Question 1

A class is divided into two sections A and B. Passing average of 20 students of section A is 80% and passing average of 30 students of sections B is 70%. What is the passing average of both the sections?

Accepted Answer

Here n1 = 20, n2 = 30, a1 = 80%, a2 = 70% ∴ Total average = (n1a1 + n2a2) / (n1 + n2) = (20 x 80 + 30 x 70) / (20 + 30) = (1600 + 2100) / 50 = 74%

Question 2

The average age of 4 member of family is 20 yr. If youngest member is 4 yr. old, What was the average age of family at the time of the birth of youngest member?

Accepted Answer

Total age of all members of the family (at present) = 20 x 4 = 80 4yr ago, total age of all members = 80 - ( 4 x 4) = 80- 16 = 64 yr. As 4 yr ago, there were only 3 members in the family ∴ Average age of the family at the time of the birth of the youngest member = 64/3 = 211/3 yr

Question 3

3 yr ago, the average age of a family of 5 members was 17 yr. Even after the birth of a child, the aveage is same today. Find out the age of child.

Accepted Answer

3 yr ago, total age of 5 members of the family = 17 x 5 = 85 yr Present age of all the members of the family = 85 + 3 x 5 = 100 yr Let the age of the child = N yr Present avrage age of family = (100 + N) / 6 [At present total number of members = 5 + 1 = 6] 17 = 100N / 6 ⇒ 102 = 100 + N ∴ N = 2 yr

Question 4

A person bought some oranges worth ₹ 36 from each of the five markets at ₹ 1, ₹ 1.50, ₹ 1.80, ₹ 2 and ₹ 2.25 per orange, respectively. What is the average price of an orange?

Accepted Answer

Number of oranges bought by the person = 36/1 + 36/1.50 + 36/1.80 + 36/2 + 36/2.25 = 36 + 24 + 20 + 18 + 16 = 114 Total expenditure = 36 x 5 = ₹ 180 Thus, average price of each orange = ₹ 180/114 = ₹ 1.58

Question 5

Average of a, b and c is 11; average of c, d and e is 17; average of e and f is 22 and average of e and c is 17. Find out the average of a, b, c, d, e and f?

Accepted Answer

According to the question, a + b + c = 11 x 3 = 33 ......(i) c + d + e = 17 x 3 = 51 ...........(ii) e + f = 22 x 2 = 44 ........... (iii) e + c = 17 x 2 = 34 ..........(iv) From Eqs. (ii) and (iv), we get 34 + d = 51 or d = 17 ....(v) Now, by adding Eqs. (i), (iii) and (v), we get a + b + c + d + e + f = 33 + 44 + 17 = 94 ∴ Average of a, b, c, d, e and f = 94/6 = 47 / 3 = 152/3

Question 6

The average age of 54 girls in a class was calculated as 14 yr. It was later relized that the actual age of one of the girls in the class was 10.5 yr but it was calculated as 13 yr. What is the actual averge age (round off) of the the girls in the c…

Accepted Answer

Total actual age of 54 girls = (54 x 14) - 13 + 10 .5 = 753.5 yr ∴ Require average age = 753.5/54 = 13.95 yr = 14 yr(approx).

Question 7

The average age of a man and his two twin sons born on the same day is 30 yr. The ratio of the ages of father and one son is 5 : 2, What is the father's age?

Accepted Answer

According to the question, Average age of man and his twin sons = 30 ∴ Total age = 30 x 3 = 90 yr. According to the question, Ratio of father and one son = 5 : 2 ∴ Ratio of father and both the sons = 5 : 2 : 2 (As sons are born on the same day.) ∴ 5k + 2k + 2k = 90 or 9k = 90 ∴ k = 10 ∴ Age of father = 5 x 10 = 50 yr.

Question 8

The ratio of pens and pencil in a stationary shop is 3 : 2, respectively, The average number of pens and pencils is 180. What is the 30% of number of pencils in the shop?

Accepted Answer

The average number of pens and pencils = 180 ∴ Totol number of pens and pencils = 180 x 2 = 360 ∴ Total number of pencils in the shop = 360 x (2/5) = 144 ∴ 30% of 144 = (30/100) x 144 = 43.2 = 43 = 43 (approx)

Question 9

If the average of the ages of Rakesh and Mohan is 15, average of the ages of Mohan and Ramesh is 12 and the average of the ages of Rakesh and Rameh is 13, then the age of Mohan, is?

Accepted Answer

Let ages of Rakesh, Mohan and Ramesh be R, M and r, respectively . Then, R + M = 15 x 2 = 30.......(i) M + r = 12 x 2 = 24 ........(ii) r + R = 13 x 2 = 26 ..... (iii) Adding Eqs. (i), (ii) and (iii), we get 2(R + M + r) = 30 + 24 + 26 = 80 ⇒ R + M + r = 40 Subtracting Eq. (iii) from Eq. (iv), we get M = 40 - 26 = 14

Question 10

The average age of 5 sisters is 20 yr. If the age of the youngest sister be 4yr. What was the average age of the group of sister at the birth of the yongest sisiter?

