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Average Formulas, Average Tricks:
 Suppose there are N numbers, then their average is their sum divided by that is,
Average=(sum / N)
 Weighted Average: The average between two sets of numbers is closer to the set with more numbers.
if 3 batsmen scored 25 runs and 2 batsmen scored 35 runs the average of the team won’t be 30. Rather it will be
= (25×3 + 35×2 )/5 = 29 . This is nearer to 25 since more batsmen scored 25 runs.
Average =total of data/No. of data
 If the value of each item is increase by x, then the average of the group will also increase by x.
 If the value of each item is decreased by y, then the average of the group of items will also decrease by y.
 If the value of each item is multiplied by the same value m, then the average of the group or items will also get multiplied by m.
 If the value of each item is multiplied by the same value n, then the average of the group or items will also get divided by n.
 If we know only the average of the two groups individually, we cannot find out the average of the combined group of items.
Average of x natural no’s = (x+1)/2
Average of even No’s = (x+1)
Average of odd No’s = x
 Change in the value of a Quantity and its effect on the Average
 When one/more than one quantity are removed but replaced with same no. of quantities of different value,
 Change in the no. of quantities and its effect on Average
+ = if quantities are Added, – = if quantities are removed
Average Solved Example, Average Short Cuts,Tricks
Ex.1: Find the average of all prime numbers between 30 and 50?
Sol: there are five prime numbers between 30 and 50.
They are 31,37,41,43 and 47.
Therefore the required average=(31+37+41+43+47)/5>199/5> 39.8.
Ex.2. find the average of first 40 natural numbers?
Sol: sum of first n natural numbers=n(n+1)/2;
So,sum of 40 natural numbers=(40*41)/2 =820.
Therefore the required average=(820/40) =20.5.
Ex.3. find the average of first 20 multiples of 7?
Sol: Required average =7(1+2+3+…….+20)/20 =(7*20*21)/(20*2) =(147/2)=73.5.
Ex.4. the average of four consecutive even numbers is 27. find the largest of these numbers?
Sol: let the numbers be x,x+2,x+4 andx+6. then,
(x+(x+2)+(x+4)+(x+6))/4) = 27
=(4x+12)/4 = 27
=x+3=27 x=24.
Therefore the largest number=(x+6)=24+6=30.
Ex.5. there are two sections A and B of a class consisting of 36 and 44 students respectively. If the average weight of section A is 40kg and that of section B is 35kg, find the average weight of the whole class?
Sol: total weight of(36+44) students=(36*40+44*35)kg =2980kg.
Therefore weight of the total class=(2980/80)kg =37.25kg.
Ex:6.nine persons went to a hotel for taking their meals 8 of them spent Rs.12 each on their meals and the ninth spent Rs.8 more than the average expenditure of all the nine.What was the total money spent by them?
Sol: Let the average expenditure of all 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.
Ex.7: Of the three numbers, second is twice the first and is also thrice the third.If the average of the three numbers is 44.Find the largest number.
Sol: Let the third number be x.
Then second number = 3x.
First number=3x/2.
Therefore x+3x+(3x/2)=(44*3) or x=24
So largest number= 2nd number=3x=72.
Ex.8:The average of 25 result is 18.The average of 1st 12 of them is 14 & that of last 12 is 17.Find the 13th result.
Sol: Clearly 13th result=(sum of 25 results)(sum of 24 results)
=(18*25)(14*12)+(17*12)
=450(168+204)
=450372
=78.
