# Average Example Question & Answer

## Average Example Question & Answer

Example #1:
The average presence of students of a class in a College on Monday, Tuesday and Wednesday is 32 and on the Wednesday, Thursday, Friday and Saturday is 30. if the average number of students on all the six days is 26 then the number of students who attended the class on Wednesday is?

32 x 3 + 30 x 4 – 26 x 6
= 96 + 120 – 156
= 60.

Example #2:
The average income of Arun, Bala and Chitra is Rs. 12,000 per month and average income of Bala, Chitra and David is Rs. 15,000 per month. If the average salary of David be twice that of Arun, then the average salary of Bala and Chitra is in Rs?

Arun + Bala + Chitra = 12000×3 Bala + Chitra + David = 15000 x 3 David – Arun = 3000 x 3 = 9000 David = 2Arun David = 18000 and Arun = 9000 Average salary of Bala and Chitra, = (45000-18000)/2 = 13,500.

Example #3:
The average expenditure of Sharma for the January to June is Rs. 4200 and he spent Rs. 1200 in January and Rs.1500 in July. The average expenditure for the months of February to July is:

Total Expenditure(Jan – June)
= 4200 x 6
= 25200 Total Expenditure(Feb – June)
= 25200 – 1200 = 24000
Total Expenditure(Feb – July) = 24000 + 1500
= 25500/6 = 4250.

Example #4:
The average price of 80 mobile phones is Rs.30,000. If the highest and lowest price mobile phones are sold out then the average price of remaining 78 mobile phones is Rs. 29,500. The cost of the highest mobile is Rs.80,000. The cost of lowest price mobile is?

The price of the costliest and cheapest mobile
= (80 x3000) – (78×29500)
= 99000 Cheapest Mobile Price
= 99000 – 80000 = 19000.

Example #5:
Ramesh walked 6 km to reach the station from his house, then he boarded a train whose average speed was 60 kmph and thus he reached his destination. In this way he took a total time of 3 hours. If the average speed of the entire journey was 32 kmph then the average speed of walking is:

Total Distance = 32 x 3
= 6 + 60 x X X
= 1.5 hour ;
Walking Speed = 6/1.5 = 4 kmph.

Example #6: In English exam, the average of Class “A” was found to be “x” marks. After deducting a computational error, the average marks of 100 candidates got reduced from 74 to 54. The average thus came down by 25 marks. The total numbers of candidates who took the English exam were ?

(74 – 54) x 100 = 25 x X
X = 20 x 100 / 25 = 80.

Example #7:The average value of property of Agil, Mugilan and Anitha is Rs.130cr.The Property of Agil is 20cr greater than the property value of Mugilan and Anitha property value is 50cr greater than the Agil property value. The value of property of Anitha is

Property value of Mugilan x 130*3 = x+x+20+x+20+50 390

= 3x+90 3x=300
X=100
Anitha = 100+20+50 = 170

Example #8:
If the average marks of 1/5th of class is 70% and 2/5th class is 45% and the average mark of remaining class is 60%, then the average % of the whole class is.

Avg = 100*[x/5 *70/100 + 2x/5 * 45/100 +2x/5*60/100 ] /x = 70+90+20/5 =56

Example #9:
The average salary of 120 employees in the bank is Rs.15,000 per month. If the no of assistant is thrice the no of POs and average salary of assistant is 1/3rdof the average salary of POs then find the average salary of POs ?

120 = 1:3 =30:90 = PO : Assistant
120*15000 = 30*x+ 90 *x/3 18,00,000 = 90x+90x/ 3 54,00,000*3 = 180x X = 30000

Example #10:
The average weight of 40 balls is 5 grams. When the weight of the basket is added to the weight of balls, the average increased by 0.5 grams. Find the weight of the basket.
B is the weight of basket
(40*5 + B)/41 = 5.5.

