Q1. The mean marks of 10 boys in a class is 70%, whereas the mean marks of 15 girls is 60%. The mean marks of all the 25 students is:
(a) 64%
(b) 60%
(c) 55%
(d) 52%
(e) None of these
Ans.(a)
Sol. The mean marks of 10 boys = 70%
Total marks of 10 boys = 70% × 10 = 700
The mean marks of 15 girls = 60%
Total marks of 15 girls = 60% × 15 = 900
∴ Sum of the total marks of 25 students = 700 + 900 = 1600
∴ The mean marks of all the 25 students =1600/25=64%
Q2. A number, x equals 80% of the average of 5, 7, 14 and a number y. If the average of x and y is 26, then value of y is:
(a) 13
(b) 26
(c) 39
(d) 12
(e) None of these
Q3. The average monthly expenditure of a family for the first four months is Rs. 2750, for the next three months is Rs. 2940, and for the last five months Rs. 3130. If the family saves Rs. 5350 throughout year, find the average monthly income of the family for the year.
(a) Rs. 3800
(b) Rs. 3500
(c) Rs. 3400
(d) Rs. 4200
(e) None of these
Ans.(c)
Sol. Total expenditure for 4 months = Rs. 2750 × 4 = Rs. 11000
Total expenditure for 3 months = Rs. 2940 × 3 = Rs. 8820 …(i)
Total expenditure of 5 months = Rs. 3130 × 5= Rs. 15650 …(ii)
Total expenditure in the whole year = Rs. 11000 + 8820 + Rs. 15650
= Rs. 35470.
Saving during the whole year = Rs. 5330
Total income of the family during the year
= Rs. 35470 + Rs. 5330 = Rs. 40800
∴ Average monthly income during the year
=40800/12= Rs. 3400
Q4. In a competitive examination, the average marks obtained was 45. It was later discovered that there was some error in computerization and the marks of 90 candidates had to be changed from 80 to 50, and the average came down to 40 marks. The total number of candidates appeared in the examination is
(a) 520
(b) 550
(c) 540
(d) 525
(e) None of these
Q5. The average age of students of a class is 15.8 years. The average age of boys in the class in 16.4 years and that of the girls is 15.4 years. The ratio of number of boys to the number of girls in the class is:
(a) 1 : 2
(b) 3 : 4
(c) 3 : 5
(d) 2 : 3
(e) None of these
Q6. The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
(a) 20
(b) 21
(c) 23
(d) 22
(e) None of these
Q7. The average of 7 consecutive numbers is 20. The largest of these numbers is:
(a) 24
(b) 23
(c) 22
(d) 20
(e) None of these
Q8. The average weight of three men A, B and C is 84 Kg. D joins them and the average weight of the four becomes 80 Kg. If E, whose weight is 3 Kg more than that of D, replaces A, the average weight of B, C, D and E becomes 79 Kg. The weight of A is:
(a) 65 Kg
(b) 70 Kg
(c) 75 Kg
(d) 80 Kg
(e) None of these
Ans.(c)
Sol. Sum of weights of A, B and C = 84 × 3 kg = 252 kg
Weight of D = 4 × 80 – 252
= 320 – 252 = 68 kg
Weight of E = 68 + 3 = 71 kg
A + B + C + D = 320
B + C + D + E = 79 × 4 = 316
⇒ A – E = 4 kg
∴ A = 4 + E = 4 + 71 = 75 kg.
Q9. Average age of seven persons in a group is 30 years. The average age of five persons of this group is 31 years. What is the average age of the other two persons in the group?
(a) 55 years
(b) 26.5 years
(c) 15 years
(d) 27.5 years
(e) None of these
Ans.(d)
Sol. The total age of 7 person = 30 × 7 = 210 years.
Total age of 5 persons = 31 × 5 = 155 years.
∴ The total age of 2 persons = (210 – 155) years = 55 years.
∴ The average age of two persons =55/2=27.5 years
Q10. 12% of Kaushal’s monthly salary is equal to 16% of Nandini’s monthly salary. Suresh’s monthly salary is half that of Nandini’s monthly salalry. If Suresh’s annual salary is Rs. 1.08 lacs. What is Kaushal’s monthly salary?
(a) Rs. 20000
(b) Rs. 18000
(c) Rs. 26000
(d) Rs. 24000
(e) None of these
Q11. The frequency distribution data is given below. If the average age is 17 years, the value of m is
Age (in years): 8 20 26 29.
Number of people: 3 2 m 1
(a) 1
(b) 2
(c) 3
(d) 4
(e) None of these
Q12. Average rainfall on Monday, Tuesday, Wednesday and Thursday is 420.5 cm and average on Tuesday, Wednesday, Thursday and Friday is 440.5 cm. If the ratio of rainfall for Monday and Friday is 20 : 21, find the rainfall in cm on Monday and Friday.
(a) 1800, 1890
(b) 1600, 1680
(c) 1700, 1470
(d) 1682, 1762
(e) None of these
Ans.(b)
Sol. M + T + W + Th = 4 × 420.5 = 1682 cm …(i)
T + W + Th + F = 4 × 440.5 = 1762 cm …(ii)
By equation (ii)-equation (i), we have
F – M = 1762 – 1682 = 80
Let the rainfall for Monday and Friday be 20x and 21x cm respectively.
Now, according the question,
21x – 20x = 80
⇒ x = 80
∴ Monday ⇒ 80 × 20 = 1600 cm
∴ Friday ⇒ 21 × 80 = 1680 cm
Q13. A batsman, in his 12th innings, makes a score of 63 runs and thereby increases his average score by 2. The average of his score after 12 th innings is:
(a) 41
(b) 42
(c) 34
(d) 35
(e) None of these
Ans.(a)
Sol. Let, the average of runs was x till 11 innings.
∴ Total runs = 11x
⇒ Total run after 12th innings = 11x + 63
Again, after 12th innings average = (x + 2)
⇒ Total run = 12(x + 2)
Now, according to the question,
12(x + 2) = 11x + 63
∴ x = 63 – 12 × 2 = 39
∴ The average of his score after 12th innings = 39 + 2 = 41
Q14. A professional institute’s total expenditure on students for a particular course is partly fixed and partly varies linearly with the number of students. The average expense per student is Rs. 615 when there are 24 students and Rs. 465 when there are 40 students. What is the average expense when there are 60 students?
(a) Rs. 370
(b) Rs. 450
(c) Rs. 350
(d) Rs. 420
(e) Rs. 390
Q15. The average age of 80 boys in a class is 15. The average age of a group of 15 boys in the class is 16 and the average age of another 25 boys in the class is 14. What is the average age of the remaining boys in the class?
(a) 15.25
(b) 14
(c) 14.75
(d) Cannot be determined
(e) None of these
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