Ex.9:The Average of 11 results is 16, if the average of the 1st 6 results is 58 & that of the last 63. Find the 6th result.
Sol: 6th result = (58*6+63*660*11)=66
Ex.10:The average waight of A,B,C is 45 Kg. The avg wgt of A & B be 40Kg & that of B,C be 43Kg. Find the wgt of B.
Sol. Let A,B,c represent their individual wgts.
Then,
A+B+C=(45*3)Kg=135Kg
A+B=(40*2)Kg=80Kg & B+C=(43*2)Kg=86Kg
B=(A+B)+(B+C)(A+B+C)
=(80+86135)Kg
=31Kg.
Ex. 11. The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
Sol. Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 – 585) years=25 years.
Ex. 12. The average weight of 10 oarsmen in a boat is increased by 1.8 kg when one of the crew, who weighs 53 kg is replaced by a new man. Find the weight of the new man.
Sol. Total weight increased =(1.8 x 10) kg =18 kg.
:. Weight of the new man =(53 + 18) kg =71 kg.
Ex. 13. There were 35 students in a hostel. Due to the admission of 7 new students, ;he expenses of the mess were increased by Rs. 42 per day while the average expenditure per head diminished by Rs 1. Wbat was the original expenditure of the mess?
Sol. Let the original average expenditure be Rs. x. Then,
42 (x – 1) – 35x=42 = 7x= 84 = x =12.
Original expenditure = Rs. (35 x 12) =Rs. 420. .
14. A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17 th inning.
Sol. Let the average after 17th inning = x.
Then, average after 16th inning = (x – 3).
:. 16 (x – 3) + 87 = 17x or x = (87 – 48) = 39.
Ex.15. Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km perhour. Find the average speed of the train during the whole journey.
Sol. Required average speed = ((2xy)/(x+y)) km / hr
=(2 x 84 x 56)/(84+56)km/hr
= (2*84*56)/140 km/hr
=67.2 km/hr.
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Question 1 of 30
1. Question
1 pointsCategory: mathAverage of all prime numbers between 30 to 50
Correct
Incorrect
Hint
Explanation:
Prime numbers between 30 and 50 are:
31, 37, 41, 43, 47Average of prime numbers between 30 to 50 will be
(31+37+41+43+475)/5=1995/5=39.8 
Question 2 of 30
2. Question
1 pointsCategory: mathWhat is the average of first 21 multiples of 7 ?
Correct
Incorrect
Hint
Answer: Option ‘B’
Required average = 7(1+2+….+21) / 21
(7/21)X ( (21×22) / 2 ) (because sum of first 21 natural numbers)
= 77 
Question 3 of 30
3. Question
1 pointsReeya obtained 65, 67, 76, 82 and 85 out of 100 in different subjects, What will be the average.
Correct
Incorrect
Hint
Answer: Option B
Explanation:
(65+67+76+82+855)/5=75 
Question 4 of 30
4. Question
1 pointsIn a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Correct
Incorrect
Hint
Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years 
Question 5 of 30
5. Question
1 pointsFind the sum of first 30 natural numbers
Correct
Incorrect
Answer: Option C
Explanation:
Sum of n natural numbers
=n(n+1)/2=n(n+1)2=30(30+1)/2=30(31)/2=465 
Question 6 of 30
6. Question
1 pointsCategory: mathA number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor?
Correct
Incorrect
Hint
Option(D) is correct
Let the original number be ‘aa’
Let the divisor be ‘dd’Let the quotient of the division of aa by dd be ‘xx’
Therefore, we can write the relation as a/d=xa/d=x and the remainder is 24.
i.e., a=dx+24a=dx+24When twice the original number is divided by d,2ad,2a is divided by dd.
We know that a=dx+24a=dx+24. Therefore, 2a=2dx+482a=2dx+48The problem states that (2dx+48)/d(2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by dd and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by dd.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.

