Question 1
The mean salary for a group of 40 female workers is Rs. 5200 per month and that for a group of 60 male workers is Rs. 6800 per month. What is the combined mean salary?
Explanation
Combined mean = (40 × 5200) + (60 × 6800)40 + 60
= 2,08,000 + 4,08,000100 = 6,16,000100 = 6160
= 2,08,000 + 4,08,000100 = 6,16,000100 = 6160
Question 2
The mean weight of 15 students is 110 kg. The mean weight of 5 of them is 100 kg and that of another five students is 125 kg, then the mean weight of the remaining students is:
Explanation
Total weight of 15 students = 15 × 110 = 1650 kg
Weight of first 5 students = 5 × 100 = 500 kg
Weight of next 5 students = 5 × 125 = 625 kg
Weight of remaining 5 students = 1650 - 500 - 625 = 525 kg
Mean of remaining 5 students = 525 / 5 = 105 kg
Weight of first 5 students = 5 × 100 = 500 kg
Weight of next 5 students = 5 × 125 = 625 kg
Weight of remaining 5 students = 1650 - 500 - 625 = 525 kg
Mean of remaining 5 students = 525 / 5 = 105 kg
Question 3
The average age of 15 students is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, then the age of the 15th student is:
Explanation
Total age of 15 students = 15 × 15 = 225 years
Sum of first 5 students' ages = 5 × 14 = 70 years
Sum of next 9 students' ages = 9 × 16 = 144 years
Sum of these 14 students = 70 + 144 = 214 years
Age of the 15th student = 225 - 214 = 11 years
Sum of first 5 students' ages = 5 × 14 = 70 years
Sum of next 9 students' ages = 9 × 16 = 144 years
Sum of these 14 students = 70 + 144 = 214 years
Age of the 15th student = 225 - 214 = 11 years
Question 4
In a group of persons, the average weight is 60 kg. If the average weight of males and females taken separately is 80 kg and 50 kg respectively, find the ratio of the number of males to that of females.
Explanation
Let the number of males and females be m and f.
80m + 50fm + f = 60
80m + 50f = 60m + 60f
20m = 10f
f = 2m, so m : f = 1 : 2
80m + 50fm + f = 60
80m + 50f = 60m + 60f
20m = 10f
f = 2m, so m : f = 1 : 2
Question 5
The mean of 100 students was 45. Later on, it was discovered that the marks of two students were misread as 85 and 54 instead of 58 and 45. Find the correct mean.
Explanation
Total (with wrong values) = 100 × 45 = 4500
Wrong values sum = 85 + 54 = 139. Correct values sum = 58 + 45 = 103
Correct total = 4500 - 139 + 103 = 4464
Correct mean = 4464 / 100 = 44.64
Wrong values sum = 85 + 54 = 139. Correct values sum = 58 + 45 = 103
Correct total = 4500 - 139 + 103 = 4464
Correct mean = 4464 / 100 = 44.64
Question 6
The average of marks obtained by 120 students in a certain examination is 35. If the average marks of passed students is 39 and that of the failed students is 15, what is the number of students who passed in the examination?
Explanation
Let p = number who passed, f = number who failed. p + f = 120.
39p + 15f = 35 × 120 = 4200
39p + 15(120 - p) = 4200
39p + 1800 - 15p = 4200
24p = 2400
p = 100
39p + 15f = 35 × 120 = 4200
39p + 15(120 - p) = 4200
39p + 1800 - 15p = 4200
24p = 2400
p = 100
Question 7
The mean of the first 3 terms is 14 and the mean of the next 2 terms is 18. The mean of the 5 numbers is:
Explanation
Sum of first 3 terms = 3 × 14 = 42
Sum of next 2 terms = 2 × 18 = 36
Total sum = 42 + 36 = 78
Mean of all 5 = 78 / 5 = 15.6
Sum of next 2 terms = 2 × 18 = 36
Total sum = 42 + 36 = 78
Mean of all 5 = 78 / 5 = 15.6
Question 8
The mean of a set of 20 observations is 18.3. The mean is reduced by 0.6 when a new observation is added to the set. The new observation is:
Explanation
Original total (20 obs) = 20 × 18.3 = 366
New mean (21 obs) = 18.3 - 0.6 = 17.7
New total = 21 × 17.7 = 371.7
New observation = 371.7 - 366 = 5.7
New mean (21 obs) = 18.3 - 0.6 = 17.7
New total = 21 × 17.7 = 371.7
New observation = 371.7 - 366 = 5.7
Question 9
The mean salary of a group of 50 persons is Rs. 5850. Later it is discovered that the salary of one person had been wrongly taken as Rs. 8000 instead of Rs. 7800. The corrected mean salary is:
Explanation
Original total = 50 × 5850 = 2,92,500
Corrected total = 2,92,500 - 8000 + 7800 = 2,92,300
Corrected mean = 2,92,300 / 50 = 5846
Corrected total = 2,92,500 - 8000 + 7800 = 2,92,300
Corrected mean = 2,92,300 / 50 = 5846
Question 10
A company's past 10 years' average earnings is Rs. 40 crores. To have the same average earnings for 11 years including these 10 years, how much earning must be made by the company in the eleventh year?
Explanation
For the average to remain unchanged after adding a new value, that new value must equal the existing average itself.
Since the average of the first 10 years is already Rs. 40 crores, the 11th year must also earn exactly Rs. 40 crores.
Since the average of the first 10 years is already Rs. 40 crores, the 11th year must also earn exactly Rs. 40 crores.