Example #11:
The average height of 50 students in a class is 165cm. On a particular day, three students P,Q and R are absent, so the average of the remaining students becomes 163cm. If the height of P and Q is equal and height of R is 2 cm less than P, then find the height of P.

sum of height (50) = 50*165 = 8250
sum of height (47) = 47*163 = 7661
sum of the height of P, Q and R = 8250-7661 = 589
P+P+P-2 = 589 (as height of P is equal to Q and height of R = P -2) P = 197.

Example #12:
A cricketer had an average number of runs as 32 after playing 10-innings. If he wants to make his average run rate increased by 4, then how much runs will he have to take in his next inning?

Average after 10 innings = 32,
so after 11 inning = 32+4 = 36
So required runs = (36*11) – (32*10) = 76.

Example #13:
The average temperature for the the first 5 month of the year is 40‟c and the average temperature from second to sixth month is 42‟c and the ratio b/w the temperature of 1st day and the 6th day is 3:4, find the temperature of the sixth day ?

1,2,3,4,5 = 200
2,3,4,5,6 = 210
4x – 3x = 10,
so temp on sixth day = 40.

Example #14:
The average age of Husband and wife was 30yr, 4 yr ago. What will be their average age at present ?

Avg of H and W age 4yr ago = 30
Present avg age of H and W = 30+4 = 34.

Example #15:
The average weight of 20 students is 60kg.If the weight of the teacher is added, average is increased by 2kg.What was the teacher‟s weight ?

x/20 =60;
x = 1200 x/21 = 62;
x = 1302
1302 – 1200 = 102.

Example #16:
3 years ago, the average age of A, B, and C was 27 years. Also 5 years ago, the average age of B and C was 20 years. What is the present age of A?

Sum of ages of A+B+C 3 yrs ago = 27*3 = 81 So after 3 yrs, i.e. at present their total = 81 + 3*3 = 90 Similarly sum of present age of B&C = 20*2 +5*2 = 50 So present age of A = 90-50 = 40

Example #17:
A trader has 600kgs of rice , a part of which he sells at 15% profit and the remaining quantity at 20% loss. On the whole , he incurs an overall loss of 6% .What is the quantity of rice he sold at 20% loss?

Quantity of rice sold at 20% loss = x kg (let) Quantity of rice sold at 15% gain = (600 – x ) kg (600 – x) * (115/100) + (x*80)/100 = (600 * 94)/100 => x = 12600/35 = 360 kg.

Example #18:
If there is a loss of 40% when a good is sold at (2/5)th of its earlier selling price. Find the profit% after selling the good at a certain price.

CP = (2/3) of SP SP = (100+P) / 100 of CP Equating both the above equations, Profit = 50%.

Example #19:
A cloth merchant uses 120cm scale while buying,instead a meter scale ,but uses an 80 cm scale while selling the same cloth. If he offers a discount of 20% on cash payment. Find the profit percent.

After discount = (80 * 120)/100 = 96 Profit = 96 – 80 = 16 Therefore , Profit% = (16*100)/80 = 20%.

Example #20:
An article is marked 50% over its cost price.Two successive discounts of 12% and 13(1/2)% are allowed on the marked price of the article.Find the profit or loss percent after selling at discount.

Let the CP be Rs. 100
SP = 150 * (88/100) * (86.5/100) = Rs. 114.18
Therefore , = (14.18/100)*100 = 14.18%.

Example #21:
A trader marked his goods at such a price that after allowing a discount of 12(1/2) % for cash payment, he makes a profit of 20% . What is the marked price of the good which costs Rs. 210 ?

Required MP = [210 * (100+20)]/(100-12.5) = (210 *120)/87.5 = Rs. 288.

Example #22:
A sold an article to B at the profit of 25%, B sold it to C at loss of 10% and C sold it to D at the profit of 20%. If D paid rs27, then how much A paid to buy this article?

125/100 * 90/100 * 120/100 * X = 27 X = Rs.20.

Example #23:
In a group of 8 boys, 2 men aged at 21 and 23 were replaced two new boys. Due to this the average cost of the group increased by 2 years. What is the average age of the 2 new boys?

