লগ ইননিবন্ধন
বিষয়সমূহ

PrepBank · বিষয়ভিত্তিক প্রশ্ন

Fraction and Simplification, Average and Mean

মোট প্রশ্ন৯৪৮এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Fraction and Simplification, Average and Mean

PrepBank · পাতা ৭ / ১০ · ৬০১–৭০০ / ৯৪৮

৬০১.
The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.
  1. ক
    20 kg
  2. খ
    85 kg
  3. গ
    67 kg
  4. ঘ
    80 kg
সঠিক উত্তর: খ
85 kg
উত্তর
সঠিক উত্তর: খ
85 kg
খ
ব্যাখ্যা
Question: The average weight of 8 women increases by 2.5 kg when a new woman replaces one of them weighing 65 kg. Find the weight of the new woman.

Solution:
Total weight increased = (8 × 2.5) kg = 20 kg.
So, weight of new woman = (65 + 20) kg = 85 kg.
৬০২.
Bipul ate 2/3 of a cake. His friend Rafi ate 2/3 of what was left. Then Rafi's sister ate 2/3 of what was still left. What fraction of the cake remains uneaten?
  1. ক
    1/13
  2. খ
    1/27
  3. গ
    1/8
  4. ঘ
    1/15
সঠিক উত্তর: খ
1/27
উত্তর
সঠিক উত্তর: খ
1/27
খ
ব্যাখ্যা

Question: Bipul ate 2/3 of a cake. His friend Rafi ate 2/3 of what was left. Then Rafi's sister ate 2/3 of what was still left. What fraction of the cake remains uneaten?

Solution:
বিপুল খেয়েছে = 2/3
∴ অবশিষ্ট = 1 - 2/3 = 1/3

রাফি খেয়েছে = 1/3 × 2/3 = 2/9
∴ অবশিষ্ট = 1/3 - 2/9 = (3 - 2)/9 = 1/9

রাফির বোন খেয়েছে = 1/9 × 2/3 = 2/27
∴ অবশিষ্ট = 1/9 - 2/27 = (3 - 2)/27 = 1/27

৬০৩.
A factory employs 130 workers on Fridays and 250 workers on other days. If a month has 30 days and starts on a Friday, what is the average number of workers per day over the month?
  1. ক
    239
  2. খ
    236
  3. গ
    233
  4. ঘ
    230
সঠিক উত্তর: ঘ
230
উত্তর
সঠিক উত্তর: ঘ
230
ঘ
ব্যাখ্যা
Question: A factory employs 130 workers on Fridays and 250 workers on other days. If a month has 30 days and starts on a Friday, what is the average number of workers per day over the month?

Solution:
Since,
the month begins with a Friday, so there will be 5 Fridays and 25 other days in this month.

Total workers on Fridays = 5 × 130 = 650
Total workers on other days = 25 × 250 = 6250

∴ Total workers in the whole month = (650 + 6250) = 6900

∴ Average number of workers per day of the month = 6900/30 = 230
৬০৪.
The average of the first five multiples of 3 is:
  1. ক
    12
  2. খ
    15
  3. গ
    9
  4. ঘ
    3
সঠিক উত্তর: গ
9
উত্তর
সঠিক উত্তর: গ
9
গ
ব্যাখ্যা

Question: The average of the first five multiples of 3 is:

Solution:
The first five multiples of 3 are:
3, 6, 9, 12, 15.

∴ Average = (3 + 6 + 9 + 12 + 15)/5
= 45/5
= 9

৬০৫.
There were 35 students in a hostel. If the number of students increases by 7, the expenses of the mess increase by Tk. 42 per day while the average expenditure per head diminishes by Tk. 1. Find the original expenditure of the mess?
  1. ক
    ক) 400
  2. খ
    খ) 420
  3. গ
    গ) 440
  4. ঘ
    ঘ) 450
সঠিক উত্তর: খ
খ) 420
উত্তর
সঠিক উত্তর: খ
খ) 420
খ
ব্যাখ্যা

Suppose the average expenditure was Tk. a.
Then total expenditure = 35a
When 7 more students join the mess, total expenditure = 35a + 42
Now, the average expenditure= (35a + 42)/(35 + 7)

Now, we have,
(35a + 42)/42 = (a - 1)
⇒ 35a + 42 = 42a – 42
⇒ 7a = 84
⇒ a = 12
Thus the original expenditure of the mess = 35 x 12 = 420.

৬০৬.
What is the average of the sum of the first 11 logical terms of the Fibonacci series if the series starts with zero?
  1. ক
    7
  2. খ
    9
  3. গ
    15
  4. ঘ
    17
  5. ঙ
    None of the above
সঠিক উত্তর: ঙ
None of the above
উত্তর
সঠিক উত্তর: ঙ
None of the above
ঙ
ব্যাখ্যা
Question: What is the average of the sum of the first 11 logical terms of the Fibonacci series if the series starts with zero?

Solution:
The first 9 logical terms of the Fibonacci series if the series starts with zero = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
So, the average = (0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55)/11
= 143/11
= 13
৬০৭.
The average of 10 numbers is 12, and the average of another 15 numbers is 18. What is the average of all 25 numbers combined?
  1. ক
    14
  2. খ
    15.6
  3. গ
    16
  4. ঘ
    18.5
সঠিক উত্তর: খ
15.6
উত্তর
সঠিক উত্তর: খ
15.6
খ
ব্যাখ্যা

Question: The average of 10 numbers is 12, and the average of another 15 numbers is 18. What is the average of all 25 numbers combined?

Solution:
10 টি সংখ্যার গড় = 12
∴10 টি সংখ্যার সমষ্টি = 10 × 12 = 120

15 টি সংখ্যার গড় = 18
∴ 15 টি সংখ্যার সমষ্টি = 15 × 18 = 270

মোট সমষ্টি = 120 + 270 = 390
মোট সংখ্যা = 10 + 15 = 25
সুতরাং, সম্মিলিত গড় = 390/25 = 15.6

৬০৮.
A sum of Tk. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is?
  1. ক
    Tk. 420
  2. খ
    Tk. 280
  3. গ
    Tk. 240
  4. ঘ
    Tk. 350
সঠিক উত্তর: গ
Tk. 240
উত্তর
সঠিক উত্তর: গ
Tk. 240
গ
ব্যাখ্যা
Question: A sum of Tk. 1360 has been divided among A, B and C such that A gets 2/3 of what B gets and B gets 1/4 of what C gets. B's share is?

Solution:
Given that,
Total amount = Tk. 1360
A gets 2/3 of what B gets ⇒ A = 2B/3
B gets 1/4 of what C gets ⇒ B = C/4 ⇒ C = 4B

ATQ,
A + B + C = 1360
⇒ (2B/3) + B + 4B = 1360
⇒ (2B + 3B + 12B)/3 = 1360
⇒ 17B/3 = 1360
⇒ B = (1360 × 3)/17
∴ B = 240

∴ B’s share = Tk. 240
৬০৯.
A can complete a certain work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed by them per minute will be ______
  1. ক
    ক) 0.40
  2. খ
    খ) 0.16
  3. গ
    গ) 0.80
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: খ
খ) 0.16
উত্তর
সঠিক উত্তর: খ
খ) 0.16
খ
ব্যাখ্যা
Question: A can complete a certain work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed by them per minute will be ______

Solution:
A 1 মিনিটে করতে পারে = 1/4 অংশ
B 1 মিনিটে করতে পারে = 1/5 অংশ
C 1 মিনিটে করতে পারে = 1/6 অংশ
D 1 মিনিটে করতে পারে = 1/10 অংশ
E 1 মিনিটে করতে পারে = 1/12 অংশ

প্রতি মিনিটে তারা গড়ে করে = (1/4 + 1/5 + 1/6 + 1/10 + 1/12)/5
= (48/60) × (1/5)
= 4/25
= 0.16 অংশ
৬১০.
The average of five consecutive integers is P. If the next two numbers are added, how shall the average vary?
  1. ক
    increase by 3
  2. খ
    increase by 1
  3. গ
    increase by 2
  4. ঘ
    remain the same
সঠিক উত্তর: খ
increase by 1
উত্তর
সঠিক উত্তর: খ
increase by 1
খ
ব্যাখ্যা
Question: The average of five consecutive integers is P. If the next two numbers are added, how shall the average vary?

Solution:
Let the five consecutive numbers be 5, 6, 7, 8, and 9 respectively.

So, the average is = (5 + 6 + 7 + 8 + 9)/5 = 35/5 = 7
Suppose, the average is, P = 7

If the next two numbers are added, then average is = (5 + 6 + 7 + 8 + 9 + 10 + 11)/7 = 56/7 = 8
So, the new average is, P = 7 + 1

So, the average increased by 1
৬১১.
The average of first five multiples of 3 is -
  1. ক
    ক) 9
  2. খ
    খ) 12
  3. গ
    গ) 3
  4. ঘ
    ঘ) 15
সঠিক উত্তর: ক
ক) 9
উত্তর
সঠিক উত্তর: ক
ক) 9
ক
ব্যাখ্যা
Question: The average of first five multiples of 3 is -

Solution: 
First five multiples of 3 are = 3, 6, 9, 12, 15.

∴ Average = (3 + 6 + 9 + 12 + 15)/5
= 45/5
= 9
৬১২.
2 years ago, the average age of a family of 5 members was 16 years. After a baby is born, the average age of family is the same today. Find the present age of the baby.
  1. ক
    ক) 4
  2. খ
    খ) 6
  3. গ
    গ) 8
  4. ঘ
    ঘ) 8(1/2)
সঠিক উত্তর: খ
খ) 6
উত্তর
সঠিক উত্তর: খ
খ) 6
খ
ব্যাখ্যা

(1) First find total age of 5 members 2 years ago
(2) Present age of 5 members
(3) Total age of 6 members
(4) Age of baby = Total age of 6 members - Present age of 5 members

We know that,
Average = Sum of Quantities/Number of Quantities

1) First calculate total age of 5 members 2 years ago = (Average age of 5 members x number of members)
First calculate total age of 5 members 2 years ago = (16 x 5) = 80 years

2) Calculate the present age of 5 members
2 years ago, their total age was 80 years. Present age can be calculated as follows:
Present age of 5 members = [80 + (2 x 5)] = 90 years

3) Calculate total age of 6 members considering baby = (16 x 6 ) = 96 years

4) Age of baby = (96 – 90)
= 6 years.

