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Question 1 of 20
1. Question
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the run rate in the remaining 40 overs to reach a target of 282 runs?
Hint
Total runs in the first 10 overs
= 10 × 3.2 = 32
Run rate required in the remaining 40 overs
runs per over -
Question 2 of 20
2. Question
A batsman in his 12th innings makes a score of 65 and thereby increases his average by 2 runs. What is his average after the 12th innings if he had never been ‘not out’?
Hint
Let ‘x’ be the average score after 12 th innings
⇒ 12 x = 11 × (x – 2) + 65
∴ x = 43
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Question 3 of 20
3. Question
A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him till the last match was:
Hint
Let the number of wickets taken till the last match be x. Then,
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Question 4 of 20
4. Question
A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning?
Hint
Let the average score of 19 innings be x.
Then,
The average score after 20th innings
= x + 4 = 22 + 4 = 26
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Question 5 of 20
5. Question
A batsman has scored an average of 46 runs for a certain number of innings played in England. When he came back to India, he played another two test matches of two innings each and scored at an average of 55 runs. For the innings in England and in India taken together, he has improved his average by 2 runs over the matches played in England. Find the number of innings played in England.
Hint
Let the number of innings played in England be x.
∴ Total runs scored in England = 46 x
Total runs scored for innings played in India = 55 × 4 = 220
(the number of innings played in India = 4)
Also,
⇒ 46x + 220 = 48 x + 192
⇒ 2x = 28
⇒ x = 14
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Question 6 of 20
6. Question
N number of persons decide to raise Rs 3 lakhs by equal contributions from each. If they contributed Rs 50 each extra, the contribution would be Rs 3.25 lakhs. How many persons are there?
Hint
Required persons
= 500
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Question 7 of 20
7. Question
Nine persons went to a hotel for taking their meals. Eight of them spent Rs 12 each on their meals and the ninth spend Rs 8 more than the average expenditure of all the nine. What was the total money spent by them?
Hint
Let the average expenditure of all the nine be Rs x.
Then, 12 × 8 + (x + 8)
= 9x or 8x = 104 or x = 13.
∴ Total money spent
= 9x = Rs (9 × 13)
= Rs 117.
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Question 8 of 20
8. Question
30 pens and 75 pencils were purchased for Rs 510. If the average price of a pencil was Rs 2.00, find the average price of a pen.
Hint
Since average price of a pencil = Rs 2
∴ Price of 75 pencils
= Rs 150
∴ Price of 30 pens
= Rs (510 – 150) = Rs 360
∴ Average price of a pen
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Question 9 of 20
9. Question
The average number of printing error per page in a book of 512 pages is 4. If the total number of printing error in the first 302 pages is 1,208, the average number of printing errors per page in the remaining pages is
Hint
Remaining pages
= 512 – 302 = 210
Let average printing error in remaining pages = x
Then,
⇒ 210x = 840
⇒ x = 4
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Question 10 of 20
10. Question
The average expenditure of a labourer for 6 months was Rs 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to Rs 60 he not only cleared off his debt but also saved Rs 30. His monthly income is
Hint
Income of 6 months
= Rs (6 × 85) – debt = Rs 510 – debt
Income of the man for next 4 months
= Rs 4 × 60 + debt + Rs 30
= Rs 270 + debt
∴ Income of 10 months = Rs 780
Average monthly income
= Rs 780 ÷ 10 = Rs 78
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Question 11 of 20
11. Question
In a coconut grove, (x + 2) trees yield 60 nuts per year, x trees yield 120 nuts per year and (x – 2) trees yield 180 nuts per year. If the average yield per year per tree be 100, then x is
Hint
⇒
⇒
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Question 12 of 20
12. Question
Nine men went to a hotel. 8 of them spent Rs 3 each over their meals and the ninth spent Rs 2 more than the average expenditure of all the nine. The total money spent by all of them was
Hint
Let the average expenditure of all the nine be Rs x
Then, 3 × 8 + x +2 = 9x
⇒ x = 3.25
∴ Total money spent
= 9x = 9 × 3.25 = Rs. 29.25
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Question 13 of 20
13. Question
There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of mess were increased by Rs. 42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
Hint
Let the original average expenditure be Rs. x. Then,
42(x – 1) – 35x = 42
⇒ 7x = 84
⇒ x = 12.