Average of 8 boys increased by 2,
this means the total age of boys increased by 8*2 = 16 yrs
So,sum of ages of two new boys = 21+23+16 = 60
Average of these = 60/2 = 30

Example #24:
The average age of 5 children of a family is 10 years but if we include the age of father and mother then the average age becomes 22 years. It is given that father age is 6 years more than the mother so what will be the age of mother at present.

sum of age of children = 50
50 + M+ F = 22*7 = 154.
M+F = 104 and F= M+6 .
So, M = 49.

Example #25:
The batting average of a batsman for 20 innings is 35 and the difference b/w the runs of best inning and worst inning is 50. If these two innings are not included the average becomes 32 for 18 innings. The best score of the batsman is.

35*20 = 700.
Best(B) – Worst(W) = 50
700 – B – H = 18*32= 576.
B+H = 124 and B-H = 50.
So, B =87.

Example #26:
The average age of Husband and wife was 30yr, 4 yr ago. What will be their average age at present ?

Avg of H and W age 4yr ago = 30
Present avg age of H and W = 30+4 = 34.

Example #27:
The average salary of all the workers in factory is 7000. The average salary of 9 mechanic is 5000 and for the rest of the workers it 4000. Find the total number of workers in the factory.

Total workers T, so 7000*T = 9*5000 + (T-9)*4000. T = 3 so 3+9 =12.

Example #28:
In a particular week the average number of people visited the museum is 70. If we exclude the holidays then the average number is increased by 28. Further if we exclude the day which the maximum of 210 visitors visited the museum, then the average become 40.Find the no of holidays in the week

Total no of visitors in a week = 70* 7 = 490
X = no of holidays Exclude hloidays (7-x)*98 = 490 7-x = 5 X = 2

Example #29:
In a class of 60 students 23 are girls. The average mark of boys is 45 and average mark of girls is 52. What is the average mark of the class?

60 students => 23 G and 37 B
Average = 23*52 + 37*45/ 60
= 2965/60 = 47.7

Example #30:
The present average age of a family of 5 members is 40 years. If the youngest member of the family is 12 years old, then find the average age of the family at the time of birth of the youngest member.

Present age of the family = 5*40 = 200 years.
12 years ago at the time of the birth of youngest member,
age of family = 200 – 12*5 = 140.
So, average age = 140/4 = 35 year.

Example #31:
The average of 10 reading is 25.5. In this the average of first three is 20 and the next four is 26. If the eight reading is 5 less than the night one and also 8 less than the tenth one, then find the eight reading?

sum of all ten reading = 255.
sum of first three = 60 and sum of next 4 = 104.
Sum of 8th, 9th and 10th reading = 91 = 3*x + 13 X = 26

Example #32:
The average age of a class is 19 years. While the average age of boys is 20 and the average age of girls is 17. If the number of boys is 20 then find the number of girls in the class

Average of class = 19 = Sum/(b+g)
sum (girls) = g*17
sum (boys) = b*20 19b + 19g = 17g + 20b
2g = b = 20.
So, girls = 10.

Example #33:
The average of 10 reading is 25.5. In this the average of first three is 20 and the next four is 26. If the eight reading is 5 less than the night one and also 8 less than the tenth one, then find the eight reading?

sum of all ten reading = 255
sum of first three = 60 and sum of next 4 = 104.
Sum of 8th, 9th and 10th reading = 91 = 3*x + 13 X = 26.

Example #34:
The average height of 50 students in a class is 165cm. On a particular day, three students P,Q and R are absent, so the average of the remaining students becomes 163cm. If the height of P and Q is equal and height of R is 2 cm less than P, then find the height of P.

sum of height (50) = 50*165 = 8250 sum of height (47) = 47*163 = 7661 sum of the height of P, Q and R = 8250-7661 = 589 P+P+P-2 = 589 (as height of P is equal to Q and height of R = P -2) P = 197.

Example #35:
The average temperature in Delhi for the first four days of the month was reported as 58o. It reported as 60o for 2nd, 3rd, 4th and 5th days. The ratio of the temperatures of 1st and 5th day was 7 : 8. Find the temperature on the first day.