৬১৩.
The average of six numbers is 14. The average of four of these numbers is 15. The average of the remaining two numbers is
  1. ক
    4
  2. খ
    8
  3. গ
    12
  4. ঘ
    16
সঠিক উত্তর: গ
12
উত্তর
সঠিক উত্তর: গ
12
গ
ব্যাখ্যা
Question: The average of six numbers is 14. The average of four of these numbers is 15. The average of the remaining two numbers is-

Solution:
6 টি সংখ্যার গড় = 14
6 টি সংখ্যার সমষ্টি = 14 × 6
= 84

4 টি সংখ্যার গড় = 15
4 টি সংখ্যার সমষ্টি = 15 × 4
= 60

2 টি সংখ্যার সমষ্টি = 84 - 60
= 24

2 টি সংখ্যার গড় = 24/2 = 12
৬১৪.
If x, y, and z are said to be the real numbers, then what is the value of (x - y)3 + (y - z)3 + (z - x)3?
  1. ক
    0
  2. খ
    (x - y)
  3. গ
    (x - y)(y - z)(z - x)
  4. ঘ
    3(x - y)(y - z)(z - x)
সঠিক উত্তর: ঘ
3(x - y)(y - z)(z - x)
উত্তর
সঠিক উত্তর: ঘ
3(x - y)(y - z)(z - x)
ঘ
ব্যাখ্যা
Question: If x, y, and z are said to be the real numbers, then what is the value of (x - y)3 + (y - z)3 + (z - x)3?

Solution:
Suppose a = (x - y), b = (y - z), and c = (z - x)
On adding a, b, and c we will get
a + b + c = x - y + y - z + z - x
∴ a + b + c =0

So, a3 + b3 + c3 = 3abc [because if a + b + c = 0, then a3 + b3 + c3 = 3abc]

We can say that (x - y)3 + (y - z)3 + (z - x)3 = 3(x - y)(y - z)(z - x)
৬১৫.
The average age of 80 boys in a class is 15. The average age of a group of 20 boys in the class is 16 and the average age of another 25 boys in the class is 14. What is the average age of the remaining boys in the class?
  1. ক
    ক) 15.14 yrs.
  2. খ
    খ) 16.25 yrs.
  3. গ
    গ) 17.15 yrs.
  4. ঘ
    ঘ) 18.10 yrs.
সঠিক উত্তর: ক
ক) 15.14 yrs.
উত্তর
সঠিক উত্তর: ক
ক) 15.14 yrs.
ক
ব্যাখ্যা
Total ages of 80 boys = 15 × 80 = 1200 yrs.
Total age of20 boys = 16 × 20 = 320 yrs
Total age of 25 boys = 14  × 25 = 350 yrs.

Average age of remaining boys = {1200 - (320 + 350)}/ {80 - (25 + 20)}
                                                   = 530/35
                                                    = 15.14 yrs.
৬১৬.
The average of the first five multiples of 5 is:
  1. ক
    20
  2. খ
    15
  3. গ
    12
  4. ঘ
    10
সঠিক উত্তর: খ
15
উত্তর
সঠিক উত্তর: খ
15
খ
ব্যাখ্যা
Question: The average of the first five multiples of 5 is:

Solution:
We know,
The first five multiples of 5 = 5, 10, 15, 20, 25.

∴ Average = (5 + 10 + 15 + 20 + 25)/5
= 75/5
= 15
৬১৭.
The average of 4 positive integers is 59. The highest integer is 83 and the lowest integer is 29. The difference between the remaining two integers is 28. Which of the following integers is higher of the remaining two integers?
  1. ক
    39
  2. খ
    48
  3. গ
    76
  4. ঘ
    Cannot be determined
সঠিক উত্তর: গ
76
উত্তর
সঠিক উত্তর: গ
76
গ
ব্যাখ্যা
Question: The average of 4 positive integers is 59. The highest integer is 83 and the lowest integer is 29. The difference between the remaining two integers is 28. Which of the following integers is higher of the remaining two integers?

Solution:
Sum of four integers = 59 × 4 = 236
Let the required integers be x and x - 28
Then, x + (x - 28) = 236 - (83 + 29)
⇒ 2x - 28 = 124
⇒ 2x = 152
⇒ x = 76
Hence, required integer = 76
৬১৮.
The average of 3, 5, 7, and x is 6, and the average of 6, 2, x, and y is 7. What are the values of x and y?
  1. ক
    0 and 1
  2. খ
    5 and 7
  3. গ
    9 and 11
  4. ঘ
    15 and 17
  5. ঙ
    2 and 3
সঠিক উত্তর: গ
9 and 11
উত্তর
সঠিক উত্তর: গ
9 and 11
গ
ব্যাখ্যা

Question: The average of 3, 5, 7, and x is 6, and the average of 6, 2, x, and y is 7. What are the values of x and y?

Solution: 
Given that,
The average of 3, 5, 7, and x is 6

Therefore,
6 = (3 + 5 + 7 + x​)/4
⇒ 24 = 15 + x
⇒ x = 24 - 15
∴ x = 9

Therefore,
7 = (6 + 2 + x + y​)/4
⇒ 7 = (6 + 2 + 9 + y​)/4
⇒ 28 = 17 + y
⇒ y = 28 - 17
∴ y = 11

৬১৯.
Which fraction has the smallest value?
  1. ক
    8/(34 × 73)
  2. খ
    27/(35 × 73)
  3. গ
    12/(33 × 73)
  4. ঘ
    2/(33 × 72)
সঠিক উত্তর: ক
8/(34 × 73)
উত্তর
সঠিক উত্তর: ক
8/(34 × 73)
ক
ব্যাখ্যা
Question: Which fraction has the smallest value?

Solution:

ক) 8/(34 × 73) = 8/27,783 = 8/27,783
খ) 27/(35 × 73) = 1/3,087 = 8/24,696
গ) 12/(33 × 73) = 4/3,087 = 8/6,174
ঘ) 2/(33 × 72) = 2/1,323 = 8/5,292

লব একই হলে যে ভগ্নাংশের হর বড় সে ভগ্নাংশটি ছোট
 সঠিক উত্তর: অপশন ক

৬২০.
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 (1/2). The number of pupils in the class is:
  1. ক
    ক) 10
  2. খ
    খ) 20
  3. গ
    গ) 40
  4. ঘ
    ঘ) 73
  5. ঙ
    ঙ) 30
সঠিক উত্তর: গ
গ) 40
উত্তর
সঠিক উত্তর: গ
গ) 40
গ
ব্যাখ্যা

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

৬২১.
While calculating the average of a batsman as 36 in 100 matches that he played, one of the scores 90 was incorrectly noted as 40. The percentage error is -
  1. ক
    ক) 0.5%
  2. খ
    খ) 1.21%
  3. গ
    গ) 1.34%
  4. ঘ
    ঘ) 1.36%
সঠিক উত্তর: ঘ
ঘ) 1.36%
উত্তর
সঠিক উত্তর: ঘ
ঘ) 1.36%
ঘ
ব্যাখ্যা

Correct sum = 36 × 100 + 90 - 40
= 3650
Correct average = 3650/100 = 36.5
Error = (36.5 - 36) = 0.5
∴ Error% = {(0.5/36.5) × 100}% = (100/73)%
= 1.36%

৬২২.
Average of five numbers is 27. If one number is excluded, the average becomes 25. What is the excluded number?
  1. ক
    32.5
  2. খ
    30
  3. গ
    35
  4. ঘ
    40
সঠিক উত্তর: গ
35
উত্তর
সঠিক উত্তর: গ
35
গ
ব্যাখ্যা

Some of five numbers = 5 × 27
After excluding one number, the sum of the remaining four numbers = 4 × 25
Excluded number = (5 × 27) - (4 × 25)
= 135 - 100
= 35.

৬২৩.
Solve it. 4376 + 3209 - 1784 + 97 = 3125 + ?
  1. ক
    2237
  2. খ
    2663
  3. গ
    2769
  4. ঘ
    2773
সঠিক উত্তর: ঘ
2773
উত্তর
সঠিক উত্তর: ঘ
2773
ঘ
ব্যাখ্যা
Question: Solve it. 4376 + 3209 - 1784 + 97 = 3125 + ?

Solution:
4376 + 3209 - 1784 + 97 = 3125 + x
⇒ 7682 - 1784 = 3125 + x
⇒ x = 7682 - 1784 - 3125
⇒ x = 2773

Hence,
The number is 2773
৬২৪.
84 is divided into two parts so that 4 times one part and 12 times the another part are together equal to 544. The parts are?
  1. ক
    58 and 26
  2. খ
    62 and 22
  3. গ
    68 and 16
  4. ঘ
    54 and 30
  5. ঙ
    None of these
সঠিক উত্তর: ক
58 and 26
উত্তর
সঠিক উত্তর: ক
58 and 26
ক
ব্যাখ্যা
Question: 84 is divided into two parts so that 4 times one part and 12 times the another part are together equal to 544. The parts are?