Question 7 of 30
7. Question
1 pointsCategory: mathFind the remainder when first 1000 digits of the number PP are divided by 16?
Correct
Incorrect
Hint
PP is obtained by writing the first 1000 natural numbers from left to right.
We need last four digits of the number formed by the first thousand digits to check the divisibility of 16.
The first 99 natural numbers wll give us 9+(90×2)=1899+(90×2)=189 digits.
We need another 1000−189=811 digits from the remaining numbers numbers.
⇒ required additional natural numbers =811/3=270 (approx)
i.e. 99+270+ one digit
i.e. first 369 natural numbers and one additional digit will form a number containing the first 1000 digits of the number P
i.e. end of the required number will look like
…………………….3683693⇒ remainder will be same as the remainder of 3693/16=13

Question 8 of 30
8. Question
1 pointsCategory: math18 is the mean of 5 numbers. What should be the exclude number if the average became 16 after excluding number?
Correct
Incorrect
Hint
5 number have the total sum = (18*5)= 90 4 number have the total sum = (16*4)= 64 So, the exclude number is = (9064)= 26

Question 9 of 30
9. Question
1 pointsCategory: math2 cow’s and 8 goats are brought for Rs.1400. If the average price of a goat be Rs.60. What is the average price of a cow.
Correct
Incorrect
Hint
Explanation:
Average price of a goat = Rs.60
total price of 8 goats = 8*60 = Rs.480
But total price of 2 cows and 8 goats = Rs. 1400
Total price of 2 cows is = 1400 – 480
= 980
Average price of a cow = 980/2
= Rs. 460 
Question 10 of 30
10. Question
1 pointsCategory: mathWhat is the average of first 21 multiples of 7 ?
Correct
Incorrect
Hint
Required average = 7(1+2+….+21) / 21
(7/21)X ( (21×22) / 2 ) (because sum of first 21 natural numbers)
= 77 
Question 11 of 30
11. Question
1 pointsCategory: math23 is the average of 3 friends if we add 1 more person then the value of average will be same or no change. Find out the age of the new person?
Correct
Incorrect
Hint
3 friends have the sum of the ages = (3*23)= 69 ...(i) 4 friend have the sum of the ages = (4*23)=92 ...(ii) Difference between the (i) and (ii) is the age of the new person. We find that the age of the new person is (9269)= 23 years.

Question 12 of 30
12. Question
1 pointsCategory: math50 marks is the average of 5 students in English. What should be the right average if 48 marks read 84 by mistake.
Correct
Incorrect
Hint
Sum of the 5 students mark = (50*5)= 250 We find the actual sum of 5 students mark = (250+48 84) = 214 Hence, the right average will be = 214/5 = 42.8

Question 13 of 30
13. Question
1 pointsCategory: mathBefore the period of 10 years, 24years is the average of 4 member�s family. After two children born, the average age of the family no change if 2 years is the age difference between 2 children then what should be the youngest child age?
Correct
Incorrect
Hint
x is the age of the youngest child. Then, elder son child age = (x+2) years. At the present day average age of 6 members = 24 years. At the present day , some of the ages of 6 members = (24*6)= 144 years. (24*4)+(10*4) +x+(x+2) =144 ⇒ 2x = 6 ⇒ x= 3 At the present time the youngest child have 3 year age old.

Question 14 of 30
14. Question
1 pointsCategory: mathN is average of 5 consecutive natural numbers if we add 2 upcoming numbers then what should be the seven number averages?
Correct
Incorrect
Hint
x, x+1, x+2, x+3 and x+4 is the 5 natural consecutive numbers. Then , x+(x+1)+(x+2)+(x+3)+(x+4)= 5n ⇒ 5x+10=5n ⇒ x = 5(n2)/5 = (n2) ∴ 7 consecutive natural numbers are (n2),(n1), n,(n+1), (n+2),(n+3) Average of 7 consecutive natural numbers =( 7n+1/7 ) = (n+1) ∴ average increase by 1.

Question 15 of 30
15. Question
1 pointsCategory: mathThe average age of three persons is 52 years. Their ages are in the proportion of 1:5:7. What is the age in years of the oldest one among them.
Correct
Incorrect
Explanation:
Let the age of three persons be x, 5x, 7x
= 13x/3 = 52
x= 12 yearsHint

Question 16 of 30
16. Question
1 pointsCategory: mathPriya covers journey from kavali to nellore by car at average speed of 70 Km/hr. She returns back by scooty with an average speed of 40 Km/hr. Find her average speed during the whole journey?
Correct
Incorrect
Hint
Explanation:
Average speed = 2 xy/x+y
= 2*70*40/110
= 50.90 Km/hr 
Question 17 of 30
17. Question
1 pointsCategory: mathSeven years ago the average age of a family of 2 members was 25 years. A child has been born. due to Which the average age of the family is 23 years today. What is the present age of the child?
Correct
Incorrect
Hint
Explanation:
Average of the family of two numbers
7 years ago = 25
= (25+ 7) * 2 = 64 years
Average age of the family of three members at present = 23 years
= 23 * 3 = 69 YEARS
Age of child = 69 – 64 = 5 years 
Question 18 of 30
18. Question
1 pointsCategory: mathIn a class, the average age of 30 boys is 13 years and the average of 20 girls is 12 years. what is the average age of the whole class?
Correct
Incorrect
Hint
Answer: Option ‘D’
Total age of 50 students
(30X 13+20 X 12) = 630
Average = 630/50 = 12.6 Years 
Question 19 of 30
19. Question
1 pointsCategory: mathThe average age of a class of 32 students is 16 yrs. if the teacher’s age is also included, the average increases by one year. Find the age of the teacher
Correct
Incorrect
Hint
Total age of students is 32 × 16 = 512 Years
Total age inclusive of teacher = 33 × (16+1) = 561
So, Teacher’s age is 561512 = 49 Yrs
There is a shortcut for these type of problems
Teacher’s age is 16+(33 × 1) = 49 Years 
Question 20 of 30
20. Question
1 pointsCategory: mathThe average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
Correct
Incorrect
Hint
The total of seven numbers = 7 × 18 = 126
The total of first 3 and last 3 numbers is = 3 × 14+3 × 19 = 99
So, the middle number is (126 – 99 ) = 27 
Question 21 of 30
21. Question
1 pointsCategory: mathAverage of five consecutive even numbers is 35. Find the greatest number in these five numbers?
Correct
Incorrect