Accepted Answer

Total age of 5 sister = 20 x 5 = 100 yr. 4 yr ago, total sum of ages = 100 - ( 5 x 4) = 100 - 20 = 80 yr But at that time (4 yr ago), there were 4 sister in the group. ∴ Average age at that time(4 yr ago) = 80/4 = 20 yr.

Question 11

Out of the three annual examinations, each with a total of 500 marks, a student secured average marks of 45% and 55% in the first and second annual examinations. To have an overall average of 60%, how many marks does the student need to secure in th…

Accepted Answer

Total marks for three examinations = 3x 500 = 1500 Total required marks in three examinations = 60% of 1500 =( 3 x 500 x 60 ) / 100 = 900 Marks secured in first examination = 45 % of 500 =( 500 x 45 ) / 100 =225 Marks secured in third examination = 55 % of 500 =( 500 x 55 ) / 100 =275 Thus, the required marks in third examination =900 - ( 225 + 275 ) =900 - 500 = 400

Question 12

The average age of women and child workers in a factory was 15 yr. The average age of all the 16 children was 8 yr and average age of women workers was 22 yr. If 10 women workers were married, then the number of unmarried women workers was.

Accepted Answer

Let the number of women workers be Y. Then, 22y + 16 x 8 = 15 (16+y) ⇒ 22y + 128 = 240 + 15y ⇒ 22y - 15y= 240 - 128 ∴ y = 16 ∴ Unmarried women workers = 16 - 10 = 6

Question 13

If the average age of Dinesh and Mahesh is 16 yr, the average age of Mahesh and Rahul is 13 yr and the average age of Dinesh and Rahul is 14 yr, then what is the age of Mahesh?

Accepted Answer

Let ages of Dinesh, Mahesh and Rahul be D, M and R, respectively. Then, D + M = 2 x 16 = 32 ...(i) M + R = 2 x 13 = 26 ....(ii) D + R = 2 x14 = 28 ....(iii) On adding Eqs. (i), (ii) and (iii), we get 2(D + M + R) =86 ⇒ D + M + R = 43 ....(iv) On subtracting Eqs. (iii) from Eq. (iv), we get M = 43 - 28 ∴ M = 15 Yr

Question 14

In a class, there are 80 students and their average marks in the annual examination are 40. If the average marks of passed students are 60 and average marks of failed students are 35, then find out the number of students who failed.

Accepted Answer

Let the number of failed student = Y ∴ Number of passed student = 80 - Y sum of marks of all students = sum of marks of passed students + sum of marks of failed students 80 x 40 = (80 - Y) x 60 + 35Y ⇒ 3200 =4800 - 60Y + 35Y ⇒ 25Y = 1600 ∴ Y = 64 ∴ Number of students who failed = 64

Question 15

Last year Sahara, Tata, Singhania and Birla each has 250 industries. This year everyone has sold out 10 factories due to the recession of the economy and poor turnout. The average number of industries which of them now has

Accepted Answer

Required average = Old average - Sold average = ( 250 ) - ( 10 ) = 240

Question 16

The ratio of ages of the father and the daughter at present is 3 : 1. Four year ago the ratio was 4 : 1 . The average age of the father and daughter 2 year hence will be

Accepted Answer

Let the present ages of father be 3x and daughter be x . so the 4 year ago father's age and daughter's age was ( 3x - 4 ) and ( x - 4 ) ⇒ ( 3x - 4 / x -4 ) = 4 / 1 ∴ x = 12 year and 3x = 36 year

Question 17

The average of three number is 42. The first is twice the second and the second is twice the third the different between the third largest and the smallest number number is?

Accepted Answer

Let third number = y Then, second number = 2y and first number =4y ⇒ ( y + 2y + 4y) / 3 = 42 ⇒ 7y = 42 x 3 ⇒ y = 18 so, (largest) - (smallest) = ( 4y - y) = 3y =54

Question 18

The average earning of a mechanic for the first-four days of a week is Rs. 18 and for the last four days is Rs. 22. If he earns Rs . 20 on the fourth day, his average earning for the whole week is?

Accepted Answer

Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day = 4 x18 + 4 x 22 -20 = Rs. 140 ∴ Average earning = 140 / 7 = Rs. 20

Question 19

The average salary per head of all the workers in a workshop is Rs. 850, if the average salary per head of 7 technician is Rs. 1000 and the average salary per head of the rest is Rs 780, the total number of workers in the work- shop is?

Accepted Answer

Let the total number of workers be y. So sum of salary for all workers = sum of salary of 7 technician + sum of salary for other y -7 workers. 7 x 1000 + 780(y -7) = 850 y ⇒ 7000 + 780y - 5460 = 850y ⇒ 70y = 1540 ∴ y = 22 So total number of workers = 22

Question 20

The average weight of 8 men is increased by 2kg when one of the men whose weight is 50 kg is replaced by a new man . The weight of the new man is?

Accepted Answer

Weight increase = 8 x 2 kg = 16 kg weight of new man= 50 + 16 = 66 kg

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