Question 1

The average weight of a class of 40 students is 40 kg. If the weight of the teacher be included , the average weight increases by 500 gm . The weight of the teacher is?

Accepted Answer

Weight of the teacher = Total weight of 40 students and teacher - total weight of 40 students = 41 x 40.5 - 40 x 40 kg = 60.5kg

Question 2

The average age of four players is 18.5 years. If the age of the coach is also included, the average age increases by 20%. The age of the coach is?

Accepted Answer

New average = 120% of old average =120% of 18.5 = (120 x 18.5) / 100 = 22.2 Age of coach = Total weight of 4 players and coach - total weight of 4 players = 5 x 22.2 - 4 x 18.5 = 37 years

Question 3

The average age of four children in a family is 12 years. If the spacing between their ages is 4 years, the age of the youngest child is?

Accepted Answer

Let the age of youngest child be y. so from question y + (y + 4) + (y + 8) + (y + 12) = 4 x 12 ⇒ 4y + 24= 48 ∴ y = 6 years

Question 4

In a T.V. factory, an average of 60 TVs are produced per day for the fist 25 days of the months. A few workers fell ill for the next five days reducing the daily average for the month to 58 sets per day . The average production per day for day last …

Accepted Answer

Production during these 5 days = Total production in a month - production in first 25 days. = 30 x 58 - 25 x 60 = 240 ∴ Average for last 5 days = 240 / 5 = 48

Question 5

The average of marks obtained by 120 candidates was 35. If the average of marks of passed candidates was 39 and that of failed candidates was 39 and that of failed candidates was 15, the number of candidates who passed the examination is?

Accepted Answer

Let the number of candidate who passed = y Then, 39y + 15(120 - y) =120 x 35 ⇒ 24y= 4200 -1800 ∴ y= 2400 / 24 = 100

Question 6

The average age of 30 students in a class is 12 years. The average age of a group of 5 of the students is 10 years and that of another group of 5 them is 14 years. The average age of the remaining students is?

Accepted Answer

Let average of the remaining student be y. Then from questions ( 5 x 10 ) + ( 5 x 14) + 20y = 30 x 12 ⇒ 50 + 70 + 20y = 360 ⇒ 20y = 360 – 120 ⇒ 20y = 240 ⇒ y = 12.

Question 7

A shopkeeper earned Rs. 504 in 12 days. His average income for the first four days was Rs. 40 a day. His average income for the remaining days is?

Accepted Answer

Let the average for remaining 8 days be Rs. y a day. Then, ( 4 x 40 ) + 8y = 504 ⇒ 8y = 344 ⇒ y = 43 ∴ required average Rs. 43

Question 8

The average weight of three men A, B and C is 84 kg. Another man D joins the group and the new average becomes 80 kg if another man E, whose weight is 3kg more than that of D, replace A, then the average weight of B , C, D and E becomes 79 kg. the w…

Accepted Answer

From question A + B + C = 3 x 84 = 252 ....(i) A + B + C + D = 4 x 80 = 320 ...(ii) From eq. (ii) - (i) D = ( 320 - 252 ) = 68 From question E = D + 3 ⇒ E =( 68 + 3 ) = 71 Now , B + C + D + E = 4 x 79 = 316 ∴ B + C + D = 316 – 71 = 245 So , A = 320 - 245 = 75 kg .

Question 9

The average age of a family of 6 member is 22 years . if the age of the youngest member be 7 years , what was the average age of the family at the birth of the youngest member was?

Accepted Answer

Total present age of the family = 6 x 22 = 132 years Total age of the family 7 years ago = 132 - 7 x 6 = 90 years At that time, the number of members was 5 ∴ Average age at time = 90 / 5 years = 18 years

Question 10

The average height of 40 student is 163 cm. On a particular day, three student A, B, C were absent and the average of the remaining 37 student was found to be 162 cm. if A, B have equal height and the height of C be 2 cm less than that of A, find th…

Accepted Answer

Let the height of A , B, C be y cm, y cm and (y - 2) cm respectively Then, y + y + (y - 2) = 163 x 40 - 162 x 37 ⇒ 3y - 2 = 526 ∴ y = 176 cm

Question 11

Columbus started his journey from Lucknow to Kolkata, Which is 200 K.M., at the speed of 40 KM/hr, then he went to Banglore which is 300 Km, at the speed of 20 KM/hr . Further he went to Ahmedabad which is 500 Km, at the speed of 10 Km/hr. The avera…

Accepted Answer

Total distance = (200 + 300 + 500) = 1000 Total time = 200/40 + 300/20 + 500/10 = 5 + 15 + 50 = 70 hr Average speed = Total distance / Total time =1000 / 70 = 14.2857 Km/hr.

