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Fraction and Simplification, Average and Mean

মোট প্রশ্ন৯৪৮এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Fraction and Simplification, Average and Mean

PrepBank · পাতা ৪ / ১০ · ৩০১–৪০০ / ৯৪৮

৩০১.
The average of the reciprocals of 4 and 5 is: 
  1. ক
    9/20
  2. খ
    18/20
  3. গ
    9/40
  4. ঘ
    5
ব্যাখ্যা
Question: The average of the reciprocals of 4 and 5 is: 

Solution:
The reciprocals of 4 and 4 are = 1/4 and 1/5

∴ Required average = {(1/4) + (1/5)}/2
= {(5 + 4)/20}/2
= {9/20}/2
= 9/40
৩০২.
In a school, students may bring breakfast, buy it, or may not eat breakfast. If 1/4 of the students bring breakfast, 1/7 don't eat breakfast, and 187 buy it, how many students bring breakfast?
  1. ক
    49
  2. খ
    58
  3. গ
    68
  4. ঘ
    77
  5. ঙ
    None
ব্যাখ্যা
Question: In a school, students may bring breakfast, buy it, or may not eat breakfast. If 1/4 of the students bring breakfast, 1/7 don't eat breakfast, and 187 buy it, how many students bring breakfast?

Solution:
Let,
Total number of student = x
The students bring breakfast = x/4
The students don't eat breakfast = x/7
The students buy breakfast = 187

ATQ,
x/4 + x/7 + 187 = x
⇒ x - x/4 - x/7 = 187
⇒ (28x - 7x - 4x)/28 = 187
⇒ 28x - 11x = 187 × 28
⇒ 17x = 187 × 28
⇒ x = (187 × 28)/17
∴ x = 308

∴ The students bring breakfast = x/4 = 308/4 = 77
৩০৩.
The average age of a family of four members is 26 years. If the youngest member is 14 years old, what is the average age of the remaining members?
  1. ক
    30 years
  2. খ
    32 years
  3. গ
    36 years
  4. ঘ
    34 years
ব্যাখ্যা
Question: The average age of a family of four members is 26 years. If the youngest member is 14 years old, what is the average age of the remaining members?

Solution:
Total age of all 4 members = 4 × 26 = 104 years
Youngest member's age = 14 years
Remaining total age = 104 - 14 = 90
Average age of 3 remaining = 90 ÷ 3 = 30 years
৩০৪.
The average height of 8 students is 150 cm. If a new student joins and the average height becomes 152 cm, what is the height of the new student?
  1. ক
    168 cm
  2. খ
    158 cm
  3. গ
    120 cm
  4. ঘ
    108 cm
ব্যাখ্যা
Question: The average height of 8 students is 150 cm. If a new student joins and the average height becomes 152 cm, what is the height of the new student?

Solution:
The average height of 8 students is 150 cm.

∴ Total height of the 8 students = 8 × 150 = 1200 cm

And
When a new student joins, the total number of students becomes 9, and the new average height is 152 cm.

∴ Total height of the 9 students = 9 × 152 = 1368 cm

So the height of the new student is = (1368 - 1200) = 168 cm.
৩০৫.
The average age of the children in a tour group is 12 years and that of the adults is 32 years. If the average age of the entire tour group is 20 years, find the ratio of children to adults in the group.
  1. ক
    3 : 2
  2. খ
    2 : 3
  3. গ
    1 : 2
  4. ঘ
    3 : 1
ব্যাখ্যা

Question: The average age of the children in a tour group is 12 years and that of the adults is 32 years. If the average age of the entire tour group is 20 years, find the ratio of children to adults in the group.

Solution: Average age of children = 12 years
Average age of adults = 32 years
Average age of the entire group = 20 years

Let, the number of adults = A
and, the number of children = C

Then, the total number of people in the group is (C + A)

ATQ,
12C + 32A = 20(C + A)
Or, 12C + 32A = 20C + 20A
Or, 32A - 20A = 20C - 12C
Or, 12A = 8C
Or, C : A = 12 : 8
Or, C : A = 3 : 2

∴ The ratio of children to adults in the group is 3 : 2.

৩০৬.
The average of the first five multiples of 11 is-
  1. ক
    ক) 165
  2. খ
    খ) 87.5
  3. গ
    গ) 66
  4. ঘ
    ঘ) 33
ব্যাখ্যা
Question: The average of the first five multiples of 11 is-

Solution: 
The  first five multiples of 11: (11 × 1), (11 × 2), (11 × 3), (11 × 4), (11 × 5)
their sum = (11 × 1) + (11 × 2) + (11 × 3) + (11 × 4) + (11 × 5)
= 11 (1 + 2 + 3 + 4 + 5)
= 11 × 15

∴ average = (11 × 15)/5
= 33
৩০৭.
What is the geometric average of 4 and 16?
  1. ক
    ক) 8
  2. খ
    খ) 10
  3. গ
    গ) 12
  4. ঘ
    ঘ) 14
ব্যাখ্যা
Queston: What is the geometric average of 4 and 16? 

Solution: 
geometric average of 4 and 16 = √(4 × 16)
= √64
= 8
৩০৮.
The average of 8 numbers is 28. If 4 more numbers , with an average 24 are added to the numbers, what will be the average of the combined 12 numbers?
  1. ক
    18
  2. খ
    24.5
  3. গ
    28.75
  4. ঘ
    26.67
ব্যাখ্যা
Question: The average of 8 numbers is 28. If 4 more numbers , with an average 24 are added to the numbers, what will be the average of the combined 12 numbers?

Solution:
Sum of the first 8 numbers is,
Total sum = Average × Number 
= 28 × 8 = 224
And the sum of the next 4 numbers is,
= 24 × 4 = 96
∴ The total sum of all 12 numbers is,
224 + 96 = 320

∴ New Average = Total Sum/Total Numbers​
= 320/12
= 26.67
৩০৯.
The average of 55 numbers is 35. If two numbers, 32 and 38, are discarded, then the average of the remaining numbers is-
  1. ক
    35
  2. খ
    39
  3. গ
    31
  4. ঘ
    29
ব্যাখ্যা
Question: The average of 55 numbers is 35. If two numbers, 32 and 38, are discarded, then the average of the remaining numbers is-

Solution:
The average of 55 numbers is 35
Sum of all the numbers = (35 × 55) = 1925

Sum of 53 numbers =1925 - (32 + 38)
= 1855

The average of the remaining numbers =1855/53 = 35
৩১০.
The average of the first seven prime numbers is- 
  1. ক
    ক) 5.286
  2. খ
    খ) 6.286
  3. গ
    গ) 8.286
  4. ঘ
    ঘ) 7.286
ব্যাখ্যা
The first seven prime numbers :2, 3, 5, 7, 11, 13, 17

The average = (2 + 3 + 5 + 7 + 11 + 13 + 17)/7
                    = 58/7
                    = 8.2857
                    = 8.286
৩১১.
The average age of A, B and C was 25 years and that of B and C was 25 years. A’s present age is-
  1. ক
    30 years
  2. খ
    25 years
  3. গ
    40 years
  4. ঘ
    42 years
  5. ঙ
    None of these
ব্যাখ্যা
Question: The average age of A, B and C was 25 years and that of B and C was 25 years. A’s present age is-

Solution:
Average of A,B,C is 25
So, sum of their ages =75
Now, the sum of B and C will be 50 (because their average is 25)
So age of A =75 - 50 = 25 years
৩১২.
The average of 6 numbers is 7. The average of three numbers of them is 5. What will be the average of the remaining numbers?
  1. ক
    ক) 15
  2. খ
    খ) 30
  3. গ
    গ) 42
  4. ঘ
    ঘ) 9
ব্যাখ্যা
Question: The average of 6 numbers is 7. The average of three numbers of them is 5. What will be the average of the remaining numbers?

Solution:
Average of 6 numbers = 7
Sum of 6 numbers = 6 × 7 = 42
Average of three numbers = 5
Sum of three numbers = 5 × 3 = 15

∴ Sum of the remaining three numbers = 42 - 15 = 27

∴ Required average = 27/3 = 9
৩১৩.
In a class, 1/4 of the male students is equal to 3/5 of the female students. What fraction of the students in the room is female?
  1. ক
    4/15
  2. খ
    7/20
  3. গ
    5/17
  4. ঘ
    8/21
  5. ঙ
    None
ব্যাখ্যা

Question: In a class, 1/4 of the male students is equal to 3/5 of the female students. What fraction of the students in the room is female?

Solution:
Let the number of male students be m
And the number of female students be f.

Given that,
(1/4)​ of the male students = (3/5)​ of the female students 
⇒ (1/4)m = (3/5)f 
∴ m = (12/5)f   ; [Cross-multiply]

∴ Total students = m + f = (12/5)f + f 
= (12f + 5f)/5
= 17f/5

∴ Fraction of students that are female = f/(m + f) = f/(17f/5) = 5/17

So the fraction of students that are female is 5/17.