Question 22 of 30
22. Question
1 pointsCategory: mathFind the average of first 10 multiples of 7
Correct
Incorrect
Hint
Explanation:
=7(1+2+3+…+10)/10
=7(10(10+1))/10×2=7(110)/10×2=38.5

Question 23 of 30
23. Question
1 pointsCategory: mathThe average of four consecutive odd numbers is 24. Find the largest number.
Correct
Incorrect
Hint
Explanation:
Let the numbers are x, x+2, x+4, x+6, then
=>x+(x+2)+(x+4)+(x+6)/4=24
=>4x+12)/4=24
=>x+3=24=>x=21So largest number is 21 + 6 = 27

Question 24 of 30
24. Question
1 pointsCategory: math105 cm is the average height of 10 students. Find out the new average height if 20 students also join the class whose average height is 120 cm.
Correct
Incorrect
Hint
10 student have total value of heights = (105* 10)= 1050 cm. 20 students have total value of heights = (120*20) = 2400 cm 30 students have total value of heights = (1050+2400) = 3450 cm. Average required = 3450/30 = 115 cm

Question 25 of 30
25. Question
1 pointsCategory: mathThe average of 50 numbers is 30. If two numbers 35 and 40 are discarded then the average of the remaining numbers is nearly?
Correct
Incorrect
Hint
Sum of 50 numbers = 30 x 50 = 1500 Sum of remaining 48 numbers = 1500  (35 + 40) = 1425. Therefore Required average = ^{1425}⁄_{48} = ^{475}⁄_{16} = 29.68

Question 26 of 30
26. Question
1 pointsCategory: mathAverage of ten positive numbers is ‾z. if each number is increased by 10%, then ‾z?
Correct
Incorrect
Hint
‾z is increased by 10%.

Question 27 of 30
27. Question
1 pointsCategory: mathThe average weight of 45 students in a class is 52kg. Five of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54kg join the class. What is the new average weight (in kg) of the class?
Correct
Incorrect
Hint
Sum of the weights of the students after replacement. = [(52 x 45)  (48 x 5) + (54 x 5)] kg = 2370kg. Therefore, new Average = ^{2370}⁄_{45}kg = 53^{2}⁄_{3}kg

Question 28 of 30
28. Question
1 pointsCategory: mathThe average weight of 3 men A, B, C is 84 kg. Another man D joins the group and the average now becomes 80kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then the average weight of B, C, D, E becomes 79kg. The weight of A is?
Correct
Incorrect
Hint
Let A, B, C, D and E represent their respective weights. Then, A + B + C = (84 x 3) = 252 kg, A + B + C + D = (80 x 4) = 320 kg. D = (320  252)kg = 68 kg, E = (68 + 3)kg = 71 kg. B + C + D + E = (79 x 4) = 316 kg Now, (A + B + C + D)  (B + C + D + E) = (320  316)kg = 4 kg A  E = 4 A = ( 4 + E ) = 75 kg.

Question 29 of 30
29. Question
1 pointsCategory: mathThe average temperature for Tuesday, Wednesday and Thursday was 42°C. The average temperature for Wednesday, Thursday and Friday was 44°C. If the temperature on Friday be 43°C, what was the Temperature on Tuesday?
Correct
Incorrect
Hint
Explanation:
T + W + T = 42 × 3 = 126°C
W+ T+ F = 44 × 3 = 132°C
Also, temperature on Friday = 43°C
Temperature on Tuesday = 126 +43 – 132 = 37°C 
Question 30 of 30
30. Question
1 pointsCategory: mathThe average of 30 numbers is 48. If three numbers namely 45, 55 and 43 are discarded, the average of remaining numbers is?
Correct
Incorrect
Hint
Explanation:
Total of 30 numbers = 30 * 48 = 1440
Average o 27 numbers = 1440 – (45 + 55 + 43) / 27
= 48.03
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