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The mean weight of a group of seven boys is 56 kg. The individual weights (in kg) of six of them are 52, 57, 55, 60, 59 and 55. Find the weight of the seventh boy.

A.

34 kg.

B.

44 kg.

C.

52 kg.

D.

54 kg.

Answer with explanation

Answer: Option DExplanation

Mean weight of 7 boys = 56 kg.

Total weight of 7 boys = (56 × 7) kg = 392 kg.

Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg

= 338 kg.

Weight of the 7th boy = (total weight of 7 boys) – (total weight of 6 boys)

= (392 – 338) kg

= 54 kg.

Hence, the weight of the seventh boy is 54 kg.

Workspace

The average height of 30 boys was calculated to be 150 cm. It was detected later that one value of 165 cm was wrongly copied as 135 cm for the computation of the mean. Find the correct mean.

A.

121 cm

B.

141 cm

C.

155 cm

D.

151 cm

Answer with explanation

Answer: Option DExplanation

Calculated average height of 30 boys = 150 cm.

Incorrect sum of the heights of 30 boys

= (150 × 30)cm

= 4500 cm.

Correct sum of the heights of 30 boys

= (incorrect sum) – (wrongly copied item) + (actual item)

= (4500 – 135 + 165) cm

= 4530 cm.

Correct mean = correct sum/number of boys

= (4530/30) cm

= 151 cm.

Hence, the correct mean height is 151 cm

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The aggregate monthly expenditure of a family was $ 6240 during the first 3 months, $ 6780 during the next 4 months and $ 7236 during the last 5 months of a year. If the total saving during the year is $ 7080, find the average monthly income of the family.

A.

7485

B.

7225

C.

7422

D.

7425

Answer with explanation

Answer: Option DExplanation

Total expenditure during the year

= $[6240 × 3 + 6780 × 4 + 7236 × 5]

= $ [18720 + 27120 + 36180]

= $ 82020.

Total income during the year = $ (82020 + 7080) = $ 89100.

Average monthly income = (89100/12) = $7425.

Hence, the average monthly income of the family is $ 7425.

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The average of 52 numbers is 45. if two numbers, namely, 55 & 45 are discarded from the set of number, then find average of the remaining numbers.

A.

43

B.

44

C.

44.2

D.

44.8

Answer with explanation

Answer: Option DExplanation

The sum of remaining 50 number ( i. e 52 – 2 )

52 x 45 – 45 – 55 = 2340 – 100 = 2240

The average of remaining numbers = 2240 / 50 = 44.8

Workspace

The average of ten numbers is 15. If each number is multiplied by 12, then find the average of the new set of numbers.

A.

150

B.

160

C.

170

D.

180

Answer with explanation

Answer: Option DExplanation

When we multiply each number by ” X “, the average would also get multiplied by “X”.

Hence the average of new set of numbers = 15 x 12 = 180.

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A batsman his 20th innings, missed a century by 5 runs and there by increased his average by 4. what is his average after 20 innings.

A.

15

B.

18

C.

17

D.

19

Answer with explanation

Answer: Option DExplanation

Take average upto 19th innings is “A”

According to given information 19A + 95 = 20 (A + 4)

So A = 15

Now average runs after 20th innings = 15 + 4 = 19

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The average of 8 readings is 24.2, out of which the average of first two is 18.5 and that of next three is 21.1. If the sixth reading is 5 less than seventh and 7 less than eighth, what is the sixth reading?

A.

26

B.

27

C.

26.1

D.

27.1

Answer with explanation

Answer: Option DExplanation

Here take sixth number = x , then

Seventh reading = x + 5 and 8th reading = x +7

Average of 8 readings is 24.2

Sum of 8 readings = 24.2 x 8 = 193.6

Sum of first five numbers = ( 18.5 x 2) + (21.1 x 3) = 37 + 63.6 = 100.3

Now the sum of 6th, 7th & 8th = 193.6 – 100.3 = 93.3

So ( x + x + 5 + x + 7) = 93.3

3x = 93.3 – 12 = 81.3

x = 27.1

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A person covers 18 km at 10 km/hr, 16km at 8 km/hr and 30km at 6 km/hr. Then find average speed in covering the whole distance.

A.

7 5/12

B.

5 3/8

C.

2 5/6

D.

