Home > Practice > Arithmetic Aptitude > Average > Miscellaneous
11. The average monthly salary of 660 workers in a factory is Rs. 380. The average monthly salary of officers is Rs. 2100 and the average monthly salary of the other workers is Rs. 340. Find the number of other workers.
Solution:
12. The average marks of four subjects is 120. If 33 was misread as 13 during the calculation, what will be the correct average?
Solve while reading method:
Average given is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to total.
Then average of is and so must be added to average, i.e.
Correct average = 120 + 5 = 125
Solution:
Solve while reading method:
Average given is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to total.
Then average of is and so must be added to average, i.e.
Correct average = 120 + 5 = 125
13. Students of three different classes appeared in common examination. Pass average of 10 students of first class was 70%, pass average of 15 students of second class was 60% and pass average of 25 students of third class was 80% then what will be the pass average of all students of three classes?
Solution:
14. A man travels equal distances of his journey at 40, 30 and 15 km/h. respectively. Find his average speed for whole journey.
Alternatively
Time taken to traveled distance of journey with speed 40 kmph,
Time taken to traveled distance of journey with speed 30 kmph,
Time taken to traveled distance of journey with speed 15 kmph,
Solution:
Required average speed,Alternatively
Time taken to traveled distance of journey with speed 40 kmph,
Time taken to traveled distance of journey with speed 30 kmph,
Time taken to traveled distance of journey with speed 15 kmph,
15. Five years ago, the average age of A, B, C and D was 45 yr. with E joining them now, the average of all the five is 49 yr. How old is E?
= (45 × 4) + (4 × 5)
= 200 years
Total age present age of A, B, C, D and E
= 49 × 5
= 245 years
So, Age of E = 45 years
Solution:
Total present age of A, B, C and D= (45 × 4) + (4 × 5)
= 200 years
Total age present age of A, B, C, D and E
= 49 × 5
= 245 years
So, Age of E = 45 years
16. Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.
= 80 × 42 = 3360
Now, total of 85 numbers
= 85 × 45 = 3825
Hence, sum of 5 numbers
= 3825 - 3360 = 465
Average of five numbers
= = 93
Alternatively,
Solve while reading method:
Average of 80 number was 42
When 5 more numbers are added average become 45
that means 3 is given to each number to make their average.
45 and 5 numbers also keep 45 as to maintain the entire average.
So, the sum of five numbers
= 240 + 225 = 465
Hence, average of five numbers = 93
Solution:
Total of 80 numbers= 80 × 42 = 3360
Now, total of 85 numbers
= 85 × 45 = 3825
Hence, sum of 5 numbers
= 3825 - 3360 = 465
Average of five numbers
= = 93
Alternatively,
Solve while reading method:
Average of 80 number was 42
When 5 more numbers are added average become 45
that means 3 is given to each number to make their average.
45 and 5 numbers also keep 45 as to maintain the entire average.
So, the sum of five numbers
= 240 + 225 = 465
Hence, average of five numbers = 93
17. Find the average increase rate, if increase in the population in the first year is 30% and that in the second year is 40%.
1st year's population increased = 30%
So, Population after first year
= (100 + 30% of 100)
= 130
Population in second year increases by 40%,
Then Population
= (130 + 40% of 130)
= 182
The final population become 182 which was originally at 100.
It means there is 82% increment in the population in 2 years
So, Average increment = = 41%
Mind Calculation Method:
Increase in population is given by,
100 == 30% ⇒ 130 == 40% ⇒ 182
Hence, average increase = = 41%
Solution:
Let 100 be the original population.1st year's population increased = 30%
So, Population after first year
= (100 + 30% of 100)
= 130
Population in second year increases by 40%,
Then Population
= (130 + 40% of 130)
= 182
The final population become 182 which was originally at 100.
It means there is 82% increment in the population in 2 years
So, Average increment = = 41%
Mind Calculation Method:
Increase in population is given by,
100 == 30% ⇒ 130 == 40% ⇒ 182
Hence, average increase = = 41%
18. One-fourth of certain journey is covered at the rate of 25 km/h, one-third at the rate of 30 km/h and the rest at 50 km/h. Find the average speed for the whole journey.
Now,
Solution:
Let distance be 120 kmHence 30 km is covered by @25 kmph and 40 km covered by @30 kmph and rest 50 km has been covered @50 kmphNow,
19. A batsman makes a score of 270 runs in the 87th inning and thus increase his average by a certain number of runs that is a whole number. Find the possible values of the new average.
Solution:
Part of the runs scored in the 87th innings will go towards increasing the average of the first 86 innings to the new average and remaining part of the runs will go towards maintaining the new average for the 87th innings. The only constraint in this problem is that there is increase in average by a whole number of runs. This is possible for all three options.
20. There are five boxes in cargo hold. The weight of the first box is 200 kg and the weight of the second box is 20% higher than the weight of the third box, whose weight is 25% higher than the first box's weight. The fourth box at 350 kg is 30% lighter than the fifth box. Find the difference in the average weight of the four heaviest boxes and the four lightest boxes.
1st box = 200 kg
2nd box = 300 kg
3rd box = 250 kg
4th box = 350 kg
5th box = 500 kg
Hence, difference between heavier 4 and lighter 4 is 300
Hence, difference in average is 75
Solution:
The weight of boxes is :1st box = 200 kg
2nd box = 300 kg
3rd box = 250 kg
4th box = 350 kg
5th box = 500 kg
Hence, difference between heavier 4 and lighter 4 is 300
Hence, difference in average is 75