৩১৪.
Find the value of 2(x + 3) - 3(x - 1) + x.
  1. ক
    x - 9
  2. খ
    9
  3. গ
    x + 9
  4. ঘ
    - x
ব্যাখ্যা
Question: Find the value of 2(x + 3) - 3(x - 1) + x.

Solution: 
2(x + 3) - 3(x - 1) + x 
= 2x + 6 - 3x + 3 + x
= 3x - 3x + 9
= 9
৩১৫.
If the mean of 5 observations x, x + 2, x + 4, x + 6, and x + 8 is 11, then the mean of the last three observations is -
  1. ক
    11
  2. খ
    13
  3. গ
    15
  4. ঘ
    17
ব্যাখ্যা
Question: If the mean of 5 observations x, x + 2, x + 4, x + 6, and x + 8 is 11, then the mean of the last three observations is -

Solution:
ATQ,
{x + (x + 2) + (x + 4) + (x + 6) + (x + 8)}/5 = 11
⇒ 5x + 20 = 55
⇒ 5x = 55 - 20
⇒ x = 35/5
∴ x = 7

So, the numbers are 7, 9, 11, 13, 15

Required mean = (11 + 13 + 15)/3
= 39/3
= 13
৩১৬.
The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is:
  1. ক
    30
  2. খ
    28
  3. গ
    25
  4. ঘ
    20
ব্যাখ্যা

Question: The average of six numbers is 30. If the average of first four is 25 and that of last three is 35, the fourth number is:

Solution:
Given that,
Average of 6 numbers = 30
∴ Sum of 6 numbers = 6 × 30 = 180

Average of first 4 numbers = 25
∴ Sum of first 4 numbers = 4 × 25 = 100

And, Average of last 3 numbers = 35
∴ Sum of last 3 numbers = 3 × 35 = 105

∴ Fourth number is = (Sum of first 4 + Sum of last 3) - Total sum
= (100 + 105) - 180
= 205 - 180
= 25

So the fourth number is 25. 

৩১৭.
The average wages of a worker during a fortnight comprising 15 consecutive working days was Tk. 90 per day. During the first 7 days, his average wages was Tk. 87 per day and the average wages during the last 7 days was Tk. 92 per day. What was his wage on the 8th day?
  1. ক
    Tk. 97
  2. খ
    Tk. 89
  3. গ
    Tk. 92
  4. ঘ
    Tk. 101
  5. ঙ
    Tk. 94
ব্যাখ্যা

Question: The average wages of a worker during a fortnight comprising 15 consecutive working days was Tk. 90 per day. During the first 7 days, his average wages was Tk. 87 per day and the average wages during the last 7 days was Tk. 92 per day. What was his wage on the 8th day?

Solution:
The total wages earned during the 15 days that the worker worked ,
= 15 × 90
= Tk. 1350

The total wages earned during the first 7 days
= 7 × 87
= Tk. 609

The total wages earned during the last 7 days
= 7 × 92
= Tk. 644

Total wages earned during the 15 days,
= wages during first 7 days + wage on 8th day + wages during the last 7 days.

ATQ,
1350 = 609 + wage on 8th day + 644
⇒ wage on 8th day = 1350 - 609 - 644 = Tk. 97
∴ wage on 8th day = Tk. 97

৩১৮.
The average age of seven boys sitting in a row facing South is 27 years. If the average age of the first three boys is 25 years and the average age of the last three boys is 29 years, what is the age of the boy who is sitting in the middle of the row?
  1. ক
    24 years
  2. খ
    28 years
  3. গ
    26 years
  4. ঘ
    27 years
  5. ঙ
    None
ব্যাখ্যা

Question: The average age of seven boys sitting in a row facing South is 27 years. If the average age of the first three boys is 25 years and the average age of the last three boys is 29 years, what is the age of the boy who is sitting in the middle of the row?

Solution: 
7 জন বালকের মোট বয়স = (27 × 7) বছর 
= 189 বছর 

১ম 3 জন বালকের মোট বয়স = (25 × 3) বছর 
= 75 বছর 

শেষ 3 জন বালকের মোট বয়স = (29 × 3) বছর 
= 87 বছর 

6 জন বালকের মোট বয়স = (87 + 75) বছর 
= 162 বছর 

মাঝখানের বালকের বয়স = (189 - 162)  বছর 
= 27 বছর 

৩১৯.
The average of six consecutive numbers A, B, C, D, E and F is 62. What is the sum of B and F?
  1. ক
    122
  2. খ
    123
  3. গ
    124
  4. ঘ
    125
ব্যাখ্যা
Question: The average of six consecutive numbers A, B, C, D, E and F is 62. What is the sum of B and F?

Solution:
Let the Numbers A, B, C, D, E, F be x, x + 1, x + 2, x + 3, x + 4, x + 5.
According to question, 
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 = 62 × 6
⇒ 6x + 15 = 372
⇒ 6x = 372 - 15 = 357
⇒ 6x = 357
⇒ x = 59.5

∴ B = x + 1 = 60.5 
∴ F = x + 5 = 64.5

∴ B + F = 60.5 + 64.5 = 125
৩২০.
A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?
  1. ক
    Tk. 4991
  2. খ
    Tk. 5991
  3. গ
    Tk. 6001
  4. ঘ
    Tk. 6991
ব্যাখ্যা
Question: A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?

Solution:
Total sale for 5 months = Tk. (6435 + 6927 + 6855 + 7230 + 6562)
= Tk. 34009.

Required sale = Tk. [ (6500 x 6) - 34009 ]
= Tk. (39000 - 34009)
= Tk. 4991.
৩২১.
The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number.
  1. ক
    44
  2. খ
    47
  3. গ
    49
  4. ঘ
    51
ব্যাখ্যা
Question: The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number.

Solution: 
ধরি, সপ্তম সংখ্যাটি x

প্রথম সাতটি সংখ্যার গড় ৬৩ 
প্রথম সাতটি সংখ্যার সমষ্টি (৬৩ × ৭) = ৪৪১
প্রথম ছয়টি সংখ্যার সমষ্টি = ৪৪১ - x

শেষ সাতটি সংখ্যার গড় ৭০ 
শেষ সাতটি সংখ্যার সমষ্টি (৭০ × ৭) = ৪৯০
শেষ ছয়টি সংখ্যার সমষ্টি = ৪৯০ - x

সাতটি সংখ্যার সমষ্টি = ৪৪১ - x + ৪৯০ - x + x
= ৯৩১ - x 

গড়, (৯৩১ - x)/১৩ = ৬৮
⇒ ৯৩১ - x = ৬৮ × ১৩ 
⇒ ৯৩১ - x = ৮৮৪ 
⇒ x = ৯৩১ - ৮৮৪ 
∴ x = ৪৭

অতএব, সপ্তম সংখ্যাটি ৪৭
৩২২.
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.
  1. ক
    ক) 40.23
  2. খ
    খ) 42.36
  3. গ
    গ) 46.12
  4. ঘ
    ঘ) 51.23
ব্যাখ্যা

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/No. of Observations
= 1845/40
= 46.125

৩২৩.
Solve the following equation:
  1. ক
    4
  2. খ
    - 6
  3. গ
    8
  4. ঘ
    3
ব্যাখ্যা
Question: Solve the following equation:

Solution:
৩২৪.
Raisa took one cup of half olive-oil and half vinegar and poured it in a jar that had equal parts of olive-oil, vinegar, and water. If the result is a three-cup mixture of salad dressing, what portion of the dressing is olive-oil?
  1. ক
    5/12
  2. খ
    5/6
  3. গ
    9/16
  4. ঘ
    7/18
  5. ঙ
    2/5
ব্যাখ্যা
Question: Raisa took one cup of half olive-oil and half vinegar and poured it in a jar that had equal parts of olive-oil, vinegar, and water. If the result is a three-cup mixture of salad dressing, what portion of the dressing is olive-oil?

Solution:
চূড়ান্ত মিশ্রণ ৩ কাপ, এবং রাইসা ১ কাপ মিশ্রণ যোগ করেছে।
তাই, জারে প্রাথমিকভাবে ছিল, 3 - 1 = 2 কাপ

জারে অলিভ অয়েল, ভিনেগার এবং পানি সমপরিমাণ ছিল। ধরি, প্রতিটির পরিমাণ x কাপ।

তাহলে,
⇒ x + x + x = 2
⇒ 3x = 2
∴ x = 2/3

সুতরাং, জারে প্রাথমিকভাবে ছিল,
অলিভ অয়েল = 2/3​ কাপ
ভিনেগার = 2/3​ কাপ
পানি = 2/3​ কাপ

আবার,
রাইসার যোগ করা অলিভ অয়েল 1/2 কাপ
জারে অলিভ অয়েল = 2/3​ কাপ

∴ জারে মোট অলিভ অয়েল আছে = (2/3) + (1/2) = (4 + 3)/6 = 7/6 কাপ

∴ চূড়ান্ত মিশ্রণে অলিভ অয়েল আছে = (7/6)/3 = 7/18 অংশ
৩২৫.
The average temperature for Wednesday, Thursday and Friday was 40°C. The average for Thursday, Friday and Saturday was 41° C. If temperature on Saturday was 42° C, what was the temperature on Wednesday?
  1. ক
    38°C
  2. খ
    39°C
  3. গ
    41°C
  4. ঘ
    43°C
ব্যাখ্যা
Question: The average temperature for Wednesday, Thursday and Friday was 40°C. The average for Thursday, Friday and Saturday was 41°C. If temperature on Saturday was 42°C, what was the temperature on Wednesday?

