Question 1

The average revenues of a company over 7 consecutive years are Rs. 79 lakhs. The average revenue of the first 4 years is Rs. 74 lakhs and the average revenue of the last 4 years is Rs. 86 lakhs. What is the revenue (in lakhs of rupees) in the 4th ye…

Accepted Answer

Introduction / Context: This problem deals with averages over overlapping time periods. We know the overall average revenue for 7 years, as well as the average for the first 4 years and the last 4 years. Because the 4th year lies in both groups, we can use overlapping totals to find the revenue for that particular year. Given Data / Assumptions: Average revenue over 7 years = Rs. 79 lakhs. Average revenue of first 4 years = Rs. 74 lakhs. Average revenue of last 4 years = Rs. 86 lakhs. Years are consecutive and numbered 1 to 7. The 4th year is common to both the first 4 and the last 4 years. Concept / Approach: Let the revenues in years 1 to 7 be R1, R2, R3, R4, R5, R6, R7. Then: (R1 + R2 + R3 + R4 + R5 + R6 + R7) / 7 = 79. (R1 + R2 + R3 + R4) / 4 = 74. (R4 + R5 + R6 + R7) / 4 = 86. We convert these into sums, then use the fact that the 4th year appears in both groups to form an equation that yields R4. Step-by-Step Solution: Step 1: Find total revenue over all 7 years. Total over 7 years = 79 * 7 = 553 lakhs. Step 2: Find total revenue for the first 4 years. R1 + R2 + R3 + R4 = 74 * 4 = 296 lakhs. Step 3: Find total revenue for the last 4 years. R4 + R5 + R6 + R7 = 86 * 4 = 344 lakhs. Step 4: Express total revenue in terms of these sums. We know total over 7 years = (R1 + R2 + R3) + R4 + (R5 + R6 + R7). From Step 2: R1 + R2 + R3 = 296 - R4. From Step 3: R5 + R6 + R7 = 344 - R4. So total = (296 - R4) + R4 + (344 - R4) = 640 - R4. Step 5: Set this equal to the known total 553 and solve for R4. 640 - R4 = 553. R4 = 640 - 553 = 87 lakhs. Verification / Alternative check: If R4 = 87, then: First 4 years total = 296, so R1 + R2 + R3 = 296 - 87 = 209. Last 4 years total = 344, so R5 + R6 + R7 = 344 - 87 = 257. Total for all 7 years = 209 + 87 + 257 = 553, and the average is 553 / 7 = 79 lakhs, which matches the given data. The first 4 year average is 296 / 4 = 74, and the last 4 year average is 344 / 4 = 86, so all conditions are satisfied. Why Other Options Are Wrong: If R4 were 89 or 85 or 83, the recomputed totals would not equal 553 and at least one of the averages would not match the given values. Only R4 = 87 ensures consistency with all three average conditions simultaneously. Common Pitfalls: Students sometimes forget that the 4th year is counted in both the first and last group, or they may try to average 74 and 86 directly. Another mistake is to ignore the overall average and only work with partial sums. The systematic approach is to express everything in terms of sums and carefully account for overlaps when constructing the total. Final Answer: The revenue in the 4th year is Rs. 87 lakhs.

Question 2

The average of the three numbers a, b and c is 20, and the average of the three numbers b, c and d is 25. If d = 30, then what is the value of a?

Accepted Answer

Introduction / Context: This algebraic average problem relates the sums of overlapping triplets of numbers. We know the averages of (a, b, c) and (b, c, d) and the actual value of d. Using these, we can find the value of a. Given Data / Assumptions: (a + b + c) / 3 = 20. (b + c + d) / 3 = 25. d = 30. We need to find a. Concept / Approach: From the given averages, we can find the sums: a + b + c = 3 * 20 = 60. b + c + d = 3 * 25 = 75. We use the known value of d to find b + c from the second sum, then substitute into the first to find a. Step-by-Step Solution: Step 1: Convert averages to sums. a + b + c = 3 * 20 = 60. b + c + d = 3 * 25 = 75. Step 2: Use d = 30 in the second equation. b + c + 30 = 75. b + c = 75 - 30 = 45. Step 3: Substitute b + c into the first equation to find a. a + (b + c) = 60. a + 45 = 60. a = 60 - 45 = 15. Verification / Alternative check: Using a = 15, b + c = 45 and d = 30, we see that: a + b + c = 15 + 45 = 60, giving an average of 60 / 3 = 20. b + c + d = 45 + 30 = 75, giving an average of 75 / 3 = 25. Both averages match the given data, confirming that a = 15 is correct. Why Other Options Are Wrong: If a were 25, then a + b + c would be 25 + 45 = 70, contradicting the required total of 60. Similarly, a = 45 or a = 30 gives sums that do not match 60. Only a = 15 makes both average equations consistent with the given value of d. Common Pitfalls: Some students attempt to average 20 and 25 or treat a and d as symmetric, which they are not. Others might miscalculate the sums when converting from averages. Always convert each average to its corresponding total sum and use substitution carefully to isolate the unknown variable. Final Answer: The value of a is 15.