Solution:
let,
The two parts be x and (84 - x)

ATQ,
⇒ 4x + 12(84 - x) = 544
⇒ 4x + 1008 - 12x = 544
⇒ - 8x = 544 - 1008
⇒ - 7x = - 464
⇒ x =  464/8
∴ x = 58

So one part is 58 and other part is = 84 - 58 = 26

∴ The two parts are 58 and 26
৬২৫.
The average (arithmetic mean) of x and y is 20. If z = 5, what is the average of x, y, and z.
  1. ক
    ক) 15
  2. খ
    খ) 12.5
  3. গ
    গ) 10
  4. ঘ
    ঘ) 25/3
সঠিক উত্তর: ক
ক) 15
উত্তর
সঠিক উত্তর: ক
ক) 15
ক
ব্যাখ্যা
x + y = 2 × 20 = 40
x + y + z = 40 + 5 = 45
Average: 45/3 = 15
৬২৬.
  1. ক
    1/2
  2. খ
    2/3
  3. গ
    5/6
  4. ঘ
    3/4
সঠিক উত্তর: ঘ
3/4
উত্তর
সঠিক উত্তর: ঘ
3/4
ঘ
ব্যাখ্যা

Question:

Solution:

৬২৭.
Denominator of a proper fraction is 3 more than the numerator. If the fraction is squared, its denominator will be 51 more than the numerator. The fraction is
  1. ক
    8/11
  2. খ
    3/5
  3. গ
    4/7
  4. ঘ
    7/10
সঠিক উত্তর: ঘ
7/10
উত্তর
সঠিক উত্তর: ঘ
7/10
ঘ
ব্যাখ্যা

Question: Denominator of a proper fraction is 3 more than the numerator. If the fraction is squared, its denominator will be 51 more than the numerator. The fraction is
(Janata RC 2022 অনুযায়ী)

Solution:
ধরি,
ভগ্নাংশের লব = x 
∴ হর = x + 3

প্রশ্নমতে,
(x + 3)2 - x2 = 51
⇒ x2 + 6x + 9 - x2 = 51
⇒ 6x = 51 - 9
⇒ 6x = 42
⇒ x = 30/6
⇒ x = 7

সুতরাং,
ভগ্নাংশটি = x/(x + 3) = 7/(7 + 3) = 7/10

৬২৮.
The average of 10 students is 13 years, if the teacher's age is included, the average increases by two. The age of the teacher is -
  1. ক
    ক) 35 years
  2. খ
    খ) 30 years
  3. গ
    গ) 32 years
  4. ঘ
    ঘ) 33 years
সঠিক উত্তর: ক
ক) 35 years
উত্তর
সঠিক উত্তর: ক
ক) 35 years
ক
ব্যাখ্যা
Question: The average of 10 students is 13 years, if the teacher's age is included, the average increases by two. The age of the teacher is -

Solution: 
Average of 10 students = 13 years
Total age of 10 students
= 10 × 13
= 130 years
When teacher included average become 15 years
Now, total age 10 students and teacher
= 15 × 11 = 165 years
∴ Age of teacher
= 165 - 130
= 35 years
৬২৯.
A student obtained 78, 82, 69, 91 marks in four subjects. What should be the 5th subject's mark to get an average of 80? 
  1. ক
    70
  2. খ
    75
  3. গ
    80
  4. ঘ
    90
সঠিক উত্তর: গ
80
উত্তর
সঠিক উত্তর: গ
80
গ
ব্যাখ্যা

Question: A student obtained 78, 82, 69, 91 marks in four subjects. What should be the 5th subject's mark to get an average of 80? 

Solution:
Desired average = 80
Number of subjects = 5

Total marks needed = 80 × 5 = 400
Sum of the first four subjects obtained = 78 + 82 + 69 + 91 = 320

∴ Required marks in the fifth subject = 400 - 320 = 80

Therefore, the student must obtain 80 in the fifth subject's to achieve an average of 80.

৬৩০.
The sum of seven consecutive odd numbers exceeds four times the largest by 15. Find the average of average of these numbers.
  1. ক
    13
  2. খ
    19
  3. গ
    76
  4. ঘ
    91
সঠিক উত্তর: ক
13
উত্তর
সঠিক উত্তর: ক
13
ক
ব্যাখ্যা

Question: The sum of seven consecutive odd numbers exceeds four times the largest by 15. Find the average of average of these numbers.

Solution:
Let the seven consecutive odd numbers be centered at n,
n - 6, n - 4, n - 2, n, n + 2, n + 4, n + 6

Sum of these consecutive odd numbers = n - 6 + n - 4 + n - 2 + n + n + 2 + n + 4 + n + 6 = 7n
And largest number = n + 6

ATQ,
7n = 4(n + 6) + 15
⇒ 7n = 4n + 24 + 15
⇒ 7n - 4n = 39
⇒ 3n = 39
∴ n = 13

∴ Average = 7n/7 = n = 13

৬৩১.
The average (arithmetic mean) of three numbers is 3x + 2. If one of the numbers is x, what is the average of the other two numbers?
  1. ক
    x + 1
  2. খ
    2x + 2
  3. গ
    4x + 1
  4. ঘ
    4x + 3
  5. ঙ
    8x + 6
সঠিক উত্তর: ঘ
4x + 3
উত্তর
সঠিক উত্তর: ঘ
4x + 3
ঘ
ব্যাখ্যা
Question: The average (arithmetic mean) of three numbers is 3x + 2. If one of the numbers is x, what is the average of the other two numbers?

Solution:
The average (arithmetic mean) of three numbers is 3x + 2
∴ The sum of three numbers is 3(3x + 2) = 9x + 6

If one of the numbers is x
∴ Sum of the other two numbers = 9x + 6 - x = 8x + 6

∴ The average of the other two numbers is = (8x + 6)/2 = 4x + 3
৬৩২.
  1. ক
    1/1000
  2. খ
    1/50
  3. গ
    100
  4. ঘ
    1/10
  5. ঙ
    None of these
সঠিক উত্তর: গ
100
উত্তর
সঠিক উত্তর: গ
100
গ
ব্যাখ্যা
Question:

Solution:
৬৩৩.
If the average of 'p' numbers is 3q2 and the average of 'q' numbers is 3p2, what is the average of the combined (p + q) numbers?
  1. ক
    3pq
  2. খ
    6pq
  3. গ
    3(p2 + q2)
  4. ঘ
    3p2q2
সঠিক উত্তর: ক
3pq
উত্তর
সঠিক উত্তর: ক
3pq
ক
ব্যাখ্যা

Question: If the average of 'p' numbers is 3q2 and the average of 'q' numbers is 3p2, what is the average of the combined (p + q) numbers?

Solution:
দেওয়া আছে, 'p' সংখ্যার গড় = 3q2
∴ p সংখ্যার সমষ্টি = p × 3q2

'q' সংখ্যার গড় = 3p2
∴ 'q' সংখ্যার সমষ্টি = q × 3p2

∴ মোট সমষ্টি = (p × 3q2) + (q × 3p2)
= 3pq2 + 3p2q
= 3pq(q + p)

∴ তাদের গড় = মোট সমষ্টি / (p + q)
= 3pq(p + q) / (p + q)
= 3pq

৬৩৪.
In a set, there are 17 consecutive integers with a maximum value of 8. What is the average of the set?
  1. ক
    ক) -2
  2. খ
    খ) 0
  3. গ
    গ) 2
  4. ঘ
    ঘ) 5
  5. ঙ
    ঙ) None
সঠিক উত্তর: খ
খ) 0
উত্তর
সঠিক উত্তর: খ
খ) 0
খ
ব্যাখ্যা

Let's go backward from 8 to the 17th digit: 8, 7, 6, 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5, -6, -7, -8
The average is = {8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 + 0 + (-1) + (-2) + (-3) + (-4) + (-5) + (-6) + (-7) + (-8)} / 17
= 0/17 = 0

৬৩৫.
The average of 3, 8, 7, and x is 6 and the average of 19, 2, 7, x and y is 9. What is the value of y?
  1. ক
    18
  2. খ
    16
  3. গ
    15
  4. ঘ
    11
সঠিক উত্তর: ঘ
11
উত্তর
সঠিক উত্তর: ঘ
11
ঘ
ব্যাখ্যা
Question: The average of 3, 8, 7, and x is 6 and the average of 19, 2, 7, x and y is 9. What is the value of y? 

Solution: 
Given that
average of 3, 8, 7, x is 6

Therefore,
6 = (3 + 8 + 7 + x​)/4
⇒ 24 = 18 + x
⇒ x = 24 - 18
∴ x = 6

Therefore,
9 = (19 + 2 + 7 + x + y​)/5
⇒ 45 = 28 + 6 + y
⇒ y = 45 - 34 
∴ y = 11
৬৩৬.
The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Tk. 4000. The total price of 12 chairs and 3 tables is-
  1. ক
    Tk. 3500 
  2. খ
    Tk. 3750 
  3. গ
    Tk. 3840 
  4. ঘ
    Tk. 3900
সঠিক উত্তর: ঘ
Tk. 3900
উত্তর
সঠিক উত্তর: ঘ
Tk. 3900
ঘ
ব্যাখ্যা

Question: The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Tk. 4000. The total price of 12 chairs and 3 tables is-

Solution:
Let the cost of a chair and a table are x and y respectively.
Then,
10x = 4y
⇒ y = (10/4)x = 5x/2
∴ y = 5x/2 .......(1)
And,
15x + 2y = 4000
⇒ 15x + 2(5x/2) = 4000
⇒ 20x = 4000
⇒ x = 4000/20
∴ x = 200

From (1), 
y = 5x/2 = (5 × 200)/2 = 500
∴ y = 500

Hence, the cost of 12chairs and 3tables is,
= 12x + 3y
= (2400 + 1500)
= 3900

So the total price of 12 chairs and 3 tables is Tk. 3900.

৬৩৭.
In Rakib's opinion, his weight is greater than 65 kg but less than 72 kg. His father does not agree with Rakib, and he thinks that Rakib's weight is greater than 60 kg but less than 70 kg. His sister's view is that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of the different possible weights of Rakib?
  1. ক
    60
  2. খ
    65
  3. গ
    67
  4. ঘ
    54
সঠিক উত্তর: গ
67
উত্তর
সঠিক উত্তর: গ
67
গ
ব্যাখ্যা
Question: In Rakib's opinion, his weight is greater than 65 kg but less than 72 kg. His father does not agree with Rakib, and he thinks that Rakib's weight is greater than 60 kg but less than 70 kg. His sister's view is that his weight cannot be greater than 68 kg. If all are correct in their estimation, what is the average of the different possible weights of Rakib?

