Q1. Shubham was conducting an experiment in which the average of 11 observations came to be 90, while the average of first five observations was 87, and that of the last five was 84. What was the measure of the 6th observation?
(a) 165
(b) 150
(c) 145
(d) 135
(e) 125
Q2. A batsman has a certain average of runs for 12 innings. In the 13th innings he scores 96 runs, thereby increasing his average by 5 runs. What is his average after the 13th innings?
(a) 64
(b) 48
(c) 36
(d) 72
(e) 89
Q3. There was one mess for 30 boarders in a certain hostel. If the number of boarders was increased by 10, the expenses of the mess increased by Rs. 40 per month, while the average expenditure per head diminished by Rs. 2. Find the original monthly expenses.
(a) Rs. 390
(b) Rs. 360
(c) Rs. 410
(d) Rs. 480
(e) Rs. 450
Q4. The mean monthly salary paid to 75 workers in a factory is Rs. 5680. The mean salary of 25 of them is Rs. 5400 and that of 30 others is Rs. 5700. The mean salary of remaining workers is:
(a) Rs. 5000
(b) Rs. 7000
(c) Rs. 6000
(d) Rs. 8000
(e) Rs. 9000
Q5. Of the three numbers, the first is twice the second and the second is twice the third. The average of these three numbers is 21. Find the largest number.
(a) 36
(b) 38
(c) 47
(d) 48
(e) 35
Q6. In a mathematics exam, a student scored 30% marks in the first paper out of a total of 180. How much should he score in the second paper out of a total of 150, if he is to get an overall average of 50%?
(a) 74%
(b) 76%
(c) 70%
(d) 80%
(e) 75%
Q7. The average marks of a student in 8 subjects is 87. Of these, the highest marks are 2 more than the next in value. If these two subjects are eliminated, the average marks of the remaining subjects is 85. What is highest score?
(a) 91
(b) 94
(c) 89
(d) 96
(e) 92
Q8. An officer’s pension on retirement from service is equal to half the average salary during last 36 months of his service. His salary from 1 January, 2014 is Rs. 3800 per month with increment of Rs. 400 on 1 October 2014, October 2015 and 1 October, 2016. If he retires on 1 January, 2017, what pension does he draw?
(a) Rs. 2100
(b) Rs. 2150
(c) Rs. 2200
(d) Rs. 2250
(e) Rs. 2300
Q9. In a one-day cricket match, Virat, Sehwag, Sachin, Dhoni and Yuvraj scored an average of 39 runs. Dhoni scored 7 more than Yuvraj. Yuvraj scored 9 fewer than Virat. Sehwag scored as many as Dhoni and Yuvraj combined; and Sehwag and Sachin together scored 110 runs between them. How many runs did Sachin score?
(a) 47
(b) 51
(c) 53
(d) 49
(e) 57
Q10. The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates, who passed the examination was:
(a) 100
(b) 110
(c) 120
(d) 150
(e) 115
Q11. A painter is paid x rupees for painting every 10 metres of a wall and y rupees for painting every extra metre. During a week, he painted 10 metres on Monday, 13 metres on Tuesday, 12 metres on Wednesday, 11 metres on Thursday and 12 metres on Friday. What is average daily earning in rupees for the five day week?
(a) x + (8/5)y
(b) (5x + 9y)/5
(c) 10x + (8/5)y
(d) 5x + 8y
(e) Cannot be determined
Q12. The average age of a husband and wife was 23 when they were married 5 years ago. The average age of the husband, the wife and a child who was born during the interval, is 20 years now. How old is the child now?
(a) 9 months
(b) 1 year
(c) 3 years
(d) 4 years
(e) 2 years
Q13. The average marks of a students in 10 papers are 80. If the highest and the lowest scores are not considered, the average is 81. If the highest score is 92, find the lowest?
(a) 55
(b) 60
(c) 62
(d) 65
(e) Cannot be determined
Q14. The average weight of 45 students in a class was calculated as 36 kg. It was later found that the weight of two students in the class was wrongly calculated. The actual weight of one of the boys in the class was 32 kg., but it was calculated as 34 kg. and the weight of another boy in the class was 45 kg. whereas it was calculated as 40 kg. What is the actual average weight of the 45 students in the class? (Rounded off to two-digits after decimal)
(a) 36.07 kg.
(b) 36.16 kg.
(c) 35.84 kg.
(d) Cannot be determined
(e) None of these
Q15. ‘Mr. Hatim’s total annual gross salary, which was Rs. 10 lakhs per year in 2007, has been reduced by 10% in 2008. In 2007 his family expenditure for food items was 40% of the total annual gross salary. The prices of average food items have increased by 5% between 2007 and 2008. Assuming that the family consumed the same amount of food in 2008, the percentage expenditure on food items, calculated on total annual gross salary in 2008, is approximately:
(a) 43%
(b) 45%
(c) 47%
(d) 49%
(e) 50%
Solutions
S1. Ans.(d)
Sol. 11 × 90 - 5 × 87 - 5 × 84
= 990- 435 - 420 = 135
S3. Ans.(b)
Sol. Let the original average expenditure be Rs. x
Then,
40(x - 2) - 30x = 40
⇒ 10x = 120 ⇒ x = 12
∴ Original expenditure = 30 × 12 = Rs. 360
S4. Ans.(c)
Sol. Total salary of 75 workers = Rs. 426000
Total salary of 25 workers = Rs. 135000
Total salary of 30 workers = Rs. 171000
∴ Total salary of remaining 20 workers
= 426000 - (135000 + 171000)
= 120000
∴ Mean salary of 20 workers =120000/20 = Rs. 6000.
S7. Ans.(b)
Sol. Total score of 8 subjects = 87 × 8 = 696
Total score of 6 subjects = 85 × 6 = 510
∴ Score of remaining two subjects = 696 - 510 = 186
Now, let the highest and the next highest score are x and x - 2, then
(x) + (x - 2) = 186
⇒ 2x = 188 ⇒ x = 94.
S9. Ans.(e)
Sol. (Virat + Sehwag + Sachin + David + Yuvraj)
Make = 39 × 5 = 195 runs
With respect to scoring runs
Dhoni = Yuvraj + 7
Yuvraj = Virat - 9
Sehwag = Dhoni + Yuvraj
Sehwag + Sachin = 110
⇒ Virat, Dhoni, Yuvraj, Sehwag and Sachin scored
= 32, 30, 23, 53 and 57 runs respectively.
S10. Ans.(a)
Sol. Suppose the number of candidates passed = x
∴ 39x + 15 (120 - x) = 120 × 35
⇒ 24x = 120 × 35 - 120 × 15
= 120 (35 - 15) = 120 × 20
⇒ x = 100
S12. Ans.(d)
Sol. Present total age of husband and wife
= (23 × 2 + 5 × 2) = 56 years
Present total age of husband, wife and child
= 20 × 3 = 60 years
∴ age of child = (60 - 56) = 4 years
S13. Ans.(b)
Sol. Total marks in 10 papers = 800
Total marks in 8 papers = 648
Total of highest and lowest marks = 152
Lowest marks = 152 - 92 = 60.
S14. Ans.(a)
Sol. Actual weight of all the students
= 36 × 45 - 34 + 32 - 40 + 45
= 1620 + 3 = 1623kg.
Actual average weight = 1623/45 = 36.07 kg