Solution:
Here,
Total temperature for Wednesday, Thursday and Friday = 3 × 40° = 120°C
Total temperature for Thursday, Friday and Saturday = 3 × 41° = 123°C

Now,
(Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123° - 120°
⇒ Saturday - Wednesday = 3°
∴ Wednesday = 42° - 3° = 39°C
৩২৬.
Among 100 students, the average marks in mathematics is 70. If the 60 girls scored an average of 72, determine the average score of the remaining boys.
  1. ক
    65.5
  2. খ
    67
  3. গ
    68
  4. ঘ
    69.5
ব্যাখ্যা
Question: Among 100 students, the average marks in mathematics is 70. If the 60 girls scored an average of 72, determine the average score of the remaining boys.

Solution:
ধরি,
ছাত্রদের গড় নম্বর = ক 

100 জন শিক্ষার্থীর মোট নম্বর = 100 × 70 = 7000 
এবং 60 জন ছাত্রীর মোট নম্বর = 60 × 72 = 4320

প্রশ্নমতে,
4320 + (100 - 60) × ক = 7000
⇒ 4320 + 40ক = 7000
⇒ 40ক = 7000 - 4320
⇒ 40ক = 2680
⇒ ক = 2680/40 
⇒ ক = 67

∴ 40 জন ছাত্রের গড় নম্বর = 67
৩২৭.
The average of first five multiples of 5 is-
  1. ক
    ক) 10
  2. খ
    খ) 15
  3. গ
    গ) 20
  4. ঘ
    ঘ) 25
ব্যাখ্যা
Question: The average of first five multiples of 5 is-

Solution:
first five multiples of 5 are
= (5 × 1)
= (5 × 2)
= (5 × 3)
= (5 × 4)
= (5 × 5)

∴ The average of first five multiples of 5 is = {(5 × 1) + (5 × 2) + (5 × 3) +  (5 × 4) + (5 × 5)}/5
= 5 (1 + 2 + 3 + 4 + 5)/5
= 1 + 2 + 3 + 4 + 5
= 15
৩২৮.
Which of the following fractions is the largest ? 
  1. ক
    7/4
  2. খ
    3/2
  3. গ
    5/3
  4. ঘ
    6/5
ব্যাখ্যা
Question: Which of the following fractions is the largest? 

Solution: 
3/2 = 1.5
7/4 = 1.75
5/3 = 1.66
6/5 = 1.2 
∴ the largest fraction is = 7/4
৩২৯.
If the average of four consecutive odd integers is x, then in terms of x, which is the smallest among the following options?
  1. ক
    x - 3
  2. খ
    0.25x - 2
  3. গ
    x - 4
  4. ঘ
    x - 2.5
  5. ঙ
    None
ব্যাখ্যা

Question: If the average of four consecutive odd integers is x, then in terms of x, which is the smallest among the following options?

Solution:
Let the four consecutive odd integers be represented by  n, n + 2, n + 4, n + 6. 
Their average is calculated by summing them and dividing by 4, which equals x. 

Their average is,
x = {(n + (n + 2) + (n + 4) + (n + 6)}/4
⇒ x = (4n + 12)/4 = 4(n + 3)/4
⇒ x = n + 3
∴ n = x - 3

So the smallest integer in terms of (x - 3).

৩৩০.
Which of the following fractions is greater than 3/4 and less than 5/6?
  1. ক
    1/2
  2. খ
    2/3
  3. গ
    4/5
  4. ঘ
    9/10
ব্যাখ্যা
Question: Which of the following fractions is greater than 3/4 and less than 5/6?

Solution:
3/4 = 0.75,   
5/6 = 0.833,   

1/2 = 0.5,   
2/3 = 0.66,   
4/5 = 0.8,   
9/10 = 0.9

Clearly, 0.8 lies between 0.75 and 0.833.
৩৩১.
The average of 7 consecutive numbers is 20. The largest of these number is -
  1. ক
    ক) 23
  2. খ
    খ) 22
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
ব্যাখ্যা

ধরি, সংখ্যাগুলো, x - 3, x - 2, x - 1, x + 1, x + 2, x + 3
(x - 3 + x - 2 + x - 1 + x + x + 1 + x + 2 + x + 3)/7 = 20
Or, 7x/7 = 20
Or, x = 20
∴ বৃহত্তম সংখ্যাটি = x + 3 = 20 + 3 = 23

৩৩২.
If the average of 'm' numbers is n2 and that of 'n' numbers is m2, then the average of (m + n) numbers is -
  1. ক
    m + n
  2. খ
    (m + n)/mn
  3. গ
    mn
  4. ঘ
    mn(n + m)
ব্যাখ্যা
Question: If the average of 'm' numbers is n2 and that of 'n' numbers is m2, then the average of (m + n) numbers is - 

Solution:
Sum of m numbers = mn2
Sum of n numbers = nm2

∴ Sum of m and n numbers = mn2 + nm2
= mn(n + m)

∴ Average of (m + n) numbers = mn(n + m)/(m + n)
= mn
৩৩৩.
The average of ten numbers is 10. If each number is multiplied by 8, what is the new average?
  1. ক
    100
  2. খ
    72
  3. গ
    64
  4. ঘ
    80
ব্যাখ্যা
Question: The average of ten numbers is 10. If each number is multiplied by 8, what is the new average? 

Solution:
The sum of ten numbers = 10 × 10 = 100

Now, 
If each number is multiplied by 8, the new average is
= (The sum of ten numbers × 8) / 10
= (100 × 8) / 10
= 80
৩৩৪.
Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then the average of the first and the third number is -
  1. ক
    52
  2. খ
    66
  3. গ
    72
  4. ঘ
    94
ব্যাখ্যা
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then the average of the first and the third number is -

Solution:
Let,
the second number be = x
So, the first number is = 2x
and the third number is = 2x × 2 = 4x (since the first is half of the third)

ATQ,
(2x + x + 4x)/3 = 56
⇒ 2x + x + 4x = 56 × 3
⇒ 7x = 168
∴ x = 24

∴ the second number = 24
So, the first number is = 2 × 24 = 48
and the third number is = 4 × 24 = 96

Then, the average of the first and the third number is = (48 + 96)/2 = 72
৩৩৫.
The average of 75 numbers is 35. If each number is increased by 5, the average of new numbers is -
  1. ক
    ক) 38
  2. খ
    খ) 45
  3. গ
    গ) 42
  4. ঘ
    ঘ) 40
ব্যাখ্যা
Question: The average of 75 numbers is 35. If each number is increased by 5, the average of new numbers is -

Solution:
Sum of 75 numbers = 75 × 35 = 2625

Total increase = 5 × 75 = 375
Increased sum = 2625 + 375 = 3000

So, the new average = 3000/75 = 40
৩৩৬.
A glass when full of milk, weighs 0.75 kg. It weighs 0.5 kg when the glass is half full. What is weight of the empty glass?
  1. ক
    0.25 kg
  2. খ
    0.35 kg
  3. গ
    0.45 kg
  4. ঘ
    0.5 kg
ব্যাখ্যা
Question: A glass when full of milk, weighs 0.75 kg. It weighs 0.5 kg when the glass is half full. What is weight of the empty glass?

Solution: 
Let,
Weight of Glass = x kg
Weight of Milk = y kg

Now,
x + y = 0.75..................(1)

And
x + y/2 = 0.5
⇒ (2x + y)/2 = 0.5
⇒  2x +y = 1.00..................(2)

(2) - (1) ⇒
2x + y - (x + y) = 1.00 - 0.75
⇒ 2x + y - x - y = 0.25
∴ x = 0.25 

∴ Weight of Glass is 0.25 kg
৩৩৭.
The average age of five members is 27. If one of them is excluded the average decreases by 2. The age of the excluded person is:
  1. ক
    ক) 40
  2. খ
    খ) 35
  3. গ
    গ) 28
  4. ঘ
    ঘ) 38
ব্যাখ্যা

The average age of five members is 27
Total age = 27× 5 = 135
After excluding one person, the new average = 27 - 2 = 25
New total age = 25× 4 = 100
Then the age of excluded person = Total age - New total age
= 135 - 100
= 35
Hence the required answer is 35.

৩৩৮.
Sanzida ate 3/4 of a pizza. Her brother Babu ate 1/2 of what was left. Then their friend Pavel ate 2/3 of what was still left. What fraction of the pizza remains uneaten? 
  1. ক
    1/14
  2. খ
    1/12
  3. গ
    1/24
  4. ঘ
    None
ব্যাখ্যা

Question: Sanzida ate 3/4 of a pizza. Her brother Babu ate 1/2 of what was left. Then their friend Pavel ate 2/3 of what was still left. What fraction of the pizza remains uneaten?