Solution:
Let Rakib's weight by X kg.
According to Rakib: 65 < X < 72
According to Rakib's father: 60 < X < 70.
According to Rakib's sister: X <= 68

The different possible weights of Rakib or the values that satisfy all the above conditions are 66, 67 and 68.
So, the Average of different possible weights of Rakib = (66 + 67 + 68)/3
= 201/3
= 67 kg.
৬৩৮.
The average age of 8 children of a family is 12 yr. If the age of 7 children is 12, 8, 14, 11, 9, 13 and 15 yr, then the age of 8th child will be-
  1. ক
    12 yr
  2. খ
    14 yr
  3. গ
    13 yr
  4. ঘ
    15 yr
  5. ঙ
    None of above
সঠিক উত্তর: খ
14 yr
উত্তর
সঠিক উত্তর: খ
14 yr
খ
ব্যাখ্যা

Total age of 8 children = 8 x 12 = 96 yr
Total age of 7 children = 12 + 8 + 14 + 11 + 9 + 13 + 15 = 82
The age of 8th child = 96 - 82 = 14 yr

৬৩৯.
The average price of three items of furniture is Tk. 25000. If their prices are in the ratio 3 : 5 : 7, what is the price of the cheapest item?
  1. ক
    ক) 5000 Tk.
  2. খ
    খ) 15000 Tk.
  3. গ
    গ) 20000 Tk.
  4. ঘ
    ঘ) 25000 Tk.
সঠিক উত্তর: খ
খ) 15000 Tk.
উত্তর
সঠিক উত্তর: খ
খ) 15000 Tk.
খ
ব্যাখ্যা
Question: The average price of three items of furniture is Tk. 25000. If their prices are in the ratio 3 : 5 : 7, what is the price of the cheapest item?

Solution:
The average price of three items of furniture is Rs. 25000.
total price = (25000 × 3) = 75000
their prices are in the ratio 3 : 5 : 7

∴ the price of the cheapest item is = 75000 × 3/15
= 15000 tk
৬৪০.
Find the average of the square of first 5 consecutive odd numbers starting from 1 to 9, where the last odd number is 9.
  1. ক
    33
  2. খ
    22
  3. গ
    16
  4. ঘ
    11
সঠিক উত্তর: ক
33
উত্তর
সঠিক উত্তর: ক
33
ক
ব্যাখ্যা
Question: Find the average of the square of first 5 consecutive odd numbers starting from 1 to 9, where the last odd number is 9.

Solution:
The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by = X(X + 2)/3
Here,
X=9
So, average = 9(9 + 2)/3
= (9 × 11)/3
= 99/3
= 33
৬৪১.
The captain of a cricket team of 11 members is 26 years old, and the wicket-keeper is three years older than the captain. If the ages of captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?
  1. ক
    18 Years
  2. খ
    20 Years
  3. গ
    23 Years
  4. ঘ
    26 Years
  5. ঙ
    None of these
সঠিক উত্তর: গ
23 Years
উত্তর
সঠিক উত্তর: গ
23 Years
গ
ব্যাখ্যা
Question: The captain of a cricket team of 11 members is 26 years old, and the wicket-keeper is three years older than the captain. If the ages of captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?

Solution:
Let, the average age of the whole team by = x years.
Total age of the whole team = 11x years
Age of the captain = 26 years
Age of the wiket-keeper = (26 + 3) = 29 years

The average age of the remaining players after excluding the ages of captain and wicketkeeper = x - 1
∴ Total age of the players without the ages of captain and wicketkeeper = 9(x - 1)

Now,
11x - (26 + 29) = 9(x - 1)
⇒ 11x - 55 = 9x - 9
⇒ 11x - 9x = - 9 + 55
⇒ 2x = 46
∴ x = 23 Years.
৬৪২.
Find the average of first 40 natural integer numbers.
  1. ক
    19.5
  2. খ
    20.5
  3. গ
    21.5
  4. ঘ
    22.5
সঠিক উত্তর: খ
20.5
উত্তর
সঠিক উত্তর: খ
20.5
খ
ব্যাখ্যা
প্রশ্ন: Find the average of first 40 natural integer numbers.

সমাধান:
আমরা জানি,
n সংখ্যক স্বাভাবিক সংখ্যার সমষ্টি = n(n + 1)/2
∴ প্রথম 40 টি স্বাভাবিক সংখ্যার যোগফল = 40 × (40 + 1)/2
= (40 × 41)/2
= 820

∴ গড় = 820/40
= 20.5
৬৪৩.
The average of 7 consecutive numbers is 20. The largest of these number is:
  1. ক
    ক) 21
  2. খ
    খ) 22
  3. গ
    গ) 23
  4. ঘ
    ঘ) 24
  5. ঙ
    ঙ) 25
সঠিক উত্তর: গ
গ) 23
উত্তর
সঠিক উত্তর: গ
গ) 23
গ
ব্যাখ্যা

Let the number 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.

৬৪৪.
The average of six numbers is A and the average of three of these is B. If the average of the remaining three is C, then which one is correct?
  1. ক
    A = B + C
  2. খ
    3A = 2(B + C)
  3. গ
    A = 2B + 3C
  4. ঘ
    2A = B + C
সঠিক উত্তর: ঘ
2A = B + C
উত্তর
সঠিক উত্তর: ঘ
2A = B + C
ঘ
ব্যাখ্যা

Question: The average of six numbers is A and the average of three of these is B. If the average of the remaining three is C, then which one is correct?

Solution:
Total sum of six numbers = 6A
Total sum of three numbers = 3B
Total sum of the other numbers = 3C

Now,
6A = 3B + 3C
or, A = 3(B + C)/6
or. A = (B + C)/2
∴ 2A = B + C

৬৪৫.
Find the average of all the numbers between 10 and 50 which are divisible by 4.
  1. ক
    28
  2. খ
    30
  3. গ
    32
  4. ঘ
    34
সঠিক উত্তর: খ
30
উত্তর
সঠিক উত্তর: খ
30
খ
ব্যাখ্যা
Question: Find the average of all the numbers between 10 and 50 which are divisible by 4.

Solution:
Numbers between 10 and 50 divisible by 4 are = 12, 16, 20, 24, 28, 32, 36, 40, 44, 48.

Required average = (12 + 16 + 20 + 24 + 28 + 32 + 36 + 40 + 44 + 48​)/10
= 300/10
= 30
৬৪৬.
The average marks of 13 papers is 40. The average marks of the first 7 papers are 42 and that of the last seven papers is 35. Find the marks obtained in the 7th paper.
  1. ক
    23
  2. খ
    38
  3. গ
    19
  4. ঘ
    57
সঠিক উত্তর: গ
19
উত্তর
সঠিক উত্তর: গ
19
গ
ব্যাখ্যা
Question: The average marks of 13 papers is 40. The average marks of the first 7 papers are 42 and that of the last seven papers is 35. Find the marks obtained in the 7th paper.

Solution:
The average of 13 papers is 40,
so the sum = 13 × 40 = 520

The average of first 7 papers is 42,
so the sum will be = 7 × 42 = 294

The average of last 7 papers is 35,
so the sum will be = 7×35 = 245

So, the marks obtained in the 7th paper will be = 539 - 520 = 19
৬৪৭.
Which of the following fractions is the largest?
  1. ক
    5/6
  2. খ
    11/14
  3. গ
    12/15
  4. ঘ
    17/21
সঠিক উত্তর: ক
5/6
উত্তর
সঠিক উত্তর: ক
5/6
ক
ব্যাখ্যা
Question: Which of the following fractions is the largest?

Solution:
A. 5/6 = 0.83
B. 11/14 = 0.79
C. 12/15 = 0.8
D. 17/21 = 0.81

So, 5/6 = 0.83 is the largest.
৬৪৮.
A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd?
  1. ক
    2
  2. খ
    3
  3. গ
    4
  4. ঘ
    5
  5. ঙ
    6
সঠিক উত্তর: খ
3
উত্তর
সঠিক উত্তর: খ
3
খ
ব্যাখ্যা
Question: A herd of cows gives 4 litres of milk each day. But each cow gives one-third of total milk each day. They give 24 litres milk in six days. How many cows are there in the herd?

Solution:
A herd of cows gives 4 litres of milk each day.
Each cow gives one-third of total milk each day = 1/3 of 4
Therefore, each cow gives 4/3 of milk each day.
Total no. of cows = 4 ÷  (4/3)
= 4 × (3/4)
= 3

Therefore there are 3 cows in the herd.
৬৪৯.
When a 60 kg member exits a group of 50, the average weight of the remaining 49 rises by 0.3 kg. Determine the new average weight of those left.
  1. ক
    72 kg
  2. খ
    75 kg
  3. গ
    65 kg
  4. ঘ
    60 kg
সঠিক উত্তর: খ
75 kg
উত্তর
সঠিক উত্তর: খ
75 kg
খ
ব্যাখ্যা

Question: When a 60 kg member exits a group of 50, the average weight of the remaining 49 rises by 0.3 kg. Determine the new average weight of those left.

Solution:
let,
The average weight of 49 people is x kg
Total weight of 49 people = 49x
Total weight of 50 people = 49x + 60

ATQ,
50(x - 0.3) = (49x + 60)
⇒ 50x - 15 = 49x + 60
⇒ 50x - 49x = 60 + 15
∴ x = 75

∴ the new average weight of the remaining 49 people is 75 kg.

৬৫০.
The sum of the weights of A and B is 80 kg. Half of the weight of A is equal to 5/6 times the weight og B. Find the weight of B.
  1. ক
    40 Kg
  2. খ
    30 Kg
  3. গ
    25 Kg
  4. ঘ
    20 Kg
সঠিক উত্তর: খ
30 Kg
উত্তর
সঠিক উত্তর: খ
30 Kg
খ
ব্যাখ্যা
Question: The sum of the weights of A and B is 80 kg. Half of the weight of A is equal to 5/6 times the weight og B. Find the weight of B.