Question 3

The average monthly salary of 19 members of a group is Rs. 16,000. If one more member, whose monthly salary is Rs. 20,000, joins the group, what will be the new average monthly salary of the group?

Accepted Answer

Introduction / Context: This question demonstrates how the average changes when a new data point is added to a group. We know the original average salary of 19 members and the salary of a new member who joins. Using this, we need to find the new average salary for the entire group of 20 members. Given Data / Assumptions: Number of members initially = 19. Average monthly salary of these 19 members = Rs. 16,000. One more member with monthly salary Rs. 20,000 joins. We assume salaries are in rupees per month. Concept / Approach: The key idea is that: Total salary of a group = average salary * number of members. When a new member joins, new total salary = old total salary + new member salary. New average = new total salary / new number of members. We will compute the original total salary, add the new salary, and then divide by 20 to get the new average. Step-by-Step Solution: Step 1: Compute the original total salary of 19 members. Original total = 16,000 * 19. 16,000 * 19 = 16,000 * (20 - 1) = 320,000 - 16,000 = Rs. 304,000. Step 2: Add the salary of the new member. New member salary = Rs. 20,000. New total salary = 304,000 + 20,000 = Rs. 324,000. Step 3: Compute new number of members. New number of members = 19 + 1 = 20. Step 4: Compute new average salary. New average = 324,000 / 20 = Rs. 16,200. Verification / Alternative check: We can see that the new member earns Rs. 4,000 more than the original average (20,000 versus 16,000). This extra Rs. 4,000 is spread across 20 members, so the average increase per member is 4,000 / 20 = Rs. 200. Therefore the new average should be 16,000 + 200 = Rs. 16,200, which matches the computed value. Why Other Options Are Wrong: An average of Rs. 18,250 or Rs. 18,000 would require a much larger total salary than 324,000. An average of Rs. 16,250 corresponds to a total of 325,000, which is not the correct total. Only Rs. 16,200 corresponds exactly to the new total salary of Rs. 324,000 divided by 20 members. Common Pitfalls: Students sometimes mistakenly average 16,000 and 20,000 directly, which ignores that there are 19 members at 16,000 and only one at 20,000. Others forget to convert averages into total sums before combining groups. The correct procedure is always to calculate the total from the original average, add the new value, and then divide by the new count. Final Answer: The new average monthly salary of the group is Rs. 16,200.

Question 4

In the first 45 overs of a 50-over cricket innings, the run rate was 5.8 runs per over. What run rate is required in the remaining overs so that the team reaches a total of 295 runs?