∴ Original expenditure
= Rs (35 × 12) = Rs. 420.
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Question 14 of 20
14. Question
In an engineering college the average salary of all engineering graduates from Mechanical trade is Rs 2.45 lacs per annum and that of the engineering graduates from Electronics trade is Rs 3.56 lacs per annum. The average salary of all Mechanical and Electronics graduates is Rs 3.12 lacs per annum. Find the least number of Electronics graduates passing out from this institute.
Hint
Let the number of Mechanical engineering graduates be M and Electronic engineering graduates be E. Then
⇒ 2.45M + 3.56E = 3.12M + 3.12E
⇒ 0.44E = 0.67M
⇒ E
For E to be an integer, the least value will be 67.
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Question 15 of 20
15. Question
The average monthly sales for the first eleven months of the year of a certain salesman were Rs 12000, but due to his illness during the last month, the average monthly sales for the whole year came down to Rs 11375. What was the value of sales during the last month?
Hint
Total sales for the first eleven months
= 12,000 × 11 = Rs 132000
Total sales for the whole year
= Rs 11375 × 12 = Rs 136500
∴ Value of sales during the last month
= 136500 – 132000 = Rs 4500.
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Question 16 of 20
16. Question
Directions (Q. 63-65) : There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D. What is the average weight of the students in group D?
Hint
Average weight of the students in group D cannot be determined since we do not know the average weight of each student. The given data is insufficient to compare its average with other groups.
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Question 17 of 20
17. Question
Directions (Q. 63-65) : There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D. If one student from Group A is shifted to group B, which of the following will be true?
Hint
If one student from group A is shifted to group B, still there is no effect on the whole class. In any case, the no. of students inside the class is same. Hence the average weight of the class remains same.
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Question 18 of 20
18. Question
Directions (Q. 63-65) : There are 60 students in a class. These students are divided into three groups A, B and C of 15, 20 and 25 students each. The groups A and C are combined to form group D. If all the students of the class have the same weight, then which of the following is false?
Hint
Since all the students of the class have the same weight, then the average of weight of any group of any no. of students will be the same as that of each students weight. Hence, the average weight of D cannot be greater than average weight of A.
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Question 19 of 20
19. Question
Directions (Q. 66 – 67) : Five heavy weight boxers measure their weights. Following results were obtained :
P is heavier than R by 14 LB. B is lighter than S by 10 LB. M’s weight is equal to the average weight of the four other boxers. P’s weight and B’s weight taken together equals the weight of M and S. The sum of the weights of all five boxers is 520 LB.
What is the average of the weights of M and R?
Hint
For Q. 66-67
Let p, m, r, s and b be the weights of boxers P, M, R, S and B respectively.
From data :
p = r + 14 … (1)
b = s – 10 … (2)
4m = p + b + r + s … (3)
p + b = m + s … (4)
p + b + m + r + s = 520 … (5)
From (3) and (5),
5m = 520
⇒ m = 104 lb
From (1) and (2),
p + b = r + s + 4 … (6)
From (4) and (6),
r + s + 4 = m + s
⇒ r = m – 4 = 100 lb
From (1),
p = r + 14 = 114 lb
From (5),
114 + b + 104 + s + 100 = 520
⇒ b + s = 202 … (7)
From (7) and (2),
b – s = 10
and b + s = 202
⇒ b = 192/2 = 96 lb
and s = 106 lb
∴ Average of the weights of M and R
= (104 + 100)/2 = 102 lb
Average of the weights of P, S and B
= (114 + 106 + 96)/3 = 105.3 lb.
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Question 20 of 20
20. Question
Directions (Q. 66 – 67) : Five heavy weight boxers measure their weights. Following results were obtained :
P is heavier than R by 14 LB. B is lighter than S by 10 LB. M’s weight is equal to the average weight of the four other boxers. P’s weight and B’s weight taken together equals the weight of M and S. The sum of the weights of all five boxers is 520 LB.
What is the average of the weights of P, S and B?
Hint
See the sol. of previous question