Solution:
Sanzida ate = 3/4
∴ Remaining = 1 - 3/4 = 1/4

Babu ate = 1/2 × 1/4 = 1/8
∴ Remaining = 1/4 - 1/8 = (2 - 1)/8 = 1/8

Pavel ate = 2/3 × 1/8 = 2/24 = 1/12
∴ Remaining = 1/8 - 1/12 = (3 - 2)/24 = 1/24

∴ Fraction of pizza remaining uneaten = 1/24.

৩৩৯.
The average runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings to increase his average of runs by 4?
  1. ক
    ক) 76
  2. খ
    খ) 79
  3. গ
    গ) 85
  4. ঘ
    ঘ) 87
ব্যাখ্যা
10টি ম্যাচের রানের গড় হলো 32
10টি ম্যাচের মোট রান = 32 × 10 = 320

11 তম ম্যাচ শেষে গড় রান = 32 + 4 = 36  রান
11 তম ম্যাচ শেষে মোট হবে = 36 x 11 = 396 রান

11 তম ম্যাচে করতে হবে = 396 - 320 = 76 রান।
৩৪০.
Find the value of 'x' if the mean of the set of the numbers 8, 5, a, 10, 15, 21 is given as 11.
  1. ক
    5
  2. খ
    6
  3. গ
    7
  4. ঘ
    8
ব্যাখ্যা
Question: Find the value of 'x' if the mean of the set of the numbers 8, 5, a, 10, 15, 21 is given as 11.

Solution:
ATQ,
(8 + 5 + a + 10 + 15 + 21)/6 = 11
⇒ (59 + a)/6 = 11
⇒ 59 + a  = 66
⇒ a = 66 - 59
∴ a = 7
৩৪১.
The average of Amit's five quiz scores is 88. What score does Amit need to get on a sixth quiz to raise his average for all six quizzes to 90?
  1. ক
    98
  2. খ
    100
  3. গ
    94
  4. ঘ
    99
ব্যাখ্যা
Question: The average of Amit's five quiz scores is 88. What score does Amit need to get on a sixth quiz to raise his average for all six quizzes to 90?

Solution:
Sum of 5 scores = 88 × 5 = 440
Sum of 6 scores = 90 × 6 = 540
Sixth quiz score = 540 - 440 = 100
৩৪২.
The average of four consecutive even numbers is 27. Find the largest of these numbers.
  1. ক
    ক) 28
  2. খ
    খ) 30
  3. গ
    গ) 32
  4. ঘ
    ঘ) 40
ব্যাখ্যা

Consider the consecutive even numbers as : x, (x + 2), (x + 4) and (x+ 6)
Average = Sum of Quantities/Number of Quantities
{x + (x + 2) + (x + 4) + (x + 6)}/4 = 27
⇒ (4x + 12)/4 = 27
⇒ x + 3 = 27
⇒ x = 27 - 3
⇒ x = 24.

Therefore,
Largest number = (x + 6) = (24 + 6) = 30
Smallest number = 24.
Hence, the answer is 30.

৩৪৩.
  1. ক
    1/64
  2. খ
    64
  3. গ
    256
  4. ঘ
    4
ব্যাখ্যা
Question:


Solution:
৩৪৪.
The average monthly income of P and Q is Tk. 4000 that of Q and R is Tk. 3250 and that P and R is Tk. 3500. what is P's monthly income? 
  1. ক
    ক) Tk. 3550
  2. খ
    খ) Tk.3250
  3. গ
    গ) Tk. 4550
  4. ঘ
    ঘ) Tk. 4250
ব্যাখ্যা
Average monthly income of P and Q = Tk. 4000
Average monthly income of Q and R = Tk. 3250
Average monthly income of P and R = Tk. 3500
Total income of P + Q
= 2 × 4000
= Tk. 8000.....(i)

Total income of Q + R
= 2 × 3250
= Tk. 6500 .....(ii)
Total income of R + P
= 2 × 3500
= Tk. 7000.....(iii)
On adding equation (i) (ii) and (iii), we have
2 (P + Q + R) = 8000 + 6500 + 7000
⇒ P + Q + R = 21500/2
⇒ P + Q + R = Tk. 10750.....(iv)

By equation (iv) - (ii)
P's monthly income
= Tk.(10750 - 6500)
= Tk. 4250
৩৪৫.
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is-
  1. ক
    17 kg
  2. খ
    20 kg
  3. গ
    31 kg
  4. ঘ
    37 kg
ব্যাখ্যা
Question: The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is-

Solution:
Let A, B, C represent their respective weights.

Then, we have:
A + B + C =(45 × 3) = 135..............(i)
A + B = (40 × 2) = 80.................(ii)
B + C=(43 × 2) = 86.................(iii)

Adding (ii) and (iii),
we get: A + 2B + C =80 + 86
A + 2B + C =166 .....(iv)

Subtracting (i) from (iv),
we get:
A + 2B + C - (A + B + C) = 166 - 135 
B = 31

∴ B's weight =31 kg.
৩৪৬.
The average temperature for the first 4 days of a week is 40.2°C and that of the last 4 days is 41.3°C. If the average temperature for the whole week is 40.6°C, then the temperature on the fourth day is-
  1. ক
    38.5°C
  2. খ
    40.8°C
  3. গ
    41.8°C
  4. ঘ
    41.3°C
ব্যাখ্যা
Question: The average temperature for the first 4 days of a week is 40.2°C and that of the last 4 days is 41.3°C. If the average temperature for the whole week is 40.6°C, then the temperature on the fourth day is-
 
Solution:
Temperature on the fourth day
= [(40.2 × 4 + 41.3 × 4) - (40.6 × 7)]° C
= 41.8° C
৩৪৭.
Average mark in a class test of 40 students is 40. Average mark of all the 25 boys is 46. Then the average mark obtained by the girls is
  1. ক
    30
  2. খ
    32
  3. গ
    35
  4. ঘ
    36
ব্যাখ্যা
Question: Average mark in a class test of 40 students is 40. Average mark of all the 25 boys is 46. Then the average mark obtained by the girls is

Solution: 
Given,
Average mark of 40 students = 40
Total mark of 40 students = (40 × 40)
= 1600 

Average mark of all the 25 boys = 46
Total mark of all the 25 boys = (46 × 25)
= 1150

∴ Total marks of all the 15 girls is (1600 - 1150) = 450

So the average mark of 15 girls = 450/15 = 30
৩৪৮.
The mean of x, x + 4, x + 8, x + 12 is 20. Find x.
  1. ক
    12
  2. খ
    14
  3. গ
    16
  4. ঘ
    18
ব্যাখ্যা

Question: The mean of x, x + 4, x + 8, x + 12 is 20. Find x.

Solution:
Given,
Total numbers = 4
Mean = 20

Sum of numbers: 
x+ (x + 4) + (x + 8) + (x + 12) 
= 4x + 24

ATQ,
(4x + 24)/4 = 20
⇒ 4x + 24 = 80
⇒ 4x = 56
∴ x = 14

৩৪৯.
Of the three numbers, the first is twice the second and the second is twice the third. The average of the reciprocal of the numbers is (7/72). The numbers are:
  1. ক
    16, 8, 32
  2. খ
    26, 8, 12
  3. গ
    16, 8, 4
  4. ঘ
    16, 8, 40
  5. ঙ
    24, 12, 6
ব্যাখ্যা

Question: Of the three numbers, the first is twice the second and the second is twice the third. The average of the reciprocal of the numbers is (7/72). The numbers are:

Solution:
Let the number be x.
Then, second number = 2x.
First number = 4x.

∴ (1/x) + (1/2x) + (1/4x) = (7/72) × 3
⇒ (4 + 2 + 1)/4x = (7/24)
⇒ 7/4x = 7/24
⇒ 4x = 24
⇒ x = 24/4
∴ x = 6

Therefore, the numbers are (4 × 6) or 24,  (2 × 6) or 12 and 6.

৩৫০.
The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?
  1. ক
    13.5 
  2. খ
    14
  3. গ
    15
  4. ঘ
    None of these
ব্যাখ্যা

Question: The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?

Solution: 
At present the total age of the family = 5 × 20 =100
The total age of the family at the time of the birth of the youngest member,
= 100 - 10 - (10 × 4)
= 50

Therefore, average age of the family at the time of birth of the youngest member,
= 50/5
= 10

৩৫১.
Before anybody could notice Rifat took one third of the chocolates from a box. Later his three sisters arrived and the remaining chocolates where distributed equally among the four of them. Rifat received a total of 36 chocolates. how many did of his each sister receive?
  1. ক
    16
  2. খ
    12
  3. গ
    8
  4. ঘ
    18
  5. ঙ
    10
ব্যাখ্যা
Question: Before anybody could notice Rifat took one third of the chocolates from a box. Later his three sisters arrived and the remaining chocolates where distributed equally among the four of them. Rifat received a total of 36 chocolates. how many did of his each sister receive?