Question 12

If the algebraic sum of deviations of 20 observation measured from 23 is 70, mean of these observation would be

Accepted Answer

Mean = (sum of observation) / (number of observation) Sum of observation is given as = 70 Number of observation = 20 ∴ Mean = 70/20 = 3.5 But, here observation starts from= 23. ∴ Mean = 23 + 3.5 = 26.5

Question 13

The average of 50 number is 38. If the two numbers 45 and 55 are not considered, What will be the average of remaining numbers?

Accepted Answer

According to the basic formula of average, Average(A)= Sum (S) / Number(N) ∴ 38 = S/50 ∵ S = 38 x 50 = 1900 Sum of remaining number after eliminating 45 and 55 = 1900 - (45 + 55) = 1800 Average of remaining numbers = (Sum of remaining number) / (Remaining number) = 1800 / ( 50 - 2) = 1800/48 = 37.5

Question 14

The average marks of 30 students are 45 but after checking there are two mistakes found. After adjustment if a student got 45 more markes and other student got 15 less marks, then What will be the adjusted average?

Accepted Answer

Total number of all students of the class = 30 x 45 = 1350 ∴ New average after adjustment = (1350 - 45 + 15)/30 = 1320/30 = 44

Question 15

The mean marks obtained by seven students group is 226. If the marks obtained by six of them are 340, 180, 260, 56, 275 and 307 respectively. Find the markes obtained by the seventh student.

Accepted Answer

Sum of marks of 7 students = Mean x Number of students = 226 x 7 = 1582 Now, total marks of 6 students = (340 + 180 + 260 + 56 + 275 + 307) = 1418 ∴ Marks obtained by seventh students = Total marks of seven students - Total marks of the six student = 1582 - 1418 = 164

Question 16

The average age of 4 member of a family is 25 yr. If head of the family is included in this group then average age increase by 20%. Find out the age of the head.

Accepted Answer

Total age of 4 member = 25 x 4 = 100 yr Total age of 5 members including the head = 5 x (25 + 25 x 20/100) = 5 x 30 = 150 yr ∴ Age of the head = 150 - 100 = 50 yr

Question 17

The average age of a committee of 11 persons increases by 2 yr when 3 men of 32 yr. 34 yr and 33 yr are replaced by 3 woman. What will be the average age of those 3 woman?

Accepted Answer

Total age of 3 woman = 2 X 11 + (32 + 33 + 34) = 22 + 99 = 121 yr. ∴ Average age of 3 woman = 121/3 = 401/3 yr

Question 18

The average weight of 10 woman is incraesed by 1 kg if 2 woman of 42 kg and 38 kg are replaced by 2 men.Find the average weight of both the men?

Accepted Answer

Total weight of 2 men = 1 x 10 + (42 + 38) = 10 + 80 = 90 kg ∴ Average weight of 2 men = 90/2 = 45 kg

Question 19

The mean weight of 150 students in class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class?

Accepted Answer

Given that total number of students = 150 = ( n1+ n2) and Mean weight of 150 students = 60 kg. The mean weight of boys a1= 70 kg and The mean weight of girls a2 = 55 kg Let n1 and n2 be the number of boys and girl, respectively. ∴ n1 + n2 = 150 ...(i) 11 n1 + 11 n2 = 1650 ...(ii) Average weight = (n1 a1 + n2 a2) / (n1 + n2) ⇒ 60 = (70 n1 + 55n2)/150 ⇒ 70 n1 + 55n2 = 9000 ⇒ 14n1 + 11n2 =1800 ...(iii) On subtracting Eq. (ii) from Eq. (iii), we get 3n1 = 150 ⇒ n1 = 50 Hence, required number of boys is 50.

Question 20

The average monthly income of 4 earning members of a family is ₹ 7350. One member passes away and the average monthly income become ₹ 6500. What was the monthly income of the person, who is no more?

Accepted Answer

Monthly income of 4 persons = 7350 x 4 = ₹ 29400 Monthly income of 3 person (excluding the dead person) = 6500 x 3 = ₹ 19500 ∴ Monthly income of dead person = 29400 - 19500 = ₹ 9900

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