 when there are 25 boarders and $60 when there are 50 boarders. What is the average expense per boarder when there are 100 borders?
A.
B.
C.
D.
Answer & Solution
Let, the fixed cost be x and the variable cost
be y per boarder.
Then, x + 25y = 70 × 25 Þ x + 25y =1750…………(i)
x + 50y = 60 × 50 Þ x + 50y = 3000………..(ii)
Subtracting (i) from (ii), we get 25y = 1250,
or y = 50.
Putting y = 50 in (i), we get x=500.
Total expenses of 100 boarders = (500+50×100)
= 5500
Hence, average expense = 5500/100 = 55.
15
A certain factory employed 600 men and 400 women and the average wage was $2.50 per day. If a woman got $0.5 less than a man, then what are their daily wages?
A.
B.
C.
D.
Answer & Solution
Let, the daily wage of a man be x.
Then, daily wage of a woman (x - 5).
Now, 600x + 400 (x - 0.5) = 2.5 × (600+400)
Or, 1000x = 2700
Or, x = 2.70
\ Man's daily wages = 2.70;
Woman's daily wages (x - 5) = (2.7 – 0.5) = 2.20
16
The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is
A.
B.
C.
D.
Answer & Solution
Let the required mean score be x.
Then, 20 × 80 + 25 × 31 + 55x = 52 × 100
Or,1600+775+55x
= 5200
Or,
55x = 2825
Or,
x = 51.4
17
A coaching institute has students in 3 batches - X, Y and Z. In a certain examination, the average marks obtained by these batches are 72, 60 and 50 respectively. The average marks of batches X and Y taken together is 69. If the ratio of the number of students in batches Y and Z is 6:7, what is the average score of all the three batches put together?
A.
B.
C.
D.
Answer & Solution
Let the number of students in batches Y and Z
be 6x & 7x respectively, and the number of students in batch X be y.
Then, 72y + 60 x 6x = 69 (6x+y)
Or, 72y + 360x = 414x + 69y
Or, 3y = 54x
Or, y = 18x
\ Required average = (72
× 18x + 60 × 6x + 50 × 7x)/(18x + 6x + 7x)
= (1296+360+350)/31
= 2006/31 = 64.7
18
The average salary of all the workers in a workshop is $8000. The average salary of 7 technicians is $12000 and the average salary of the rest is $6000 The total number of workers in the workshop is
A.
B.
C.
D.
Answer & Solution
Let the total number of workers be x.
Then, 8000x = (12000 × 7) + 6000(x - 7)
Or, 2000x = 42000
Or, x = 21
19
In an engineering college the average salary of all engineering graduates from Mechanical trade is $0.245 million per annum and that of the engineering graduates from Electronics trade is $0.356 million per annum. The average salary of all Mechanical and Electronics graduates is 0.312 million per annum. Find the least number of Electronics graduates passing out from this institute.
A.
B.
C.
D.
Answer & Solution
Let, the number of Mechanical Engineering
graduates M and the number of Electronics Engineering grad be E.
Then, 2.45 M + 3.56E = 3.12 (M+E)
Þ 2.45 M + 3.56 E = 3.12M
+ 3.12E
Þ 0.44 E = 0.67M
Þ M/E = 44/67
Since the ratio 44/67 is in its simplest form,
so least number of Electronics graduates = 67.
20
In a class with a certain number of students, if one student weighing 50 kg is added then the average weight of the class increases by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?
A.
B.
C.
D.
Answer & Solution
Let, the original average weight of the class
be x & let there be n students.
Then, sum of weights of n students = (nx) kg
\ (nx + 50)/(n + 1) = x
+ 1
Þ nx + 50 = (n + 1)(x +
1)
Þ nx + 50 = nx + x + n
+ 1
Þ 2x + 2n = 98…………(i)
and, (nx + 100)/(n + 2) = x + 1.5
Þ nx + 100 = (n + 2)(x
+ 1.5)
Þ nx + 100 = nx + 1.5n
+ 2x + 3
Þ 2x +1.5n = 97………….(ii)
Subtracting (ii) from (i), we get 0.5n = 1
Þ n = 2
Putting n = 2 in (i), we get: x = 47.