Solution:
Let,
Total Chocolates = x
First time Rifat took = x/3
Rest Amount = x - (x/3) = 2x/3
Amount of Chocolate when it divided equally = (2x/3) × (1/4)
= x/6

ATQ,
⇒ (x/6) + (x/3) = 36
⇒ (x + 2x)/6 = 36
⇒ 3x/6 = 36
⇒ x/2 = 36
∴ x = 72

So, each sister got = 72/6 = 12
৩৫২.
Average of six non-zero positive integers is 15 and the median is 18. The modal value is less than the median. What is the maximum possible value of the largest of the six integers?
  1. ক
    28
  2. খ
    29
  3. গ
    30
  4. ঘ
    31
  5. ঙ
    32
ব্যাখ্যা
Question: Average of six non-zero positive integers is 15 and the median is 18. The modal value is less than the median. What is the maximum possible value of the largest of the six integers?

Solution:
দেওয়া আছে,
শূণ্য নয় এমন ৬ টি সংখ্যার গড় = ১৫

∴ ৬ টি সংখ্যার সমষ্টি = (১৫ × ৬) = ৯০


আবার, মধ্যমা = ১৮
∴ ৬টি সংখ্যাকে ছোট থেকে বড় ক্রমে সাজালে, ৩য় ও ৪র্থ সংখ্যার গড় হবে ১৮।
∴ ৩য় ও ৪র্থ সংখ্যা দুটি হবে = ১৭ ও ১৯

যেহেতু, প্রচুরক মধ্যমা হতে ছোট হবে,

প্রদত্ত তথ্যের ভিত্তিতে সর্বনিম্ন মান নিয়ে ৫ টি সংখ্যা হবে = ১, ১, ১৭, ১৯, ২০ [যেহেতু ৩য় ও ৪র্থ সংখ্যা ১৭ ও ১৯]

তাদের সমষ্টি = ১ + ১ + ১৭ + ১৯ + ২০ = ৫৮

∴ বৃহত্তম সংখ্যাটি হবে = ৯০ - ৫৮ = ৩২
৩৫৩.
The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average is increased by 0.2 years. The average age of new students is?
  1. ক
    8 years
  2. খ
    25 years
  3. গ
    18 years
  4. ঘ
    15 years
  5. ঙ
    16 years
ব্যাখ্যা
Question: The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average is increased by 0.2 years. The average age of new students is?

Solution:
40 জনের মোট বয়স = 40 × 15 = 600 বছর
10 জন নতুন student ভর্তি হওয়ায় মোট = 40 + 10 = 50 জন

∴ গড় বয়স = 15 + 0.2 = 15.2 বছর

∴ 50 জনের মোট বয়স = 15.2 × 50 = 760 বছর

∴ নতুন 10 জনের বয়স = 760 - 600 = 160 বছর
∴ নতুন 10 জনের গড় বয়স 160 ÷ 10 = 16 বছর
৩৫৪.
The average of 4 consecutive numbers is 5.5 . The largest of these numbers is:
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 7
ব্যাখ্যা
প্রশ্ন: The average of 4 consecutive numbers is 5.5 . The largest of these numbers is:

সমাধান:
৪ টি সংখ্যার গড় ৫.৫
৪ টি সংখ্যার সমষ্টি = ৫.৫ × ৪ = ২২

ধরি, সংখ্যাগুলি হল a, a + ১, a + ২, a + ৩
প্রশ্নমতে,
a + a + ১ + a + ২ + a + ৩ = ২২
⇒ ৪a + ৬ = ২২
⇒ ৪a = ১৬
⇒ a = ৪

∴ বড় সংখ্যাটি হল a + ৩ 
= ৪ + ৩
= ৭
৩৫৫.
A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in the month of June beginning with a Sunday?
  1. ক
    250
  2. খ
    260
  3. গ
    265
  4. ঘ
    285
ব্যাখ্যা

Question: A library has an average of 510 visitors on Sundays and 240 on other days. What is the average number of visitors per day in the month of June beginning with a Sunday?

Solution:
Given that,
The month begins with a Sunday, so there will be five Sundays in the month.
Number of the visitor in five sunday
⇒ 510 × 5 = 2550
Number of the other days visitor
⇒ 240 × 25 = 6000
Average = (2550 + 6000)/30 = 285

∴ The average number of visitors per day in a month of 30 days beginning with a Sunday is 285.

৩৫৬.
If x = 3 - 5a and y = 2a + 3, then for what value of a, x is equal to y?
  1. ক
    - 2
  2. খ
    5
  3. গ
    0
  4. ঘ
    - 3
ব্যাখ্যা
Question: If x = 3 - 5a and y = 2a + 3, then for what value of a, x is equal to y?

Solution:
Given that,
x = 3 - 5a
y = 2a + 3

Now,
x = y
⇒ 3 - 5a = 2a + 3
⇒ 5a + 2a = 3 - 3
⇒ 7a = 0
∴ a = 0

∴ The value of a is 0
৩৫৭.
If Tk. 4,500 was invested in a share when the price per share was Tk. 9 and Tk. 3,000 was invested in another share when the price per share was Tk. 10. What was the average price per share purchased?
  1. ক
    ক) Tk. 9.20
  2. খ
    খ) Tk. 9.625
  3. গ
    গ) Tk. 9.4
  4. ঘ
    ঘ) Tk. 9.375
ব্যাখ্যা
Question: If Tk. 4,500 was invested in a share when the price per share was Tk. 9 and Tk. 3,000 was invested in another share when the price per share was Tk. 10. What was the average price per share purchased?

Solution: 
প্রতি শেয়ার ৯ টাকা দরে শেয়ার কিনে ৪৫০০ টাকার 
শেয়ার কিনে = ৪৫০০/৯ টি 
= ৫০০ টি 

অন্য শেয়ারে ১০ টাকা দরে শেয়ার কিনে ৩০০০ টাকার 
শেয়ার কিনে ৩০০০/১০ = ৩০০ টি 

মোট শেয়ার কিনে = ৫০০ + ৩০০ টি 
= ৮০০ টি 

∴ গড়ে প্রতি শেয়ারের মূল্য = (৪৫০০ + ৩০০০)/৮০০ টাকা 
= ৭৫০০/৮০০ টাকা 
= ৯.৩৭৫ টাকা 
৩৫৮.
Which of the following fraction is smaller than 3/4 and greater than 1/2?
  1. ক
    2/5
  2. খ
    5/8
  3. গ
    3/7
  4. ঘ
    4/9
ব্যাখ্যা

Question: Which of the following fraction is smaller than 3/4 and
greater than 1/2?

Solution:
3/4 = 0.75
1/2 = 0.5

ক) 2/5 = 0.4
খ) 5/8 = 0.625
গ) 3/7 = 0.428
ঘ) 4/9 = 0.444

∴ 5/8 is the required fraction.

৩৫৯.
The average weight of 40 students in a class is 45 kg. If three students weighing 52 kg, 48 kg, and 50 kg leave the class, what is the new average weight of the remaining students?
  1. ক
    44.6 kg
  2. খ
    43.7 kg
  3. গ
    42.3 kg
  4. ঘ
    41.9 kg
ব্যাখ্যা
Question: The average weight of 40 students in a class is 45 kg. If three students weighing 52 kg, 48 kg, and 50 kg leave the class, what is the new average weight of the remaining students?

Solution:
Total weight = 45 × 40 = 1800 kg

Students leaving = 52 kg + 48 kg + 50 kg = 150 kg
Remaining total weight = 1800 - 150 = 1650 kg

Remaining students = 40 - 3 = 37 students
New average = 1650/37
= 44.59 kg

Therefore, the new average weight is approximately 44.6 kg.
৩৬০.
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:
  1. ক
    40
  2. খ
    30
  3. গ
    25
  4. ঘ
    17
ব্যাখ্যা
Question: 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:

Solution:
Let there be 'p' pupils in the class.

Total increase in marks = p × 1/2= p/2
∴ p/2 = (83 - 63)
⇒ p/2 = 20
⇒ p = 40

Hence, The number of pupils in the class is = 40
৩৬১.
The average of three consecutive multiples of 5 is 50. What is the largest of these multiples?
  1. ক
    45
  2. খ
    65
  3. গ
    58
  4. ঘ
    50
  5. ঙ
    55
ব্যাখ্যা
Question: The average of three consecutive multiples of 5 is 50. What is the largest of these multiples?

Solution:
Let the three consecutive multiples of 5 are, 5x, 5x + 5, 5x + 10

Average = 5x + (5x + 5) + (5x + 10)​/3
= (15x + 15)/3

As per question;
⇒ (15x + 15)/3 = 50
⇒ 15x + 15 = 150
⇒ 15x = 135
⇒ x = 135/15 = 9
∴ x = 9

So, the largest multiple is = 5x + 10 = 45 + 10 = 55.
৩৬২.
The difference of 13/12 and its reciprocal is equal to-
  1. ক
    169/144
  2. খ
    15/16
  3. গ
    4/3
  4. ঘ
    None
ব্যাখ্যা
Question: The difference of 13/12 and its reciprocal is equal to-

Solution:
The reciprocal of 13/12​ is 12/13
Now, calculate the difference between 13/12​ and 12/13
= (13/12)​ - (12/13)
= (169 - 144)/156
= 25/156

∴ The difference between 13/12​ and its reciprocal is 25/156.
৩৬৩.
  1. ক
    42
  2. খ
    38
  3. গ
    44
  4. ঘ
    43
ব্যাখ্যা

Question: 

Solution: 

৩৬৪.
In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to each the target of 282 runs?
  1. ক
    ক) 7
  2. খ
    খ) 6
  3. গ
    গ) 6.25
  4. ঘ
    ঘ) 5.50
ব্যাখ্যা
Question: In the first 10 overs of a cricket game, the run rate was only 3.2. What should be the rate in the remaining 40 overs to each the target of 282 runs?