Solution: 
A + B = 80 and
A/2 = 5B/6
∴ A = 5B/3

A + B = 80
or, 5B/3 + B = 80
or, 8B/3 = 80
∴ B = 30 Kg
৬৫১.
The average age of three boys is 20 years and their age ratio is 4 : 5 : 6. What is the age of the youngest boy?
  1. ক
    ক) 12 years
  2. খ
    খ) 15 years
  3. গ
    গ) 16 years
  4. ঘ
    ঘ) 18 years
সঠিক উত্তর: গ
গ) 16 years
উত্তর
সঠিক উত্তর: গ
গ) 16 years
গ
ব্যাখ্যা
Question: The average age of three boys is 20 years and their age ratio is 4 : 5 : 6. What is the age of the youngest boy?

Solution:
Sum of the three boy's age = 20 × 3 = 60 years
So, age of the youngest boy is = 60 × (4/15) = 16 years
৬৫২.
The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
  1. ক
    ক) 0
  2. খ
    খ) 1
  3. গ
    গ) 10
  4. ঘ
    ঘ) 19
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: ঘ
ঘ) 19
উত্তর
সঠিক উত্তর: ঘ
ঘ) 19
ঘ
ব্যাখ্যা

Average of 20 numbers = 0
∴ Sum of 20 numbers (0 × 20) = 0
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a)

৬৫৩.
If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average (arithmetic mean) annual increase in the index over this period?
  1. ক
    (x + 100)/18
  2. খ
    x/18
  3. গ
    (100 - x)/18
  4. ঘ
    (x - 100)/18
  5. ঙ
    (100x)/18
সঠিক উত্তর: ঘ
(x - 100)/18
উত্তর
সঠিক উত্তর: ঘ
(x - 100)/18
ঘ
ব্যাখ্যা
Question: If the consumer price index for a sample of goods and services purchased in Dallas rose from 100 at the end of 1967 to x at the end of 1985, what was the average (arithmetic mean) annual increase in the index over this period?

Solution:
consumer price index at End Of 1967 = 100
consumer price index at End Of 1985 = x
It says that CPI rose which means x > 100

Total Number of Years = 1985 - 1967 = 18 Years

Average = Total Gain/No. Of Years
Average = (x - 100)/18
৬৫৪.
If the average of 6, 15, 22, and 'x' is 15, what is the value of 'x'?
  1. ক
    ক) 24
  2. খ
    খ) 17
  3. গ
    গ) 23
  4. ঘ
    ঘ) 19
সঠিক উত্তর: খ
খ) 17
উত্তর
সঠিক উত্তর: খ
খ) 17
খ
ব্যাখ্যা
Question: If the average of 6, 15, 22, and 'x' is 15, what is the value of 'x'?

Solution:
According to the question,
(6 + 15 + 22 + x) / 4 = 15
⇒ 43 + x  = 60
⇒ x  = 17
৬৫৫.
The mean of the five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Then the mean of the first three observations is?
  1. ক
    9
  2. খ
    12
  3. গ
    8
  4. ঘ
    15
সঠিক উত্তর: ক
9
উত্তর
সঠিক উত্তর: ক
9
ক
ব্যাখ্যা

Question: The mean of the five observations x, x + 2, x + 4, x + 6, x + 8 is 11. Then the mean of the first three observations is?

Solution:
Given that,
The mean of the five observations = 11
Number of observations = 5
The observations = x, x + 2, x + 4, x + 6, x + 8

We know, 
Mean or Average = Sum of observations ÷ Number of observations
Sum of observations = x + x + 2 + x + 4 + x + 6 + x + 8
⇒ 5x + 20 = 5(x + 4)

∴ Mean = [5(x + 4)] ÷ 5
⇒ 11 = x + 4
⇒ x = 7

∴ First three observations,
x = 7, x + 2 = 9, x + 4 = 11

∴ Mean of first three = (7 + 9 + 11)/ 3
= 27/3
= 9

৬৫৬.
A box contains a total of 300 coins, some worth 25 paise and others worth 50 paise. If the total value of these coins is Tk 120, how many 50 paise coins are there?
  1. ক
    200
  2. খ
    180
  3. গ
    160
  4. ঘ
    140
সঠিক উত্তর: খ
180
উত্তর
সঠিক উত্তর: খ
180
খ
ব্যাখ্যা
Question: A box contains a total of 300 coins, some worth 25 paise and others worth 50 paise. If the total value of these coins is Tk 120, how many 50 paise coins are there?

Solution:
Let the number of 50 paise coins be = x
So, the number of 25 paise coins is = 300 - x

According to the question,
50x + {25 × (300 - x)} = 120 × 100
⇒ 50x + 7500 - 25x  = 12000
⇒ 25x = 4500
∴ x = 180
৬৫৭.
The average of four numbers 13, 27, 35, and X is 25. Find the number X.
  1. ক
    ক) 20
  2. খ
    খ) 25
  3. গ
    গ) 30
  4. ঘ
    ঘ) 35
  5. ঙ
    ঙ) None of above
সঠিক উত্তর: খ
খ) 25
উত্তর
সঠিক উত্তর: খ
খ) 25
খ
ব্যাখ্যা

Average = (13 + 27 + 35 + X)/4 = 25
Or, X + 75 = 100
So, X = 25

৬৫৮.
The average weight of 47 balls is 4 g. If the weight of the bag (in which the balls are kept) be included; the calculated average weight per ball increases by 0.3 g. What is the weight of the bag?
  1. ক
    14.1 g
  2. খ
    16.1 g
  3. গ
    18.1 g
  4. ঘ
    30 g
সঠিক উত্তর: ক
14.1 g
উত্তর
সঠিক উত্তর: ক
14.1 g
ক
ব্যাখ্যা
Question: The average weight of 47 balls is 4 g. If the weight of the bag (in which the balls are kept) be included; the calculated average weight per ball increases by 0.3 g. What is the weight of the bag?

Solution:
Total increased weight
= 0.3 × 47
= 14.1 g
৬৫৯.
In June a baseball team that played 60 games had won 30% of its games played. After a phenomenal winning streak this team raised its average to 50%. How many games must the team have won in a row to attain this average?
  1. ক
    ক) 30
  2. খ
    খ) 45
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
সঠিক উত্তর: ঘ
ঘ) 24
উত্তর
সঠিক উত্তর: ঘ
ঘ) 24
ঘ
ব্যাখ্যা

Let, Additional match = x
Now,
(30% of 60) + x = 50% of (60+x)
⇒ 18 + x = 30 + 0.5x
⇒ 0.5x = 12
⇒ x = 24

৬৬০.
Given that (12 + 22 + 32 + .......... + 102) = 385, then the value of (22 + 42 + 62 + .......... + 202) is equal to = ?
  1. ক
    1480
  2. খ
    1520
  3. গ
    1540
  4. ঘ
    None of these
সঠিক উত্তর: গ
1540
উত্তর
সঠিক উত্তর: গ
1540
গ
ব্যাখ্যা
Question: Given that (12 + 22 + 32 + .......... + 102) = 385, then the value of (22 + 42 + 62 + .......... + 202) is equal to = ?

Solution:
(22 + 42 + 62 + .......... + 202)
= (1 × 2)2 + (2 × 2)2 + (3 × 2)2 + ............. + (2 × 10)2
= (12 × 22) + (22 × 22) + (32 × 22) ............ + (22 × 102)
= 22(12 + 22 + 32 + .......... + 102)
= 4 × 385 [Putting the value (12 + 22 + 32 + .......... + 102) = 385]
= 1540
৬৬১.
A teacher accidentally entered a student's marks as 82 instead of 67. Due to this error, the class average increased by 0.3 marks. Find the number of students in the class.
  1. ক
    50
  2. খ
    55
  3. গ
    57
  4. ঘ
    60
  5. ঙ
    62
সঠিক উত্তর: ক
50
উত্তর
সঠিক উত্তর: ক
50
ক
ব্যাখ্যা
Question: A teacher accidentally entered a student's marks as 82 instead of 67. Due to this error, the class average increased by 0.3 marks. Find the number of students in the class.

Solution:
Let the number of students in the class be x.
Total increase in marks = x × 0.3
According to the question
⇒ x × 0.3 = (82 - 67)
⇒ x × 0.3 = 15
⇒ x = 15/0.3
⇒ x = 50
৬৬২.
The average of a class of 39 students is 15 years. If the age of the teacher is included, then the average increase's by 3 months. Find the age of the teacher.
  1. ক
    ক) 25 years
  2. খ
    খ) 30 years
  3. গ
    গ) 32 years
  4. ঘ
    ঘ) 40 years
সঠিক উত্তর: ক
ক) 25 years
উত্তর
সঠিক উত্তর: ক
ক) 25 years
ক
ব্যাখ্যা
Question: The average of a class of 39 students is 15 years. If the age of the teacher is included, then the average increase's by 3 months. Find the age of the teacher.

Solution:
Total age of 39 persons  = 39 × 15 = 585 years
The average age of 40 persons = 15 years + 3 months = 15 + (3/12) = 61/4 years

Total age of 40 person = (61/4) × 40 = 610 years

So, the age of the teacher = 610 - 585 = 25 years
৬৬৩.
The average of four consecutive even numbers is 27. Find the smallest of these numbers.
  1. ক
    24
  2. খ
    30
  3. গ
    20
  4. ঘ
    40
সঠিক উত্তর: ক
24
উত্তর
সঠিক উত্তর: ক
24
ক
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 24.

৬৬৪.
(√6 + √6)2 = ?
  1. ক
    24
  2. খ
    12
  3. গ
    36
  4. ঘ
    48
সঠিক উত্তর: ক
24
উত্তর
সঠিক উত্তর: ক
24
ক
ব্যাখ্যা

Question: (√6 + √6)2 = ?

