1.The average annual income (in Rs.) of certain agricultural workers is P and that of other workers is Q . The number of agricultural workers is 9 times that of other workers. Then the average monthly income (in Rs.) of all the workers is :

A. [latex]\frac{(P + Q)}{10}[/latex] B. [latex]\frac{(P + 9Q)}{10}[/latex] C. [latex]\frac{1}{( P + Q)}[/latex] D. [latex]\frac{(9P + Q)}{10}[/latex] E. None of these

2. A family consist of grandparents, parents and two grandchildren. The average age of the grandparents is 56 years, that of the parents is 27 years and that of the grandchildren is 7 years. What is the average of the family?

A. 10 years B. 20years C. 30 years D. 40 years E. None of these

3. A library has an average of 430 visitors on Sundays and 270 on other days. The around average of the number of visitors per day in a month of 31 days beginning with a Saturday is:

A. 260 B. 275 C. 285 D. 296 E. None of these

4. If the average marks of three batches of 40, 50 and 60 students respectively is 30, 50 and 70, then the average marks of all the students is:

A. 63.33 B. 52.66 C. 60 D. 65 E. None of these

5. The average weight of 18 boys in a class is 45.55 kgs and that of the remaining 4 boys is 35.25 kgs. Find the average weight of all the boys in the class.

A. 44.33 kgs B. 42 kgs C. 43.67 kgs D. 49.23 kgs E. None of these

Answer & Explanation:
1. Answer: Option D
Explanation: Let the number of other workers be x. Then, number of agricultural workers = 9x. Total number of workers = 9x + x = 10x. So, Average monthaly income [latex]\frac{P * (9x) + Q * (x)}{10x}[/latex]= [latex]\frac{(9P + Q)}{10}[/latex]
2. Answer: Option C
Explanation: First, we find out the normal ages of candidates: Grand parents(2 candidates) = 56 x 2 Parents (2 candidates) = 27 x 2 Two grandchildren = 7 x 2. The total candidates are 6. then, Average =[latex]\frac{56 \times 2 + 27 \times 2 + 7 \times 2}{2 + 2 + 2}[/latex]= 30 years
3. Answer: Option
Explanation: Since the month begins with a saturady , So there will be five sundays in the month, Req. Avg. =[latex]\frac{430 \times 5 + 270 \times 26}{31}[/latex]= 295.80 ≈ 296
4. Answer: Option B
Explanation: Req Avg = [latex]\frac{40 \times 30 + 50 \times 50 + 60 \times 70}{30 + 50+ 70}[/latex] = 52.66
5. Answer: Option C
Explanation: Reqd Avg =[latex]\frac{18 \times 45.55 + 4 \times 35.25}{18 + 4}[/latex] = [latex]\frac{ 960.9}{22}[/latex]= 43.67 kgs

1. 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 the target of 282 runs?

A. 6.25 B. 6.5 C. 6.75 D. 7

2. A family consists of two grandparents, two parents and three grandchildren. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?

A. 28[latex]\frac{4}{7}[/latex] B. 31[latex]\frac{5}{7}[/latex] C. 32[latex]\frac{1}{7}[/latex] D. None of these

3. A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?

A. Rs. 4991 B. Rs. 5991 C. Rs. 6001 D. Rs. 6991

4. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?

A. 0 B. 1 C. 10 D. 19

5. The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?

A. 76 kg B. 76.5 kg C. 85 kg D. Data inadequate E. None of these

Answer & Explanation:
1. Answer: Option A
Explanation: Required run rate =[latex]\frac{282 - (3.2 \times 10)}{40}[/latex]= 6.25
2. Answer: Option B
Explanation: Required average = [latex]\frac{67 \times 2 + 35 \times 2 + 6 \times 3}{2 + 2 + 3}[/latex] =[latex]\frac{222}{7}[/latex] =31[latex]\frac{5}{7}[/latex]
3. Answer: Option A
Explanation: Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009. Required sale = Rs. [ (6500 x 6) - 34009 ] = Rs. (39000 - 34009) = Rs. 4991.
4. Answer: Option D
Explanation: Average of 20 numbers = 0. Sum of 20 numbers (0 x 20) = 0. It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
5. Answer: Option C
Explanation: otal weight increased = (8 x 2.5) kg = 20 kg. Weight of new person = (65 + 20) kg = 85 kg.

1. The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

A. 23 years B. 24 years C. 25 years D. None of these

2. The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

A. 3500 B. 4000 C. 4050 D. 5000

3. The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

A. 35 years B. 40 years C. 50 years D. None of these

4. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?

A. Rs. 7.98 B. Rs. 8 C. Rs. 8.50 D. Rs. 9

5. n Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?

A. 67 kg. B. 68 kg. C. 69 kg. D. Data inadequate E. None of these

Answer & Explanation:
1. Answer: Option A
Explanation: Let the average age of the whole team by x years. 11x - (26 + 29) = 9(x -1) 11x - 9x = 46 2x = 46 x = 23.
2. Answer: Option B
Explanation: Let P, Q and R represent their respective monthly incomes. Then, we have: P + Q = (5050 x 2) = 10100 .... (i) Q + R = (6250 x 2) = 12500 .... (ii) P + R = (5200 x 2) = 10400 .... (iii) Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 33000 or P + Q + R = 16500 .... (iv) Subtracting (ii) from (iv), we get P = 4000. P's monthly income = Rs. 4000.
3. Answer: Option B
Explanation: Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years. Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years. Husband's present age = (90 - 50) years = 40 years.
4. Answer: Option A
Explanation: Total quantity of petrol consumed in 3 years=[latex]\frac{4000}{7.50}[/latex]+[latex]\frac{4000}{8}[/latex]+[latex]\frac{4000}{8.50}[/latex] = [latex]\frac{76700}{51}[/latex]litres Total amount spent = Rs. (3 x 4000) = Rs. 12000. Average cost = Rs. [latex]\frac{12000 \times 51}{76700}[/latex] = [latex]\frac{6120}{767}[/latex]= Rs. 7.98
5. Answer: Option A
Explanation: Let Arun's weight by X kg. According to Arun, 65 ≤ X ≤ 72 According to Aruns brother, 60 ≤ X ≤ 70. According to Aruns mother, X ≤ 68 The values satisfying all the above conditions are 66, 67 and 68. Required average =[latex]\frac{66 + 67 + 68}{3}[/latex]=[latex]\frac{201}{3}[/latex]=67 kg