Solution:
First 10 overs total run was = (3.2 × 10) = 32

Required run rate = (282 - 32)/40
= 250/40
= 6.25
৩৬৫.
If the mean of a, b, c is 4 and ab + bc + ca = 0, then the mean of a2, b2 and c2 is-
  1. ক
    ক) 4/3
  2. খ
    খ) 3
  3. গ
    গ) 48
  4. ঘ
    ঘ) 64/3
ব্যাখ্যা
Question: If the mean of a, b, c is 4 and ab + bc + ca = 0, then the mean of a2, b2 and c2 is-

Solution:
Given that 
(a + b + c)/3 = 4
a + b + c = 12

We know,
(a + b + c)2 = a2 + b2 + c2 + 2 (ab + ba + ca)
⇒ (a + b + c)2 = a2 + b2 + c2 + 2 × 0
⇒ (a + b + c)2 = a2 + b2 + c2
⇒ a2 + b2 + c2 = 122
⇒ a2 + b2 + c2 =144

∴the mean of a2, b2 and c2 is = ( a2 + b2 + c2)/3
= 144/3
= 48
৩৬৬.
If on a test, three people answered 90% of the questions correctly and two people answered 80% correctly. then the average for the group of five people is-
  1. ক
    80%
  2. খ
    85%
  3. গ
    86%
  4. ঘ
    90%
ব্যাখ্যা
Question: If on a test, three people answered 90% of the questions correctly and two people answered 80% correctly, then the average for the group of five people is-

Solution:
- ৩ জন পরীক্ষার্থী ৯০% সঠিক উত্তর দিয়েছে
- ২ জন পরীক্ষার্থী ৮০% সঠিক উত্তর দিয়েছে
- Total students (মোট পরীক্ষার্থী) = 3+2=5

- মোট শতাংশ:
3×90 %+2×80%
=(270+160)%
=430%

- গড় শতাংশ নির্ণয়:
430%÷5 (মোট ৫ জন পরীক্ষার্থী)
=86%

- তাই গড় হবে: 86%.
৩৬৭.
The average of 20 numbers is 40. If the numbers 30 and 50 are discarded, then the average of the remaining numbers is -
  1. ক
    ক) 30
  2. খ
    খ) 36
  3. গ
    গ) 40
  4. ঘ
    ঘ) 42
ব্যাখ্যা
Question: The average of 20 numbers is 40. If the numbers 30 and 50 are discarded, then the average of the remaining numbers is - 

Solution:
Sum of 20 numbers = 20 × 40 = 800
Sum of remaining 18 numbers = 800 - (30 + 50) = 720
Average of the remaining numbers = 720/18 = 40
৩৬৮.
Rahim's present age is 9 times as Karim's age. After 9 years, Rahim's age would be 3 times as Karim's age. What is the present age of Karim?
  1. ক
    ক) 3 years
  2. খ
    খ) 9 years
  3. গ
    গ) 12 years
  4. ঘ
    ঘ) 27 years
ব্যাখ্যা
Question: Rahim's present age is 9 times as Karim's age. After 9 years, Rahim's age would be 3 times as Karim's age.  What is the present age of Karim?

Solution:
Let, Karim's present age be x years
and Rahim's present age is = 9x years

Now,
Karim's age after 9 years = (x + 9) years
Rahim's age after 9 years = (9x + 9) years

ATQ,
9x + 9 = 3(x + 9)
⇒ 9x + 9 = 3x + 27
⇒ 6x = 18
⇒ x = 3
৩৬৯.
The captain of a cricket team of 11 members is 25 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 average age of the team?
  1. ক
    ক) 23 years
  2. খ
    খ) 22 years
  3. গ
    গ) 24 years
  4. ঘ
    ঘ) 25 years
ব্যাখ্যা
Let the average age of the whole team by x years.
11x - (25 + 28) = 9(x -1)
11x - 53 = 9x - 9 
11x - 9x = 44
2x = 44
 x = 22.

So, average age of the team is 22 years.
৩৭০.
The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the eldest boy is-
  1. ক
    ক) 9 years 
  2. খ
    খ) 15 years 
  3. গ
    গ) 21 years 
  4. ঘ
    ঘ) 27 years 
ব্যাখ্যা
Question: The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the eldest boy is-

Solution: 
The average age of three boys is 15 years.
sum of three boys = (15 × 3)
= 45 years

their ages are in ratio 3 : 5 : 7
so, there ages are 3x, 5x, 7x

3x + 5x + 7x = 45 
⇒ 15x = 45
∴ x = 3

age of the eldest boy is (7 × 3) years 
= 21 years
৩৭১.
The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first one is 18 greater than the actual number and the second number added is 13 instead of 33. Find the correct average -
  1. ক
    ক) 40.2
  2. খ
    খ) 40.6
  3. গ
    গ) 40.4
  4. ঘ
    ঘ) 40.8
ব্যাখ্যা
প্রশ্ন : The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly added. The first one is 18 greater than the actual number and the second number added is 13 instead of 33. Find the correct average - 
সমাধান : 
১০টি সংখ্যার প্রকৃত সমষ্টি 
= (40.2 × 10 - 18 + 33 - 13)
= 404

∴ প্রকৃত গড় = (404/10) = 40.4
৩৭২.
The number of students in Class A is 15, and in Class B is 25. The average marks of Class A are 80, and the average marks of Class B are 70. What is the combined average marks of the two classes?
  1. ক
    70.50
  2. খ
    75.25
  3. গ
    67.72
  4. ঘ
    73.75
  5. ঙ
    74.50
ব্যাখ্যা
Question: The number of students in Class A is 15, and in Class B is 25. The average marks of Class A are 80, and the average marks of Class B are 70. What is the combined average marks of the two classes?

Solution:
The sum of Class A = 15 × 80 = 1200
The sum of group B = 25 × 70 =1750

∴ Combined Average of the two groups = (1200 + 1750)/(15 + 25)
= 2950/40
= 73.75
৩৭৩.
Tahsan scored 87 on his 17th class test, increasing his average score by 3. What is Tahsan's average score after this test?
  1. ক
    36
  2. খ
    39
  3. গ
    40
  4. ঘ
    42
  5. ঙ
    None
ব্যাখ্যা
Question: Tahsan scored 87 on his 17th class test, increasing his average score by 3. What is Tahsan's average score after this test?

Solution:
ধরি,
17তম টেস্টের পর তার গড় x নম্বর
16তম টেস্টের পর তার গড় ছিল (x - 3) নম্বর

প্রশ্নমতে,
16(x - 3) + 87 = 17x
16x - 48 + 87 = 17x
∴ x = 39
৩৭৪.
The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:
  1. ক
    ক) 17
  2. খ
    খ) 20
  3. গ
    গ) 26
  4. ঘ
    ঘ) 31
ব্যাখ্যা

Let A, B, C represent their respective weights. Then, we have:
A + B + C = (45 x 3) = 135 .... (i)
A + B = (40 x 2) = 80 .... (ii)
B + C = (43 x 2) = 86 ....(iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 .... (iv)
Subtracting (i) from (iv), we get : B = 31
∴ B's weight = 31 kg.

৩৭৫.
  1. ক
    0.97
  2. খ
    0.95
  3. গ
    0.86
  4. ঘ
    1.06
ব্যাখ্যা
Question:

Solution:
৩৭৬.
  1. ক
    3/2
  2. খ
    3
  3. গ
    2/3
  4. ঘ
    2
৩৭৭.
In a class of 150 students, the average score in mathematics is 82. If the 90 girls scored an average of 85, what is the average score of the remaining boys?
  1. ক
    70.8
  2. খ
    72
  3. গ
    75.6
  4. ঘ
    77.5
ব্যাখ্যা

Question: In a class of 150 students, the average score in mathematics is 82. If the 90 girls scored an average of 85, what is the average score of the remaining boys?