Accepted Answer

Introduction / Context: This is a run rate problem in a limited overs cricket match. We know the scoring rate for an initial block of overs and the total target runs. The task is to compute the required run rate in the remaining overs so that the team can reach the target score exactly by the end of the innings. Given Data / Assumptions: Total overs in the innings = 50. Overs already completed = 45. Run rate in the first 45 overs = 5.8 runs per over. Target total runs to be achieved = 295 runs. We assume the team continues to bat for the full 50 overs. Concept / Approach: We apply two main ideas: Runs scored = run rate * number of overs. Remaining runs required = target runs minus runs already scored. Required run rate = remaining runs / remaining overs. First we will compute runs scored in the first 45 overs, then determine how many runs are needed from the last 5 overs, and finally compute the required average run rate for those overs. Step-by-Step Solution: Step 1: Compute runs scored in first 45 overs. Runs scored = run rate * overs = 5.8 * 45. 5.8 * 45 = (5.8 * 40) + (5.8 * 5) = 232 + 29 = 261 runs. Step 2: Compute remaining runs to reach 295. Remaining runs = target - already scored = 295 - 261 = 34 runs. Step 3: Compute remaining overs. Total overs = 50, overs used = 45, so remaining overs = 5. Step 4: Compute required run rate. Required run rate = remaining runs / remaining overs. Required run rate = 34 / 5 = 6.8 runs per over. Verification / Alternative check: If the team scores at 6.8 runs per over for the last 5 overs, it will score 6.8 * 5 = 34 runs in those overs. Adding this to the 261 runs already scored gives 261 + 34 = 295, which matches the target total. The computation is straightforward and consistent, confirming the required rate. Why Other Options Are Wrong: A required run rate of 6.9 would yield 6.9 * 5 = 34.5 runs, slightly overshooting the target. A rate of 6.7 gives 33.5 runs, leaving the team short, and 6.6 gives only 33 runs, also short. Only 6.8 runs per over gives exactly 34 runs in 5 overs, making the final total exactly 295. Common Pitfalls: Some students mistakenly recalculate an overall run rate for all 50 overs instead of focusing on the remaining overs. Others may round prematurely or compute 45 * 5.8 incorrectly. The safest approach is to first find the runs scored so far, then subtract from the target to get the remaining runs, and then divide by the number of overs left to obtain the required run rate. Final Answer: The required run rate in the remaining overs is 6.8 runs per over.

Question 5

The average of 15 numbers is 7. If the average of the first 8 numbers is 6.5 and the average of the last 8 numbers is 8.5 then middle number is

Accepted Answer

15

Question 6

In the first 40 overs of a 50 over innings, the run rate was 4.8 runs/over. What is the required run rate in the remaining 10 overs to reach the target of 241 runs?

Accepted Answer

4.9

Question 7

What is the average of all numbers between 11 and 80 which are divisible by 6?

Accepted Answer

45

Question 8

The average of marks obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates is 35 and that of the failed candidates is 10, what is the number of candidates who passed the examination?

Accepted Answer

80

Question 9

The average height of 30 boys out of a class of 50 is 160 cm. If the average height of the remaining boys is 165 cm, the average height of the whole class (in cm) is:

Accepted Answer

162

Question 10

The average marks obtained by a class of 60 students is 65. The average marks of half of the students is found to be 85. The average marks of the remaining students is

Accepted Answer

45

Question 11

The average weight of 10 parcels is 1.7 kg. Addition of another new parcel reduces the average weight by 60 gram. What is the weight , in kg, of the new parcel?

Accepted Answer

1.04

Question 12

In a class of 50 students there are 27 boys. The average weight of these boys is 72 Kg and average weight of the full class is 55.44 kgs. What is the average weight (in kgs) of the girls of the class?

Accepted Answer

36

Question 13

What is the average of all numbers between 9 and 90 which are divisible by 8?

Accepted Answer

52

Question 14

An army of 12000 consists of Europeans and Indians. The average height of a European is 5ft 10 inches and that of an Indian is 5ft 9 inches and that of the whole army is 5ft 9 3/4 inches. Then the number of Indians in the army is ?

Accepted Answer

3000

Question 15

The average weight of 3 men A, B and C is 84 Kg. Another man D joins the group and the average now becomes 80 Kg. If another man E whose weight is 3 Kg more than that of D, replaces A then the average weight of B, C, D and E becomes 79 Kg. What is t…

Accepted Answer

75 Kg

Question 16

The average weight of L, M and N is 93 kg. If the average weight of L and M be 89 kg and that of M and N be 96.5 kg, then the weight (in kg) of M is ________.

Accepted Answer

92

Question 17

Average of all even numbers between 222 and 250 is __________.

Accepted Answer

236

Question 18

In a class of 60 students there are 20 girls who scored an average of 40 marks in the test, what is the average marks of the boys if the class average is 60 marks?

Accepted Answer

70

Question 19

An oil refinery buys oil at Rs 3600 per barrel. There is 10% wastage. If the refinery wants to earn 5% profit then at what price should it sell including 8% tax on selling price? (in Rs per barrel)

Accepted Answer

4536

Question 20

Two students appeared for an examination. One of them secured 26 marks more than the other and his marks were 75% of the sum of their marks. The marks obtained by them are

Accepted Answer

39 and 13

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