Question 1

The average of five consecutive odd numbers is 61. What is the difference between the highest and lowest numbers :

Accepted Answer

Let the numbers be x, x + 2, x + 4, x + 6 and x + 8. Then [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61. or 5x + 20 = 305 or x = 57. So, required difference = (57 + 8) - 57 = 8

Question 2

The average weight of a class of 24 students is 35 kg. If the weight of the teacher be included, the average rises by 400 g. The weight of the teacher is :

Accepted Answer

Weight of the teacher = (35.4 x 25 - 35 x 24) kg = 45 kg.

Question 3

The average of 7 consecutive numbers is 20. The largest of these numbers is :

Accepted Answer

Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6, Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20. or 7x + 21 = 140 or 7x = 119 or x =17. Latest number = x + 6 = 23.

Question 4

The mean temperature of Monday to Wednesday was 37 degree celsius and of Tuesday to Thursday was 34 degree celsius . If the temperature on Thursday was (4/5) th that of Monday, the temperature on Thursday was?

Accepted Answer

Let, temperature of Monday = a Temperature of Tuesday = b Temperature of Wednesday = c Temperature of Thursday = 4a/5 Sum of temperatures of Monday to Wednesday = 3×37 = 111 => a+b+c=111------(1) Sum of temperatures of Tuesday to Thursday = 3×34 = 102 b+c+(4a/5) = 102 ------(2) (1)-(2)=> a−(4a/5)=111−102 a/5=9 a=45 Temperature on Thursday = 4a/5 =4×45/5 =36

Question 5

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member ?

Accepted Answer

i) Let the ages of the five members at present be a, b, c, d & e years. And the age of the new member be f years. ii) So the new average of five members' age = (a + b + c + d + f)/5 ------- (1) iii) Their corresponding ages 3 years ago = (a-3), (b-3), (c-3), (d-3) & (e-3) years So their average age 3 years ago = (a + b + c + d + e - 15)/5 = x ----- (2) ==> a + b + c + d + e = 5x + 15 ==> a + b + c + d = 5x + 15 - e ------ (3) iv) Substituting this value of a + b + c + d = 5x + 15 - e in (1) above, The new average is: (5x + 15 - e + f)/5 Equating this to the average age of x years, 3 yrs, ago as in (2) above, (5x + 15 - e + f)/5 = x ==> (5x + 15 - e + f) = 5x Solving e - f = 15 years. Thus the difference of ages between replaced and new member = 15 years.

Question 6

A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is :

Accepted Answer

Let there be x pupils in the class. Total increase in marks = (x * 1/2) = x/2. x/2 = (83 - 63) => x/2 = 20 => x = 40.

Question 7

The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is :

Accepted Answer

Correct Sum = (36 * 50 + 48 - 23) = 1825. Correct mean = = 1825/50 = 36.5

Question 8

Of the four numbers, whose average is 60, the first is one-fourth of the sum of the last three. The first number is :

Accepted Answer

Let the first number be x, Then, sum of the four numbers = x + 4x = 5x. so, 5x/4 = 60 or x = (60 * 4) / 5 = 48.

Question 9

10 years ago, the average age of a family of 4 members was 24 years. Two children having been born (with age diference of 2 years), the present average age of the family is the same. The present age of the youngest child is :

Accepted Answer

Total age of 4 members, 10 years ago = (24 x 4) years = 96 years. Total age of 4 members now = [96 + (10 x 4)] years = 136 years. Total age of 6 members now = (24 x 6) years = 144 years. Sum of the ages of 2 children = (144 - 136) years = 8 years. Let the age of the younger child be x years. Then, age of the elder child = (x+2) years. So, x+(x+2) =8 <=> x=3 Age of younger child = 3 years.

Question 10

Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was :

Accepted Answer

Let the average expenditure be Rs. x Then, 9x=[(8*30)+(x+20)]<=>9x =x+260 <=> x =32.50 Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50

Question 11

In an examination, a pupil's average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination ?

Accepted Answer

Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11.

Question 12

The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is :

Accepted Answer

Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11] = (131.4 - 119-9) = 11.5.

Question 13

The average age of 8 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is :

Accepted Answer

Total age increased = (8 * 2) years = 16 years. Sum of ages of two new men = (21 + 23 + 16) years = 60 years Average age of two new men = (60/2) years = 30 years.

Question 14

The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :

Accepted Answer

Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years. Required average = (57/3) = 19 years.

Question 15

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 …

Accepted Answer

Let the average age of the whole team be x years. 11x - (26 + 29) = 9 (x - 1) => 11x - 9x = 46 => 2x = 46 => x = 23. So, average age of the team is 23 years.

Question 16

The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the …

Accepted Answer

Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1) Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2) Subtracting (1) From (2), we get : Temp, on 5th day - Temp on 1st day = 8 degrees. Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively. Then, 8x - 7x = 8 or x = 8. Temperature on the 5th day = 8x = 64 degrees.

Question 17

The average monthly salary of the employees of a firm is Rs.60 out of the employees 12 officers get an average of Rs.400 per month and the rest an average of Rs. 56 per month , Find the number of emp

Accepted Answer

The actual average salary of 12 officers = 400 therefore Total salary of 12 officers = 400 x 12 = 4800 Average of these 12 officers as a whole =60 Total salary of 12 officers as a whole = 60 x 12 = 720 The total salary of rest = 4800 - 720 = 4080 The difference in average of the rest of officers = 60 - 56 = 4 Rest of the officers = 4080/4=1020 Total number of employees = 1020 + 12 = 1032

Question 18

The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is :

Accepted Answer

Lot the total number of workers be v Then, 8OOOv = (12000 * 7) + 6000 (v - 7) <=> 2000v = 42000 <=> v = 21.

Question 19

A team of 8 persons joins in a shooting competition. The best marksman scored 85 points. If he had scored 92 points, the average score for the team would have been 84. The number of points, the team scored was :

Accepted Answer

Let the total score be x. (x + 92 - 85) / 8 = 84. So, x + 7 = 672 => x = 665.

Question 20

If the arithmetic mean of seventy-five numbers is calculated, it is 35. if each number is increased by 5, then mean of new numbers is :

Accepted Answer

Let the numbers are x 1 , x 2 , . . . . . . . x 75 By Hypothesis , x 1 + x 2 + . . . . x 75 75 = 35 ......(i) Mean of new numbers = x 1 + 5 + x 2 + 5 + . . . . . . . x 75 + 5 75 x 1 + x 2 + . . . . . . x 75 + 5 * 75 75 x 1 + x 2 + . . . . . . x 75 75 + 375 75 = 35 + 5 = 40 By (i)

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