Solution:
ধরি, ছেলেদের গড় নম্বর = x

150 জন শিক্ষার্থীর মোট নম্বর = 150 × 82 = 12300
90 জন ছাত্রীর মোট নম্বর = 90 × 85 = 7650

প্রশ্নমতে,
7650 + (150 - 90) × x = 12300
⇒ 7650 + 60x = 12300
⇒ 60x = 12300 - 7650
⇒ 60x = 4650
⇒ x = 4650/60
⇒ x = 77.5

∴ 60 জন ছেলের গড় নম্বর = 77.5

৩৭৮.
The average age of girls in a nursery class is 5 years and that of boys is 5.7 years. If the average age of the students in the class is 5.5 years, what could be the possible number of boys and girls respectively in the class?
  1. ক
    ক) 10, 20
  2. খ
    খ) 30, 50
  3. গ
    গ) 100, 500
  4. ঘ
    ঘ) 150, 375
ব্যাখ্যা
Let the number of boy and girl be y and z
5z + 5.7y = 5.5(y + z)
5.5z - 5z = 5.7y - 5.5y
0.5z = 0.2y
5z = 2y
z : y = 2 : 5 = 75 × 2 : 75 × 5 = 150 : 375
--------------------------------------------
নার্সারি শ্রেণির বালিকাদের গড় বয়স ৫ বছর এবং বালকদের গড় বয়স ৫.৭ বছর। ছাত্রছাত্রীদের গড় বয়স ৫.৫ বছর হলে, ছাত্রছাত্রীদের সম্ভাব্য সংখ্যা কত?

মনে করি, ছাত্র ও ছাত্রীদের সংখ্যা যথাক্রমে y ও z
সুতরাং 5z + 5.7y = 5.5(y + z)
5.5z - 5z = 5.7y - 5.5y
0.5z = 0.2y
5z = 2y
z : y = 2 : 5
সুতরাং ছাত্রীদের সংখ্যা ২ জন হলে ছাত্রদের সংখ্যা ৫ জন
ছাত্রীদের সংখ্যা ১৫০ জন হলে ছাত্রদের সংখ্যা ৫ × ১৫০/২ = ৩৭৫ জন যা অপশনে আছে।
৩৭৯.
13 chairs and 5 tables were bought for 8280. If the average cost of a table be Tk. 1227, what is the average cost of a chair?
  1. ক
    Tk. 165
  2. খ
    Tk. 145
  3. গ
    Tk. 175
  4. ঘ
    Tk. 135
ব্যাখ্যা
Question: 13 chairs and 5 tables were bought for 8280. If the average cost of a table be Tk. 1227, what is the average cost of a chair?

Solution:
The total cost of 5 tables = (1227 × 5) = Tk. 6135
The total cost of 13 chairs = 8280 - 6135 = Tk. 2145

∴ Average cost of a chair = 2145/13
= Tk. 165
৩৮০.
The average of 4 terms is 20 and the 1st term is 1/3 of the remaining terms. What will be the first number?
  1. ক
    15
  2. খ
    20
  3. গ
    25
  4. ঘ
    30
ব্যাখ্যা
Question: The average of 4 terms is 20 and the 1st term is 1/3 of the remaining terms. What will be the first number?

Solution:
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
৩৮১.
When 35 - [30 - {35 - (15 - *)}] = 60, then * is equal to-
  1. ক
    - 19
  2. খ
    35
  3. গ
    20
  4. ঘ
    - 29
ব্যাখ্যা
Question: When 35 - [30 - {35 - (15 - *)}] = 60, then * is equal to-

Solution:
35 - [30 - {35 - (15 - *)}] = 60
⇒ 35 - [30 - {35 -15 +*}] = 60
⇒ 35 - [30 - {20 + *}] = 60
⇒ 35 - [30 - 20 - *] = 60
⇒ 35 - [10 - *] = 60
⇒ 35 - 10 + * = 60
⇒ 25 + * = 60
∴ * = 60 - 25 = 35
৩৮২.
The average of 5 consecutive numbers is n. What will be the average if the next two numbers are included?
  1. ক
    n + 2
  2. খ
    n - 1
  3. গ
    n - 2
  4. ঘ
    n + 1
  5. ঙ
    None of these
ব্যাখ্যা

Question: The average of 5 consecutive numbers is n. What will be the average if the next two numbers are included?

Solution:
The average of 5 consecutive terms is n, implies that the 3rd term is n. Now as the next 2 terms are included implies that the new average for 7 terms would be the 4th term. So, the 4th term would be n + 1.

Example:
(1 + 2 + 3 + 4 + 5)/5
= 15/5
= 3

(1 + 2 + 3 + 4 + 5 + 6 + 7)/7
= 28/7
= 4

৩৮৩.
Find the average of the first 20 natural numbers.
  1. ক
    ক) 10.5
  2. খ
    খ) 11
  3. গ
    গ) 11.5
  4. ঘ
    ঘ) 12
ব্যাখ্যা
Question: Find the average of the first 20 natural numbers.

Solution:
প্রথম ২০ টি স্বাভাবিক সংখ্যার সমষ্টি = ২০(২০ + ১)/২
= ২১০

∴ গড় = ২১০/২০ = ১০.৫
৩৮৪.
The average of the first four multiples of 5 is:
  1. ক
    10
  2. খ
    12.5
  3. গ
    15
  4. ঘ
    17.5
ব্যাখ্যা
The first four multiples of 5 are 5, 10, 15 and 20.
Required average
= total sum of multiple of 5 / 4
= (5 + 10 + 15 + 20)/4
= 50/4
= 12.5
৩৮৫.
The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 and of girls is 40 kg. Therefore, the number of boys is-
  1. ক
    64
  2. খ
    70
  3. গ
    55
  4. ঘ
    60
ব্যাখ্যা

Question: The mean weight of 100 students in a class is 46 kg. The mean weight of boys is 50 and of girls is 40 kg. Therefore, the number of boys is-

Solution:
Given that, 
Total students = 100
Mean weight of all students = 46 kg
∴ Total weight of all students = 100 × 46 = 4600 kg.

Let,
The number of boys = x. Then, the number of girls = 100 - x 
Mean weight of boys = 50 kg,
∴ total weight of boys = 50x
And, 
Mean weight of girls = 40 kg,
∴ total weight of girls = 40(100 - x)

ATQ,
50x + 40 × (100 - x) = 4600
⇒ 50x + 4000 - 40x = 4600
⇒ 10x = 4600 - 4000
⇒ x = 600/10
∴ x = 60

So the number of boys is 60.

৩৮৬.
If the average of four consecutive odd numbers is 42, find the largest numbers.
  1. ক
    41
  2. খ
    43
  3. গ
    45
  4. ঘ
    47
ব্যাখ্যা
Question: If the average of four consecutive odd numbers is 42, find the largest numbers.

Solution:
Let
the first number is x,
then the next three odd numbers would be (x + 2), (x + 4), (x + 6)

ATQ,
{x + (x + 2) + (x + 4) + (x + 6)}/4 = 42
⇒ (4x + 12)/4 = 42
⇒ 4x + 12 = 168
⇒ 4x = 156
∴ x = 39

Largest number would be = 39 + 6 = 45
৩৮৭.
Three numbers are in the ratio 1 : 2 : 3 and their HCF 12. The average of three numbers is -
  1. ক
    ক) 24
  2. খ
    খ) 36
  3. গ
    গ) 48
  4. ঘ
    ঘ) 72
ব্যাখ্যা
Question: Three numbers are in the ratio 1 : 2 : 3 and their HCF 12. The sum of three numbers is -

Solution:
Let the three numbers are x, 2x, 3x respectively 
Their HCF = x

ATQ,
x = 12

So, the three numbers are 12, 24, and 36 respectively 
The average of the three number = (12 + 24 + 36)/3 = 24
৩৮৮.
The sum of the three consecutive even numbers is 44 more than the average of these numbers. Which of the following is the smallest of these numbers?
  1. ক
    ক) 18
  2. খ
    খ) 20
  3. গ
    গ) 22
  4. ঘ
    ঘ) 24
ব্যাখ্যা
Question: The sum of the three consecutive even numbers is 44 more than the average of these numbers. Which of the following is the smallest of these numbers?

Solution:
Let the number be x, x + 2, and x + 4

ATQ,
(x + x + 2 + x + 4) - (x + x + 2 + x + 4)/3 = 44
⇒ (3x + 6) - (3x + 6)/3 = 44
⇒ 9x + 18 - 3x - 6 = 132
⇒ 6x = 120
⇒ x = 20
৩৮৯.
The mean of 7 numbers is 24. If one of the numbers is removed, the mean increases by 3. Find the value of the removed number.
  1. ক
    18
  2. খ
    15
  3. গ
    12
  4. ঘ
    6
ব্যাখ্যা
Question: The mean of 7 numbers is 24. If one of the numbers is removed, the mean increases by 3. Find the value of the removed number.

Solution:
Mean of 7 numbers = 24
Sum of these 7 numbers = (24 × 7) = 168

Mean of the remaining 6 numbers = (24 + 3) = 27
Sum of these remaining 6 numbers = (27 × 6) = 162

Removed number = (sum of the given 7 numbers) - (sum of the remaining 6 numbers)
= (168 - 162)
= 6

Hence, the removed number is 6
৩৯০.
A sum of money is sufficient to pay A's wages for 21 days or B's wages for 28 days. The same money is sufficient to pay the wages of both for?
  1. ক
    12 days
  2. খ
    10 days
  3. গ
    14 days
  4. ঘ
    8 days
ব্যাখ্যা
Question: A sum of money is sufficient to pay A's wages for 21 days or B's wages for 28 days. The same money is sufficient to pay the wages of both for?