A+B+C+D = 58*4
B+C+D+E = 60*4 Subtract both,
E – A = 8 So 8x – 7x = 8, x = 8
So, temperature of A(1st day) = 7x = 7*8 = 56.

Example #36:
3 years ago, the average age of A, B, and C was 27 years. Also 5 years ago, the average age of B and C was 20 years. What is the present age of A?

Sum of ages of A+B+C 3 yrs ago = 27*3 = 81
So, after 3 yrs,
i.e. at present their total = 81 + 3*3 = 90.
Similarly sum of present age of B&C = 20*2 +5*2 = 50.
So, present age of A = 90-50 = 40.

Example #37:
Sachin scored 8000 runs in a certain number of innings. In the next five innings, he was out of form and hence, could make only 85 runs, as a result his average reduced by 1 run. How many innings did he play in total?

8000/n = a
8085/n+5 = a-1
n² + 90n – 40000 = 0
n = 160
n² + 5 = 165

Example #38:
The average price of 80 mobile phones is Rs.30,000. If the highest and lowest price mobile phones are sold out then the average price of remaining 78 mobile phones is Rs. 29,500. The cost of the highest mobile is Rs.80,000. The cost of lowest price mobile is?

The price of the costliest and cheapest mobile = (80*3000) – (78*29500) = 99000 Cheapest Mobile Price = 99000 – 80000 = 19000

Example #39:
The average weight of all the 11 players of KKR is 50 kg. If the average of first six lightest weight players of KKR is 49 kg and that of the six heaviest players of KKR is 52 kg. The average weight of the player which lies in the sixth position in the list of players when all the 11 players of KKR are arranged in the order of increasing or decreasing weights.

Average of First six players = 49 * 6 = 294
Average of Last six players = 52 * 6 = 312;
Average of all players = 50 * 11 = 550
Average weight of sixth player = 294 + 312 – 550 = 56

Example #40:
Ramen walked 6 km to reach the station from his house, then he boarded a train whose average speed was 60 kmph and thus he reached his destination. In this way he took a total time of 3 hours. If the average speed of the entire journey was 32 kmph then the average speed of walking is:

Total Distance = 32 * 3 = 6 + 60 * x
x = 1.5 hour ;
Walking Speed = 6/1.5 = 4 kmph.

Example #41:
Bajaj travels first one-third of the total distance at the speed of 10 kmph and the next one-third distance at the speed of 20 kmph and the last one – third distance at the speed of 60 kmph. What is the average speed of Bajaj?

= 3 * 10 * 20 * 60 / (200 + 1200 + 600) = 18 kmph.

Example #42:
The average salary of the entire staff in a office is Rs 250 per month. The average salary of officers is Rs 520 and that of non-officers is Rs. 200. If the number of officers is 15, then find the number of non–officers in the office

Let the required number of non–officers = x 200x + 520 x 15 = 250 ( 15 + x ) 250x – 200x = 520 * 15 – 250 x 15 50x = 4050 x = 81.

Example #43:
Mr.Sujan average monthly expenditure for the first four months of the year was Rs.260 For the next five months,the average monthly expenditure was Rs.40 more than what it was during the first four months. If he spent Rs.560 in all during the remaining three months of the year, Find what percentage of his annual income of Rs.5000 did he save in the year?

Sujan average monthly expenditure for
the first four months of the year = Rs.260.
260 * 4 = Rs. 1040
For the next five months,the average
monthly expenditure was Rs.40 more than
what it was during the first four months.
He spent 260 + 40 for one month
In 5 months he spent 300 * 5 = 1500
He spent Rs.560 in all during the remaining three months of the year.
Total expenditure = 1040 + 1500 + 560 = 3100
Savings = 5000-3100 = 1900
percent savings = 1900/5000 * 100 = 38%.

Example #44:
The average value of property of Ajay, Mona and Anita is Rs.130cr.The Property of Ajay is 20cr greater than the property value of Mona and Anita property value is 50cr greater than the Ajay property value. The value of property of Anita is

Property value of Mona x
130*3 = x+x+20+x+20+50
390 = 3x+90
3x=300
X=100
Anita = 100+20+50 = 170.

