21
The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D and E becomes 79 kg. The weight of A is
A.
B.
C.
D.
Answer & Solution
Let A, B, C, D and E represent their
respective weights.
Then, A + B + C = (84 × 3) = 252kg
A + B + C + D = (80 × 4) = 320kg
\ D = 320 – 252 = 68kg,
E = 68 + 3 = 71kg
B + C + D + E = (79 × 4) = 316 kg
Now, (A+B+C+D) – (B+C+D+E)
= (320 - 316) kg
= 4kg
\ A - E = 4
Þ A = (4 + E1)kg = 75kg
22
The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is
A.
B.
C.
D.
Answer & Solution
Let, the ratio be k : 1.
Then, k ×16.4 +1 × 15.4 = (k+1) × 15.8
Þ (16.4 -15.8)k = (15.8
-15.4)
Þ k = 0.4/0.6 = 2/3
\Required ratio = 2/3 :
1 = 2:3.
23
The mean monthly salary paid to graduating MBA class of a management institute is $16000. The mean monthly salary paid to students with work experience is $18000. The corresponding figure for the students without any work experience is 12000$. Determine the percentage of students with work experience and those without any work experience in the class.
A.
B.
C.
D.
Answer & Solution
Let the number of students with work
experience be x
& those without work experience be y.
Then, 18000x + 12000y =16000 (x+y)
Þ 2000x = 4000у
Þ x/y = 2/1
\ Percentage of
students with work experience = (2/3) x100 = 66.67%
Percentage of students without work experience
= (100 - 66.67)% = 33.33%
24
My car gives an average of 40 kmpl of petrol. But after recent filling at the new petrol pump, its average dropped to 38 kmpl. I investigated and found out that it was due to adulterated petrol. Petrol pumps add kerosene, which is 2/3 cheaper than petrol, to increase their profits. Kerosene generates excessive smoke and knocking and gives an average of 18 km per 900 ml. If I paid $0.30 for a liter of petrol, what was the additional amount the pump-owner was making?
A.
B.
C.
D.
Answer & Solution
Let, p = petrol in 1 liter of mixture
k = kerosene in 1 liter of mixture
Given that, p+k =1
Using
mileage equation:
40p + 20k = 38
Substituting k = 1−p,
Þ 40p + 20(1−p) = 38
Þ 40p + 20 - 20p = 38
Þ 20p =18 ⇒p=0.9, k=0.1
Now, Cost of 0.9L petrol = 0.9×0.30=0.27
Cost of 0.1L
kerosene = 0.1×0.10=0.01
Total cost =
$0.28
Selling price = $0.30
Extra profit per liter = $0.02.
25
Average score of a class of 60 students, in an exam, was 43. Average score of the students who had passed is 52 and the average score of students who had failed is 16. How many failed the exam?
A.
B.
C.
D.
Answer & Solution
Let x be the number of students who failed.
Given that:
Total
students = 60
Total score
= 60 × 43 = 2580
Passed
students' total score = (60 − x) × 52
Failed
students' total score = x ×16
Now, (60 −x) × 52 + x ×16 = 2580
Þ 3120 − 52x+16x = 2580
Þ 3120 – 2580 = 36x
Þ 540 = 36x
Þ x =15
26
In a primary school the average weight of male students is 65.9 kg and the average weight of female students is 57 kg. If the average weight of all the students (both male and female) is 60.3 kg and the number of male students in the school is 66, what is the number of female students in the school?
A.
B.
C.
D.
Answer & Solution
Let, the number of female students be x and
weight of female students 57x.
Number of male students = 66
Total weight of male students = 65.9 × 66
Average weight of all the students = 60.3 kg
Total weigh of all the students = 60.3(66 + x)
According to given information,
60.3 (66 + x) = 66 × 65.9 + 57x
Or, 3.3x = 66(65.9 – 60.3)
Or, 3.3x = 66 × 5.6
Or, x = 2 × 56
Or, x = 112
27
Out of 10 teachers of a school, one teacher retires and in place of him a new teacher 25 years old joins. As a result of it average age of the teachers reduces by 3 years. Age of the retired teacher (in years) is:
A.
B.
C.
D.
Answer & Solution
Total number of teachers = 10
Age of new teacher = 25 years
Age of the retired teacher = (25 + 3 × 10)
years
= 55
years
28
Six numbers are arranged in decreasing order. The average of the first five numbers is 30 and the average of the last five numbers is 25. The difference of the first and the last numbers is
A.
B.
C.
D.
Answer & Solution
Numbers are
x > y > z > p > q > r
According to the question,
Average of first five numbers = 30
Sum of first five number = a+y+z+p+q = 5 × 30
= 150 ……….. (i)
Average of last five number = 25
Sum of last five numbers
= y+z+p+q+r = 5 × 25 =125………..(ii)
By equation (1) and (ii) a – r = 150 - 125 = 25
29
The average weight of A, B and C is 40 kgs. Weight of C is 24 kgs more than A's weight and 3 kgs less than B's weight. What will be the average weight of A, B, C and D, if D weights 15 kgs less than C
A.
B.
C.
D.
Answer & Solution
Average weight of A, B and C = 40 kgs
Total weights of A, B and C = 40 × 3 = 120 kgs
Weight of C = (A+24) kg and C = (B - 3) kg
\ A + 24 = B – 3
Þ B = A + 27
Now, A + B + C = 120
Þ A + A + 27 + A + 24 =
120
Þ 3A + 51 = 120
Þ A = 69/3 = 23 kg
B = A+27
= 23 + 27 = 50 kg
C = 120
- 23 – 50 = 47 kg
D = 47 - 15
= 32 kg
\ Required average
weight of A, B, C and D
= (23+50+47+32)/4
= 152/4
= 38 kg
30
The mean high temperature of the first four days of a week is 25°C whereas the mean of the last four days is 25.5°C. If the mean of the whole week is 25.2°C, then the temperature of the 4th day is
A.
B.
C.
D.
Answer & Solution
Average temperature of first four days = 25°C
Total temperature of first four days = 25˚ × 4
= 100˚C
Average temperature last four days = 25.5˚
Total temperature of last four days = 25.5˚× 4 = 102°C
Average temperature of whole week = 25.2˚
Total temperature of whole week = 25.2˚× 7 =
176.4˚C
\ Temperature of 4th
day = 100˚ + 102˚ - 176.4˚ = 25.6˚C