Solution:
Let
total money be Tk. x
A's 1 day's wages = Tk. x/21
B's 1 day's wages = Tk. x/28

∴ (A + B)'s 1 day's wages = Tk. (x/21 + x/28)
= Tk. (4x + 3x)/84
= Tk. 7x/84
= Tk. x/12

∴ Money is sufficient to pay the wages of both for 12 days.
৩৯১.
The average age of A, B and C is 30 years. If the difference between B's age and A's age is same as the difference between C's age and B's age. If D is 40 years older than B then what is the sum of the age of B and D?
  1. ক
    ক) 70 years
  2. খ
    খ) 30 years
  3. গ
    গ) 80 years
  4. ঘ
    ঘ) 100 years
ব্যাখ্যা
The average age of A, B and C is 30 years. Therefore, the total age of (A + B + C) = 3 × 30 = 90 years
age of (B - A) = age of (C - B)
age of (A + C) = age of 2B
age of (2B + B) = 90
age of 3B = 90
age of B = 30 years 
age of D = age of (B + 40) = (40 + 30) years = 70 years
Therefore, age of ( B + D) = (30 + 70) years = 100 years
-------------------------------------------------------------
A, B ও C এর গড় বয়স ৩০ বছর। B ও A এর বয়সের পার্থক্য C ও B এর বয়সের পার্থক্যের সমান। যদি D, B এর চেয়ে ৪০ বছরের বড় হয় তবে B ও D এর বয়সের সমষ্টি কত?

A, B ও C এর গড় বয়স ৩০ বছর। সুতরাং মোট বয়স ৩০ × ৩ = ৯০ বছর। 
B ও A এর বয়সের পার্থক্য C ও B এর বয়সের পার্থক্যের সমান।
(A + C) এর বয়স = ২B এর বয়স
(২B + B) এর বয়স = ৯০ বছর
৩B এর বয়স = ৯০
B এর বয়স = ৯০/৩ = ৩০ বছর
D এর বয়স = (B + ৪০) বছর = (৪০ + ৩০) বছর = ৭০ বছর
সুতরাং ( B + D) এর বয়স = (৩০ + ৭০) বছর = ১০০ বছর
৩৯২.
  1. ক
    12
  2. খ
    14
  3. গ
    144
  4. ঘ
    196
ব্যাখ্যা
Question:

Solution:
৩৯৩.
The average of the first twenty-five natural numbers is-
  1. ক
    28
  2. খ
    35
  3. গ
    13
  4. ঘ
    25
ব্যাখ্যা
Question: The average of the first 25 natural numbers is-

Solution:
প্রথম n সংখ্যক সংখ্যার সমষ্টি,
Sn = n(n + 1)/2

প্রথম 25 সংখ্যার সমষ্টি, S25 = 25(25 + 1)/2
= 25 × 13
= 325

∴ গড় = সংখ্যার গুলোর সমষ্টি/মোট সংখ্যা
= 325/25
= 13

গড় হলো 13.
৩৯৪.
Person 1 to 4 receive equal shares of an income, while Person 5 receives half of what each of Persons 1 to 4 receives. If the total income is 18000 taka, how much does Person 5 get?
  1. ক
    1500
  2. খ
    2000
  3. গ
    2500
  4. ঘ
    3000
ব্যাখ্যা

Question: Person 1 to 4 receive equal shares of an income, while Person 5 receives half of what each of Persons 1 to 4 receives. If the total income is 18000 taka, how much does Person 5 get?

Solution: 
Let the amount each of Persons 1 to 4 receives = x taka.
Then Person 5 receives = x/2 taka.

ATQ,
Total income = amount received by all 5 persons
⇒ x + x + x + x + (x/2) = 18000
⇒ 4x + x/2 = 18000
⇒ (8x + x)/2 = 18000
⇒ 9x/2 = 18000
⇒ 9x = 36000
⇒ x = 36000/9
∴ x = 4000

Therefore, Person 5 receives = x/2 = 4000/2 = Tk. 2000

৩৯৫.
Find the average of first 20 consecutive natural numbers.
  1. ক
    12.20
  2. খ
    10.78
  3. গ
    16.45
  4. ঘ
    10.5
ব্যাখ্যা
Question: Find the average of first 20 consecutive natural numbers.

Solution:
The average of first n consecutive natural numbers is
=(n + 1)/2

Here,
n=20

So, average = (20 + 1)/2
= 21/2
= 10.5
৩৯৬.
The average weight of 17 students is 90 kg. If the weight of teacher is also included, then the average weight is increased by 200 grams. Find the weight of the teacher?
  1. ক
    ক) 93.6 kg
  2. খ
    খ) 94 kg
  3. গ
    গ) 93.4 kg
  4. ঘ
    ঘ) 94.6 kg
ব্যাখ্যা

Total weight including teacher = 18 × 90.2 = 1623.6 kg
Total weight of 17 students = 17 × 90 = 1530 kg
So, weight of the teacher = 1623.6 – 1530 = 93.6 kg

৩৯৭.
The average of 17 numbers is 45. The average of first 9 of these numbers is 51 and the last 9 of these numbers is 36. What is the ninth number?
  1. ক
    18
  2. খ
    22
  3. গ
    20
  4. ঘ
    24
  5. ঙ
    None
ব্যাখ্যা
Question: The average of 17 numbers is 45. The average of first 9 of these numbers is 51 and the last 9 of these numbers is 36. What is the ninth number?

Solution:
Total of 17 numbers = 17 × 45 = 765
Total of first 9 numbers = 9 × 51 = 459
Total of last 9 numbers = 9 × 36 = 324

∴ Tenth number = ( 459 + 324) - 765
= 783 - 765
= 18
৩৯৮.
A man travels equal distances of his journey at 40, 30 and 15 km/h respectively. Find his average speed for whole journey.
  1. ক
    ক) 24 km/hour
  2. খ
    খ) 14 km/hour
  3. গ
    গ) 32 km/hour
  4. ঘ
    ঘ) 36 km/hour
ব্যাখ্যা
Required average speed
= (3 ×15 ×30 × 40) / {(40 × 30) + (40 × 15) + (30 × 15)}
= 54000/(1200 + 600 + 450)
= 54000/2250
= 24 km/hour
৩৯৯.
The average of a, b, c is 6 and a - b = 4, ab = 21, what is the value of c?
  1. ক
    ক) 4
  2. খ
    খ) 16
  3. গ
    গ) 28
  4. ঘ
    ঘ) 4
ব্যাখ্যা
The average of a, b, c is 6
∴  (a + b + c)/3 = 6
⇒ a + b + c = 18
a - b = 4
and ab = 21
⇒ a = 21/b

Therefore,
a - b = 4
⇒ 21/b - b = 4
⇒ 21 - b2 - 4b = 0
⇒ b2 + 4b - 21 = 0
⇒ b2 + 7b - 3b - 21 = 0
⇒ b(b + 7) - 3(b - 7) = 0
⇒ (b + 7)(b - 3) = 0
⇒ b = 3, - 7
Therefore,
(a + b + c) - (a - b) = 18 - 4 
⇒ 2b + c = 14
⇒ c = 14 - 2b
⇒ c = 14 - 2 × 3 = 14 - 6 = 8 (when b = 3)
⇒ c = 14 - 2 × ( - 7) = 14 + 14 = 28 (when b = -7)
---------------------------------------------------------
a, b, c এর গড় 6 ও a - b = 4, ab = 21 হলে, c এর মান কত?

a, b, c এর গড় 6
∴  (a + b + c)/3 = 6
⇒ a + b + c = 18
a - b = 4
এবং ab = 21
⇒ a = 21/b
অতএব, 
a - b = 4
⇒ 21/b - b = 4
⇒ 21 - b2 - 4b = 0
⇒ b2 + 4b - 21 = 0
⇒ b2 + 7b - 3b - 21 = 0
⇒ b(b + 7) - 3(b - 7) = 0
⇒ (b + 7)(b - 3) = 0
⇒ b = 3, - 7
অতএব, 
(a + b + c) - (a - b) = 18 - 4 
⇒ 2b + c = 14
⇒ c = 14 - 2b
⇒ c = 14 - 2 × 3 = 14 - 6 = 8 (যখন b = 3)
⇒ c = 14 - 2 × ( - 7) = 14 + 14 = 28 (যখন b = -7)
৪০০.
The average weight of three friends is 35 kg. None of the friends weighs less than 33 kg. What can be the maximum weight of any of the three friends?
  1. ক
    37 kg
  2. খ
    39 kg
  3. গ
    40 kg
  4. ঘ
    41 kg
ব্যাখ্যা

Question: The average weight of three friends is 35 kg. None of the friends weighs less than 33 kg. What can be the maximum weight of any of the three friends?

Solution:
Here,
The average weight of three friends is 35 kg

∴ Total weight of three friends = (35 × 3) kg 
= 105 kg

Minimum weight of two friends (33 × 2) kg
= 66 kg

∴ The maximum weight of any three friends is (105 - 66) kg
= 39 kg