7 3/11

Answer with explanation

Answer: Option DExplanation

Here using the formula

P =18 km , Q = 16 km , R =30 km , X = 10 km/hr, Y= 8 km/hr & Z = 6 km/hr

=

= 80/11

The average speed of the whole distance = 80/11 = km/hr.

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There are two batches A and B of a class. Batch A consists of 36 students and batch B consists of 44 students. Find the average weight of whole class, if average weight of batch A is 40 kg and that of batch B is 35 kg.

A.

29.23 kg

B.

32.56 kg

C.

35.66 kg

D.

37.25 kg

Answer with explanation

Answer: Option DExplanation

Given: Average weight of batch A = 40 kg , average weight of batch B = 35 kg

1) First find the total weight of all students

– Weight of batch A = (36 x 40) = 1440

– Weight of batch B = (44 x 35) = 1540

Total weight of all students = (1440 + 1540) = 2980 kg

2) Find average weight of whole class

(Batch A + Batch B) students = (36 + 44) = 80 students

Average Weight = | Total weight of all the students | = | 2980 | = 37.25 kg |

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The mean of 40 observations was 46. Later on it was found that an observation 38 was wrongly taken as 33. find the corrected value of mean.

A.

40.23

B.

42.36

C.

46.12

D.

51.23

Answer with explanation

Answer: Option CExplanation

Average = | Sum of Quantities |

Number of Quantities |

**1)** Sum of observations = Average x No. of observations

= 46 x 40 = 1840

**2)** Correct sum = Sum of observations + (38 – 33)

= 1840 + (5)

= 1845

Corrected Mean Value = | Corrected Sum | = | 1845 | = 46.125 |

No. of Observations | 40 |

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In a cricket match, 6 players had an average X of their runs. Average increases by 10 runs, if seventh player makes a score of 112 runs. What is the average of first 6 players.

A.

36

B.

39

C.

40

D.

42

Answer with explanation

Answer: Option DExplanation

The average of 6 players = X

Average increases by 10, when seventh player makes a score of 112 runs.

Therefore, average of 7 players = X + 10

Average = | Sum of Scores | ——- (1) |

Number of Players |

Here, average = X, number of players = 6

Hence,

Sum of scores = 6X

Score of 7 players = (Score of 6 players + score of 7 player) = (6X + 112) ——- (2)

Total average = (X + 10) ——— (3)

Substitute (2) and (3), in (1)

(X + 10) | (6X + 112) |

7 |

Solving we get,

X = 42

Average of first 6 players = 42

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The average weight of 39 men travelling to Ladakh is 30. If an obese man with weight 130 kg join them. What will be the average weight of the people travelling to Ladakh?

A.

52

B.

30

C.

32.5

D.

130

Answer with explanation

Answer: Option CExplanation

If the weight of the man would have been 30, then the average weight would have been the same. So, the extra 100 kg that the obese man brings with him would be distributed equally amongst all of them, i.e. 100/40 = 2.5

So, the average becomes 30 + 2.5 = 32.5

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The average salary of 30 officers in a firm is Rs.120 and the average salary of laborers is Rs. 40. Find the total number of laborers if the average salary of the firm is Rs. 50.

A.

Rs. 180

B.

Rs. 420

C.

Rs. 240

D.

Rs. 210

Answer with explanation

Answer: Option DExplanation

The sum of salary of officers will be = 30×120 = 3600

Let the number of labourers = X.

ATQ, 3600 + 40X = 50(30+X)

2100 = 10X

X= 210

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The average of 4 terms is 20 and the 1st term is 1/3 of the remaining terms. What will be the first number?

A.

30

B.

20

C.

60

D.

80

Answer with explanation

Answer: Option BExplanation

Average of 4 terms = 20

Hence, the total sum of 4 terms = 80

Let terms be A,B,C,D

So, the sum will be A+B+C+D =80

Given, 3A = B+C+D

So, 4A = 80,

A = 20

Workspace

For 9 innings, Boman has an average of 75 runs. In the tenth inning, he scores 100 runs, thus increasing his average . His new average is

A.

Rs. 75

B.

Rs. 100

C.

Rs. 72

D.

Rs. 77.5

Answer with explanation

Answer: Option DExplanation

Total score for 9 innings is 75×9 = 675

Total score after 10th innings = 675 + 100 = 775

So, average = 775 / 10 = 77.5

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