Solution: 
Given that, 
(√6 + √6)2
= (2√6)2
= 22 × (√6)2
= 4 × 6
= 24

৬৬৫.
The average of a set of 12 numbers, which includes 34 is A. If 34 is removed from the set and 38 is included to the set. What is the average of new set of numbers in terms of A?
  1. ক
    A + (2/3)
  2. খ
    A + (1/5)
  3. গ
    A + (1/3)
  4. ঘ
    None of the above
সঠিক উত্তর: গ
A + (1/3)
উত্তর
সঠিক উত্তর: গ
A + (1/3)
গ
ব্যাখ্যা
Question: The average of a set of 12 numbers, which includes 34 is A. If 34 is removed from the set and 38 is included to the set. What is the average of new set of numbers in terms of A?
(১২টি সংখ্যার একটি সেটের গড় A, যেখানে ৩৪ রয়েছে। যদি ৩৪ বাদ দিয়ে ৩৮ যুক্ত করা হয়, তাহলে নতুন গড় কত হবে A-এর হিসেবে?)

Solution:
12টি সংখ্যার সমষ্টি = 12A - 34 + 38
= 12A + 4

12টি সংখ্যার গড় = (12A + 4)/12
= (12A/12) + (4/12)
= A + (1/3)
৬৬৬.
The average of 10 numbers is 12. If 5 is subtracted from each of 6 of these numbers, what is the new average?
  1. ক
    8.5
  2. খ
    9
  3. গ
    11.25
  4. ঘ
    7
সঠিক উত্তর: খ
9
উত্তর
সঠিক উত্তর: খ
9
খ
ব্যাখ্যা
Question: The average of 10 numbers is 12. If 5 is subtracted from each of 6 of these numbers, what is the new average?

Solution:
দেওয়া আছে,
10 টি নম্বরের গড় = 12
∴ 10 টি নম্বরের সমষ্টি = (10 × 12) = 120

10 টি নম্বরের মধ্যে 6 টি নম্বরের প্রতিটি থেকে 5 বিয়োগ করা হলে নতুন সমষ্টি,
= 120 - (6 × 5)
= 120 - 30
= 90

সুতরাং 10 টি সংখ্যার নতুন গড় = 90/10 = 9
৬৬৭.
Labonno walks 5 miles from point A to point B in one hour, then bicycles back to point A along the same route at 15 miles per hour. Benu makes the same round trip but does so at half of Labonno's average speed. How many minutes does Benu spend on his round trip?
  1. ক
    80 minutes 
  2. খ
    100 minutes 
  3. গ
    120 minutes
  4. ঘ
    160 minutes 
সঠিক উত্তর: ঘ
160 minutes 
উত্তর
সঠিক উত্তর: ঘ
160 minutes 
ঘ
ব্যাখ্যা
Question: Labonno walks 5 miles from point A to point B in one hour, then bicycles back to point A along the same route at 15 miles per hour. Benu makes the same round trip but does so at half of Labonno's average speed. How many minutes does Benu spend on his round trip?

Solution: 
বাইসাইকেলে লাবণ্যের ফিরতে সময় লাগে = 5/15 = 1/3 hr = 20 min 

লাবণ্যের গড় বেগ = (5 + 5)/(60 + 20) = 10/80 miles/min 
= 1/8 miles/min 

বেণুর গড় বেগ = 1/16 miles/min 

10 মাইল যেতে বেণুর সময় লাগবে = 10 × 16 min 
= 160 min 
৬৬৮.
If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?
  1. ক
    44
  2. খ
    48
  3. গ
    50
  4. ঘ
    52
  5. ঙ
    None
সঠিক উত্তর: খ
48
উত্তর
সঠিক উত্তর: খ
48
খ
ব্যাখ্যা
Question: If the average of 5 positive integers is 40 and the difference between the largest and the smallest of these 5 numbers is 10, what is the maximum value possible for the largest of these 5 integers?

Solution:
Since average is 40, Sum of all 5 numbers = 40 × 5 = 200
Let's call the largest number L and smallest number S
We know, L - S = 10
So, S = L - 10

The other 3 numbers must be Greater than or equal to S (L - 10); Less than or equal to L and Must be integers.
To maximize L, the other 3 numbers should be as small as possible while staying within constraints
They cannot be smaller than S (L - 10); So all 3 middle numbers must be (L - 10)

ATQ,
L + (L - 10) + 3(L - 10) = 200
⇒ L + (L - 10) + 3L - 30 = 200
⇒ 5L - 40 = 200
⇒ 5L = 240
∴ L = 48
৬৬৯.
The average temperature on Wednesday, Thursday and Friday was 25°. The average temperature on Thursday, Friday and Saturday was 24°. If the temperature on Saturday was 27°, what was the temperature on Wednesday?
  1. ক
    21°
  2. খ
    27°
  3. গ
    30°
  4. ঘ
    32°
সঠিক উত্তর: গ
30°
উত্তর
সঠিক উত্তর: গ
30°
গ
ব্যাখ্যা
Question: The average temperature on Wednesday, Thursday and Friday was 25°. The average temperature on Thursday, Friday and Saturday was 24°. If the temperature on Saturday was 27°, what was the temperature on Wednesday?

Solution:
The total temperature on Wednesday, Thursday and Friday was 25° × 3 = 75°
The total temperature on Thursday, Friday and Saturday was 24° × 3 = 72°
 
Hence, the difference between the temperature on Wednesday and Saturday = 3°

If Saturday temperature =27°,
Then Wednesday's temperature = 27 + 3 = 30°
৬৭০.
In a company of only 20 employees, 10 employees make Tk. 80,000/yr, 6 employees make Tk.150,000/yr, and the 4 highest-paid employees all make the same amount.  If the average annual salary for the 20 employees is Tk. 175,000/yr, then what is the annual salary of each highest-paid employee?
  1. ক
    Tk. 350000
  2. খ
    Tk. 400000
  3. গ
    Tk. 450000
  4. ঘ
    Tk. 500000
সঠিক উত্তর: গ
Tk. 450000
উত্তর
সঠিক উত্তর: গ
Tk. 450000
গ
ব্যাখ্যা
Question: In a company of only 20 employees, 10 employees make Tk. 80,000/yr, 6 employees make Tk.150,000/yr, and the 4 highest-paid employees all make the same amount.  If the average annual salary for the 20 employees is Tk. 175,000/yr, then what is the annual salary of each highest-paid employee?

Solution: 
Total salary = 20 × 175,000
= 3500000 taka 

Salary of 4 highest-paid employees = 3500000 - 10 × 80000 - 6 × 150000 
= 3500000 - 800000 - 900000
= 1800000

Each gets = 1800000/4
= Tk. 450000
৬৭১.
A certain factory employed 600 men and 400 women and the average wage was TK. 25.50 per day, If a woman got TK. 5 less than a man, then what are their daily wages?
  1. ক
    ক) m:25.50 w:27.50
  2. খ
    খ) m:27.50 w:22.50
  3. গ
    গ) m:26.50 w:27.50
  4. ঘ
    ঘ) m: 24.50 w:26.50
  5. ঙ
    ঙ) m:26.00 w:27.00
সঠিক উত্তর: খ
খ) m:27.50 w:22.50
উত্তর
সঠিক উত্তর: খ
খ) m:27.50 w:22.50
খ
ব্যাখ্যা

Then, daily wage of a woman = TK. (x - 5).
Now,
600x + 400 (x - 5) = 25.50 &times; (600 + 400)
=> 1000x = 27500
=> x = 27.50.
Man's daily wages = TK. 27.50;
Woman's daily wages = (x - 5)
= TK. 22.50.

৬৭২.
The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is-
  1. ক
    ক) 4
  2. খ
    খ) 8
  3. গ
    গ) 16
  4. ঘ
    ঘ) Data inadequate
সঠিক উত্তর: খ
খ) 8
উত্তর
সঠিক উত্তর: খ
খ) 8
খ
ব্যাখ্যা

The average of the remaining two numbers is = (8×14 - 6×16)/2 = 8

৬৭৩.
If a : b = 4 : 3 then what is the value of (3a + 2b)/(3a - 2b).
  1. ক
    1
  2. খ
    6
  3. গ
    3
  4. ঘ
    2
সঠিক উত্তর: গ
3
উত্তর
সঠিক উত্তর: গ
3
গ
ব্যাখ্যা
Question: If a : b = 4 : 3 then what is the value of (3a + 2b)/(3a - 2b).

Solution: 
a : b = 4 : 3
a/b = 4/3
a = 4b/3

given,
(3a + 2b)/(3a - 2b)
= (4b + 2b)/(4b - 2b)
= 6b/2b
= 3
৬৭৪.
The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is :
  1. ক
    ক) 35
  2. খ
    খ) 45
  3. গ
    গ) 55
  4. ঘ
    ঘ) 120
সঠিক উত্তর: গ
গ) 55
উত্তর
সঠিক উত্তর: গ
গ) 55
গ
ব্যাখ্যা
Question: The average of five numbers is 27. If one number is excluded, the average becomes 20. The excluded number is :

Solution:
The average of five numbers is 27
The sum of five numbers is (27 × 5)
= 135

let, the excluded number is x

so,
(135 - x)/4 = 20
⇒ 135 - x = 80
⇒ x = 135 - 80
∴ x = 55
৬৭৫.
A batsman scores 72 runs in the 18th innings and increases his average by 2. What is his average after the 18th innings?
  1. ক
    38
  2. খ
    35
  3. গ
    40
  4. ঘ
    32
সঠিক উত্তর: ক
38
উত্তর
সঠিক উত্তর: ক
38
ক
ব্যাখ্যা

Question: A batsman scores 72 runs in the 18th innings and increases his average by 2. What is his average after the 18th innings?