Example #45:
There are 10 compartments in passenger train carries on average 15 passengers per compartment. If atleast 15 passengers were sitting in each compartment, no any compartment has equal no of passengers , and any compartment does not exceed the number of average passengers except 10th compartment.Find how many passengers can be accommodated in 10thcompartment ?

No of passengers = 15*10 = 150
15+14+13+12+11+10+9+8+7 = 99 150 -99 = 51.

Example #46:
There are five times the number of two wheelers as there are three wheelers. The no of four wheelers are equal to the number of two wheelers. Find the average number of wheel per vehicle ?

No of 3 wheeler = x, no of wheels = 3x
No of 2 wheeler = 5x, no of wheels = 10x
No of 4 wheeler =5x, no of wheels = 20x
Avg = 3x+10x+20x/x+5x+5x = 33x/11x = 3.

Example #47:
Ramesh walked 6 km to reach the station from his house, then he boarded a train whose average speed was 60 kmph and thus he reached his destination. In this way he took a total time of 3 hours. If the average speed of the entire journey was 32 kmph then the average speed of walking is:

Total Distance = 32 * 3 = 6 + 60 * x x = 1.5 hour ; Walking Speed = 6/1.5 = 4 kmph.

Example #48:
Balaji travels first one-third of the total distance at the speed of 10 kmph and the next one-third distance at the speed of 20 kmph and the last one – third distance at the speed of 60 kmph. What is the average speed of Balaji?

= 3 * 10 * 20 * 60 / (200 + 1200 + 600) = 18 kmph.

Example #49:
The average income of Arun, Bala and Chitra is Rs. 12,000 per month and average income of Bala, Chitra and David is Rs. 15,000 per month. If the average salary of David be twice that of Arun, then the average salary of Bala and Chitra is in Rs?

Arun + Bala + Chitra = 12000*3
Bala + Chitra + David = 15000*3
David – Arun = 3000*3 = 9000
David = 2 Arun
David = 18000 and Arun = 9000
Average salary of Bala and Chitra,
= (45000-18000)/2 = 13,500.

Example #50:
In a famous hotel the rooms were numbered from 201 to 230, each room gives an earning of Rs. 5000 for the first fifteen days of a month and for the latter half, Rs. 3000 per room. Find the average income per room per day over the month. (September)?

Total number of rooms = 29
Average = [(5000 * 30 * 15) + (3000 * 30 * 15)]/(30*30)
Average earning per room = 4000.

Example #51:
There were 46 students in a Boys hostel. Due to the admission of eight new students the expenses of the hostel mess were increased by Rs.42 per day while the average expenditure per head diminished by Rs 1. What was the original expenditure of the hostel mess?

54*(x−1)−46*x = 42
8x = 96 x = 12
Original total expenditure: 46*x = 46*12 = Rs.552.

Example #52:
The average of 5 numbers is 40. Average of first two and last two is 25 and 45 respectively. Find the middle number.

5*40 – (2*25 + 2*45)
= 200 – 50+90
=60

Example #53:
The average temperature for the the first 5 month of the year is 40‟c and the average temperature from second to sixth month is 42‟c and the ratio b/w the temperature of 1st day and the 6th day is 3:4, find the temperature of the sixth day ?

1,2,3,4,5 = 200 2,3,4,5,6 = 210 4x – 3x = 10, so temp on sixth day = 40.

Example #54:
The average age of Husband and wife was 30yr, 4 yr ago. What will be their average age at present ?

Avg of H and W age 4yr ago = 30 Present avg age of H and W = 30+4 = 34.

Example #55:
The average weight of 20 students is 60kg.If the weight of the teacher is added, average is increased by 2kg.What was the teacher‟s weight ?

x/20 =60; x = 1200 x/21 = 62; x = 1302 1302 – 1200 = 102.

Example #56:
The average mark in 2 subjects is 35 and in three other subject is 40.Then find the average mark in all the five matches ?