Solution:
ধরি,
17 তম ইনিংসে তার গড় রান = x 
∴ মোট রান = 17x

18 তম ইনিংসে 72 রান করায় তার গড় 2 রান বৃদ্ধি পায়।
∴ নতুন গড় = x + 2
∴ মোট রান = 18(x + 2)

প্রশ্নমতে,
17x + 72 = 18(x + 2)
⇒ 17x + 72 = 18x + 36
⇒ 18x - 17x = 72 - 36
⇒ x = 36

∴ 18 তম ইনিংস পর নতুন গড় = x + 2
= 36 + 2 = 38 রান

৬৭৬.
If 1/2 of the money in a certain trust fund was invested in stocks, 1/4 in bonds, 1/5 in a mutual fund, and the remaining Tk. 10000 in a government certificate, what was the total amount of the trust fund?
  1. ক
    Tk. 100000
  2. খ
    Tk. 150000
  3. গ
    Tk. 200000
  4. ঘ
    Tk. 500000
  5. ঙ
    Tk. 2000000
সঠিক উত্তর: গ
Tk. 200000
উত্তর
সঠিক উত্তর: গ
Tk. 200000
গ
ব্যাখ্যা
Question: If 1/2 of the money in a certain trust fund was invested in stocks, 1/4 in bonds, 1/5 in a mutual fund, and the remaining Tk. 10000 in a government certificate, what was the total amount of the trust fund?

Solution:
If we let T = the total amount of the trust fund, we can create the following equation:

(1/2)T + (1/4)T + (1/5)T + 10000 = T
Multiplying the entire question by 20 gives us:
⇒ 10T + 5T + 4T + 200000 = 20T
⇒ 19T + 200000 = 20T
∴ 200000 = T
৬৭৭.
The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and ?
  1. ক
    15
  2. খ
    20
  3. গ
    25
  4. ঘ
    30
সঠিক উত্তর: ক
15
উত্তর
সঠিক উত্তর: ক
15
ক
ব্যাখ্যা
Question: The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and ?

Solution:
The average of 10, 30, and 50 is = (10 + 30 + 50)/3 = 30
The average of 20, 40 and x must be 30 - 5 = 25

ATQ,
(20 + 40 + x)/3 = 25
⇒ 60 + x = 75
∴ x = 15
৬৭৮.
In a parking lot, there are bicycles and cars. There are 35 vehicles and a total of 96 wheels. How many bicycles are there?
  1. ক
    22
  2. খ
    28
  3. গ
    13
  4. ঘ
    7
সঠিক উত্তর: ক
22
উত্তর
সঠিক উত্তর: ক
22
ক
ব্যাখ্যা
Question: In a parking lot, there are bicycles and cars. There are 35 vehicles and a total of 96 wheels. How many bicycles are there?

Solution:
বাইসাইকেলের সংখ্যা = x
গাড়ির সংখ্যা = y

প্রশ্নমতে,
মোট যানবাহন, x + y = 35 ........(১)
এবং,
মোট চাকা, 2x + 4y = 96 .......(২) [একটি bicycle-এর ২টি এবং একটি car-এর ৪টি চাকা থাকে]

এখন,
(১)⇒ x + y = 35
⇒ y = 35 - x ......(৩)

y এর মান (২) নং এ বসিয়ে পাই,
⇒ 2x + 4(35 - x) = 96
⇒ 2x + 140 - 4x = 96
⇒ - 2x = 96 - 140
⇒ - 2x = - 44
⇒ x = - 44/- 2
∴ x = 22

∴ 22টি বাইসাইকেল আছে।
৬৭৯.
Denominator of a proper fraction is 3 more than the numerator. If the fraction is squared, its denominator will be 39 more than the numerator. The fraction is
  1. ক
    5/8
  2. খ
    4/7
  3. গ
    2/5
  4. ঘ
    8/11
সঠিক উত্তর: ক
5/8
উত্তর
সঠিক উত্তর: ক
5/8
ক
ব্যাখ্যা
Question: Denominator of a proper fraction is 3 more than the numerator. If the fraction is squared, its denominator will be 39 more than the numerator. The fraction is

Solution:
ধরি,
ভগ্নাংশের লব = x 
∴ হর = x + 3

প্রশ্নমতে,
(x + 3)2 - x2 = 39
⇒ x2 + 6x + 9 - x2 = 39
⇒ 6x = 39 - 9
⇒ 6x = 30 
⇒ x = 30/6
⇒ x = 5

সুতরাং,
ভগ্নাংশটি = x/(x + 3) = 5/(5 + 3) = 5/8
৬৮০.
In a class average age of 15 boys is 11. If 5 boys each of age 12 years are added, what would be the new average?
  1. ক
    20 years
  2. খ
    10.5 years
  3. গ
    11.25 years
  4. ঘ
    23 years
সঠিক উত্তর: গ
11.25 years
উত্তর
সঠিক উত্তর: গ
11.25 years
গ
ব্যাখ্যা
Question: In a class average age of 15 boys is 11. If 5 boys each of age 12 years are added, what would be the new average?

Solution:
Sum of ages of 15 boys = 15 × 11= 165
Sum of ages of 5 boys = 5 × 12 = 60
Total age of 20 boys = 165 + 60 = 225
Average of ages of 20 boys = 225/20= 11.25 years
৬৮১.
For 9 innings, Roman has an average of 70 runs. In the tenth inning, he scores 210 runs, thus increasing his average. His average increased by-
  1. ক
    11
  2. খ
    12
  3. গ
    13.5
  4. ঘ
    14
সঠিক উত্তর: ঘ
14
উত্তর
সঠিক উত্তর: ঘ
14
ঘ
ব্যাখ্যা
Question: For 9 innings, Roman has an average of 70 runs. In the tenth inning, he scores 210 runs, thus increasing his average. His average increased by-

Solution:
Total score for 9 innings = 70 × 9 = 630
Total score after 10th innings = 630 + 210 = 840
So, the new average is 840/10 = 84


So, the increment is 84 - 70 = 14 
৬৮২.
The sum of 10 numbers is 490. If the average of their first 4 numbers is 53 and that of the last five is 42, then what is the 5th number?
  1. ক
    68
  2. খ
    64
  3. গ
    59
  4. ঘ
    57
সঠিক উত্তর: ক
68
উত্তর
সঠিক উত্তর: ক
68
ক
ব্যাখ্যা
Question: The sum of 10 numbers is 490. If the average of their first 4 numbers is 53 and that of the last five is 42, then what is the 5th number?

Solution:
Given,
the average of their first 4 numbers = 53
∴ The total of their first 4 numbers = 4 × 53 = 212
and,
the average of their last five = 42
The total of the last 5 numbers = 5 × 42 = 210

∴ The sum of the (4 + 5) = 9 numbers = (212 + 210) = 422

∴ The 5th number = 490 - 422 = 68
৬৮৩.
In the list S = {17, 9, 24, X, 14, 17, 21} the mean, median and mode are all equal to one another. What is the value of X?
  1. ক
    17
  2. খ
    27
  3. গ
    24
  4. ঘ
    92
সঠিক উত্তর: ক
17
উত্তর
সঠিক উত্তর: ক
17
ক
ব্যাখ্যা

Question: In the list S = {17, 9, 24, X, 14, 17, 21} the mean, median and mode are all equal to one another. What is the value of X?

Solution:
Let the list be: 9, 14, 17, 17, 21, 24, X (sorted, except X).
Since mean = median = mode, and mode = 17 (appears twice, others once),
⇒ mean = median = 17.

We know,
Mean = (sum of all numbers)/7 = 17
17 = (17 + 9 + 24 + X + 14 + 17 + 21)/7
⇒ 17 = (102 + X)/7
⇒ 102 + X = 119
⇒ X = 119 - 102
∴ X = 17 

 So the value of X is 17.

৬৮৪.
When a person weighing 60 kg leaves a group of 50 people, the average weight of the remaining people increases by 0.3 kg. What is the new average weight of the remaining 49 people?
  1. ক
    62 kg
  2. খ
    66 kg
  3. গ
    75 kg
  4. ঘ
    72 kg
  5. ঙ
    78 kg
সঠিক উত্তর: গ
75 kg
উত্তর
সঠিক উত্তর: গ
75 kg
গ
ব্যাখ্যা

Question: When a person weighing 60 kg leaves a group of 50 people, the average weight of the remaining people increases by 0.3 kg. What is the new average weight of the remaining 49 people?

Solution:
let,
The average weight of 49 people is x kg
Total weight of 49 people = 49x
Total weight of 50 people = 49x + 60

ATQ,
50(x - 0.3) = (49x + 60)
⇒ 50x - 15 = 49x + 60
⇒ 50x - 49x = 60 + 15
∴ x = 75

∴ the new average weight of the remaining 49 people is 75 kg.

৬৮৫.
The average age of A, B, C, D & E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is
  1. ক
    ক) 48
  2. খ
    খ) 46
  3. গ
    গ) 42
  4. ঘ
    ঘ) 45
  5. ঙ
    ঙ) 47
সঠিক উত্তর: খ
খ) 46
উত্তর
সঠিক উত্তর: খ
খ) 46
খ
ব্যাখ্যা

Sum of their ages = 40 × 5 = 200 years
Sum of A & B’s ages = 35 × 2 = 70 years
Sum of C & D’s ages = 42 × 2 = 84
So, Age of E = 200 - (70 + 84) = 46

৬৮৬.
Shakib has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:
  1. ক
    ক) 24
  2. খ
    খ) 30
  3. গ
    গ) 28
  4. ঘ
    ঘ) 32
সঠিক উত্তর: গ
গ) 28
উত্তর
সঠিক উত্তর: গ
গ) 28
গ
ব্যাখ্যা
Question: Shakib has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:

Solution:
Let Shakib's average be x for 9 innings.
So, Shakib scored 9x run in 9 innings.

In the 10th inning, he scored 100 runs then the average became (x + 8).
And he scored (x + 8) × 10 runs in 10 innings.

Now,
⇒ 9x + 100 = 10 × (x + 8)
or, 9x + 100 = 10x + 80
or, x =100 - 80
or, x = 20

New average = (x + 8) = 28 runs
৬৮৭.
If x + y = 21 and xy = 110, find the value of x2 + y2 = ?
  1. ক
    221
  2. খ
    241
  3. গ
    331
  4. ঘ
    321
সঠিক উত্তর: ক
221
উত্তর
সঠিক উত্তর: ক
221
ক
ব্যাখ্যা

Question: If x + y = 21 and xy = 110, find the value of x2 + y2 = ?

Solution:
Given that,
x + y = 21 and xy = 110

We know that,
(x + y)2 = x2 + y2 + 2xy
⇒ x2 + y2 = (x + y)2 - 2xy
⇒ x2 + y2 = 212 - 2 × 110
⇒ x2 + y2 = 441 - 220
∴ x2 + y2 = 221

৬৮৮.
The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
  1. ক
    29
  2. খ
    27
  3. গ
    31
  4. ঘ
    33
সঠিক উত্তর: খ
27
উত্তর
সঠিক উত্তর: খ
27
খ
ব্যাখ্যা
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
 
Solution:
Given,
Average of 10 numbers = 23
⇒ Sum/Total numbers = 23
⇒ Sum/10 = 23
∴ Sum of the 10 numbers = 230


If each number is increased by 4, the total increase = 4 × 10 = 40
New sum = 230 + 40 = 270


Therefore, the new average = 270/10 = 27
৬৮৯.
Which of the following fractions is greater than 2/5 and less than 3/4 ?
  1. ক
    1/3
  2. খ
    3/8
  3. গ
    5/8
  4. ঘ
    4/5
সঠিক উত্তর: গ
5/8
উত্তর
সঠিক উত্তর: গ
5/8
গ
ব্যাখ্যা

Question: Which of the following fractions is greater than 2/5 and less than 3/4 ?

Solution:
2/5 = 0.40
3/4 = 0.75

Than,   
1/3 = 0.333   
3/8 = 0.375
5/8 = 0.625
4/5 = 0.8

Clearly, 0.625 lies between 0.40 and 0.75

∴ 5/8 lies between 2/5 and 3/4.

৬৯০.
A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?
  1. ক
    1/16
  2. খ
    13/16
  3. গ
    9/16
  4. ঘ
    7/16
সঠিক উত্তর: ঘ
7/16
উত্তর
সঠিক উত্তর: ঘ
7/16
ঘ
ব্যাখ্যা
Question: A lemonade stand sold only small and large cups of lemonade on Tuesday. 3/5 of the cups sold were small and the rest were large. If the large cups were sold for 7/6 as much as the small cups, what fraction of Tuesday's total revenue was from the sale of large cups?

Solution:
Let, the total cups sold 15
small cups = (3/5) × 15 = 9
large cups = 15 - 9 = 6

let, small cups were sold 6 taka each, then large cups were sold 7 taka each.

large cup's revenue = 7 × 6 = 42 taka
small cup's revenue = 6 × 9 = 54 taka

fraction of Tuesday's total revenue was from the sale of large cups = 42/(42 + 54)
= 42/96
= 7/16
৬৯১.
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?
  1. ক
    ক) 2
  2. খ
    খ) 4
  3. গ
    গ) 8
  4. ঘ
    ঘ) 15
সঠিক উত্তর: ঘ
ঘ) 15
উত্তর
সঠিক উত্তর: ঘ
ঘ) 15
ঘ
ব্যাখ্যা

Age decreased = (5 × 3) years
= 15 years
So the required difference = 15 years

৬৯২.
What is the difference between the biggest and the smallest fraction among 3/7, 4/9, 5/11 and 6/13?
  1. ক
    3/35
  2. খ
    3/67
  3. গ
    3/91
  4. ঘ
    3/97
সঠিক উত্তর: গ
3/91
উত্তর
সঠিক উত্তর: গ
3/91
গ
ব্যাখ্যা

Question: What is the difference between the biggest and the smallest fraction among 3/7, 4/9, 5/11 and 6/13?

Solution:
Converting each of the given fractions into decimal form, we get,
3/7 = 0.4286
4/9 = 0.4444
5/11 = 0.4545
6/13 = 0.4615

Since, 0.4615 > 0.4545 > 0.4444 > 0.4286 So, 6/13 > 5/11 > 4/9 > 3/7

∴ Required difference = 6/13 - 3/7
= (42 - 39)/91
= 3/91

৬৯৩.
The average of 11 numbers is 30. If the average of the first six numbers is 17.5 and that of the last six is 42.5, then what is the sixth number?
  1. ক
    ক) 30
  2. খ
    খ) 36
  3. গ
    গ) 45
  4. ঘ
    ঘ) 47
সঠিক উত্তর: ক
ক) 30
উত্তর
সঠিক উত্তর: ক
ক) 30
ক
ব্যাখ্যা

Average of 11 numbers = 30

Step 1: Calculate total of 11 numbers by multiplying it by average value 30 = 11 x 30 = 330
Step 2: Calculate the total of the first six members by multiplying it by average value 17.5 = 17.5 x 6 = 105
Step 3: Calculate the total of the last six members by multiplying it by average value 42.5 = 42.5 x 6 = 255

Therefore,
we can find the sixth number by adding the value of the first six and last six numbers and subtracting it from the total value of 11 numbers.
Sixth number = (105 + 255) - 330
= 30.

৬৯৪.
The average temperature on Wednesday, Thursday and Friday was 25°C. The average temperature on Thursday, Friday and Saturday was 24°C. If the temperature on Saturday was 27°C, what was the temperature on Wednesday?
  1. ক
    ক) 24°C
  2. খ
    খ) 21°C
  3. গ
    গ) 27°C
  4. ঘ
    ঘ) 30°C
  5. ঙ
    ঙ) None of these
সঠিক উত্তর: ঘ
ঘ) 30°C
উত্তর
সঠিক উত্তর: ঘ
ঘ) 30°C
ঘ
ব্যাখ্যা
Question: The average temperature on Wednesday, Thursday, and Friday was 25°C. The average temperature on Thursday, Friday, and Saturday was 24°C. If the temperature on Saturday was 27°C, what was the temperature on Wednesday?

Solution:
average temperature on Wednesday, Thursday, and Friday was 25°C.
Total temperature = 25° × 3
= 75°

The average temperature on Thursday, Friday, and Saturday was 24°C.
Total temparature = 24° × 3
= 72°

 the temperature of Wednesday -  the temperature of Saturday = 75° - 72°
⇒  the temperature of Wednesday - 27° = 3°
∴ the temperature of Wednesday = 27° + 3°
= 30°
৬৯৫.
A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?
  1. ক
    34
  2. খ
    36
  3. গ
    35
  4. ঘ
    37
  5. ঙ
    38
সঠিক উত্তর: ঘ
37
উত্তর
সঠিক উত্তর: ঘ
37
ঘ
ব্যাখ্যা
16x + 85 = 17(x + 3)
x = 34 + 3 = 37
৬৯৬.
Find the value of,
  1. ক
    12
  2. খ
    16
  3. গ
    2
  4. ঘ
    4
সঠিক উত্তর: ঘ
4
উত্তর
সঠিক উত্তর: ঘ
4
ঘ
ব্যাখ্যা
Question: Find the value of,


Solution:
৬৯৭.
The average weight of A, B and C is 45kg. If the average weight of A and B is 40 kg and that of B and C is 43 kg, then the weight of B is-
  1. ক
    ক) 17 kg
  2. খ
    খ) 31 kg
  3. গ
    গ) 20 kg
  4. ঘ
    ঘ) None of these
সঠিক উত্তর: খ
খ) 31 kg
উত্তর
সঠিক উত্তর: খ
খ) 31 kg
খ
ব্যাখ্যা
Question: The average weight of A, B and C is 45kg. If the average weight of A and B is 40 kg and that of B and C is 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.
৬৯৮.
The average of the first nine prime numbers is-
  1. ক
    ক) 12.12
  2. খ
    খ) 11.11
  3. গ
    গ) 13.22
  4. ঘ
    ঘ) 14.05
সঠিক উত্তর: খ
খ) 11.11
উত্তর
সঠিক উত্তর: খ
খ) 11.11
খ
ব্যাখ্যা
First 9 prime numbers.= 2, 3, 5, 7, 11, 13, 17, 19, 23
Average = Sum of all numbers / Total numbers.
              = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23)/9
              = 100/9
              = 11.11
Therefore the avg of first 9 prime numbers is 11.11
৬৯৯.
A Petrol tank now is 1/2 full. After you remove 8 gallons petrol from the 1/2 full tank the tank is then 1/10 full. What is the capacity, in gallons, of the tank? 
  1. ক
    40
  2. খ
    20
  3. গ
    31/2
  4. ঘ
    30
  5. ঙ
    None of these
সঠিক উত্তর: খ
20
উত্তর
সঠিক উত্তর: খ
20
খ
ব্যাখ্যা
Question: A Petrol tank now is 1/2 full. After you remove 8 gallons petrol from the 1/2 full tank the tank is then 1/10 full. What is the capacity, in gallons, of the tank?

Solution:
A Petrol tank now is 1/2 full
Here,
(1/2 - 1/10)
= (5 - 1)/10
= 4/10
= 2/5

So,
Capacity of 2/5 of the tank is 8 gallons
∴ Capacity of full tank is (8 × 5)/2 = 20 gallons
৭০০.
If the average of three consecutive even numbers is 34, find the smallest of these numbers.
  1. ক
    30
  2. খ
    32
  3. গ
    34
  4. ঘ
    28
সঠিক উত্তর: খ
32
উত্তর
সঠিক উত্তর: খ
32
খ
ব্যাখ্যা
Question: If the average of three consecutive even numbers is 34, find the smallest of these numbers.

Solution:
Let the first number is x, then the next two even numbers would be x + 2, x + 4

As per question;
(x + x + 2 + x + 4)/3 = 34
⇒ (3x + 6)/3 = 34
⇒ 3x + 6 = 102
⇒ 3x = 96
∴ x = 32

Smallest number would be = 32