Fraction and Simplification, Average and Mean

PrepBank · পাতা ৬ / ১০ · ৫০১–৬০০ / ৯৪৮

৫০১.

The average of six numbers is 32. If each of the first three numbers is increased by 2 and each of the remaining three numbers is decreasing by 4, then the new average is?

ক
32
খ
37
গ
29
ঘ
31

ব্যাখ্যা

Question: The average of six numbers is 32. If each of the first three numbers is increased by 2 and each of the remaining three numbers is decreasing by 4, then the new average is?

Solution:
Given that,
The average of the six number = 32

ATQ,
The sum of the six numbers = 32 × 6 = 192
The total increase of first three numbers = 2 × 3 = 6
The total decrease in last three numbers = 4 × 3 = 12

∴ The new sum of the all six numbers = 192 + 6 - 12 = 192 - 6 = 186

∴ The new average of the six numbers = 186 ÷ 6 = 31

৫০২.

A student was asked to find the arithmetic mean of the numbers 3, 12, 7, 9, 15, 13, 8, 18, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?

ক
ক) 5
খ
খ) 6
গ
গ) 7
ঘ
ঘ) 8

ব্যাখ্যা

Question: A student was asked to find the arithmetic mean of the numbers 3, 12, 7, 9, 15, 13, 8, 18, 17, 21, 14 and x. He found the mean to be 12. What should be the number in place of x?

Solution:
the arithmetic mean of the numbers 3, 12, 7, 9, 15, 13, 8, 18, 17, 21, 14 and x
= (3 + 12 + 7 + 9 + 15 + 13 + 8 + 18 + 17 + 21 + 14 + x )/12
= (137 + x)/12

∴ (137 + x)/12 = 12
⇒ 137 + x = 144
⇒ x = 7

৫০৩.

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

ক
52
খ
30
গ
32.5
ঘ
130
ঙ
None of these

ব্যাখ্যা

Question: The average weight of 39 men travelling to Cox's Bazar is 30. If an obese man with weight 130 kg join them. What will be the average weight of the people travelling to Cox's Bazar?

Solution:
If the weight of the man would have been 30,
then the average weight would have been the same. So, the extra 100 kg that the obese man brings with him would be distributed equally amongst all of them, i.e. 100/40 = 2.5
So, the average becomes 30 + 2.5 = 32.5

৫০৪.

In a class, if 5 students are seated on each bench, 5 benches remain vacant. But if 4 students are seated on each bench, 8 students have to stand. How many students are there in the class?

ক
220
খ
180
গ
140
ঘ
120

ব্যাখ্যা

Question: In a class, if 5 students are seated on each bench, 5 benches remain vacant. But if 4 students are seated on each bench, 8 students have to stand. How many students are there in the class?

Solution:
Let the number of benches = b

1^stcondition,
5 students are seated per bench then 5 benches remain vacant
∴ Students = 5 × (b - 5)

2^nd condition,
4 students are seated per bench then 8 students are left standing
∴ Students = 4 × b + 8

ATQ,
5(b - 5) = 4b + 8
⇒ 5b - 25 = 4b + 8
⇒ 5b - 4b = 8 + 25
∴ b = 33

Now, total students = 5 × (33 - 5)
= 5 × 28
= 140

∴ There are 140 students in the class.

৫০৫.

26 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]. Simplify the expressi

ক
41
খ
31
গ
21
ঘ
11

ব্যাখ্যা

Question: 26 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]. Simplify the expression.

Solution:
26 - [18 - {14 - (15 - 4 ÷ 2 × 2)}]
= 26 - [18 - {14 - (15 - 2 × 2)}]
= 26 - [18 - {14 - (15 - 4)}]
= 26 - [18 - {14 - 11}]
= 26 - [18 - 3]
= 26 - 15
= 11

৫০৬.

What is the value of (255 - 55) ÷ 4 × 15 - 504 ÷ 3 =?

ক
426
খ
672
গ
364
ঘ
582

ব্যাখ্যা

Question: What is the value of (255 - 55) ÷ 4 × 15 - 504 ÷ 3 =?

Solution:
(255 - 55) ÷ 4 × 15 - 504 ÷ 3
= 200 ÷ 4 × 15 - 504 ÷ 3
= 50 × 15 - 168
= 750 - 168
= 582

৫০৭.

In a class 3/4th of the students do not know either English or Spanish. But 1/6th of the students know English. How much students know both English and Spanish if students who know Spanish are 1/8th of total students in the class?

ক
1/24
খ
10/17
গ
100/24
ঘ
2/37
ঙ
None of these

ব্যাখ্যা

Question: In a class 3/4th of the students do not know either English or Spanish. But 1/6th of the students know English. How much students know both English and Spanish if students who know Spanish are 1/8th of total students in the class?

Solution:
Let's say total number of students = x

Let's say number of students who know both languages = y
According to set theory:
Total students who know at least one language = Students who know English + Students who know Spanish - Students who know both languages
⇒ x - (3/4)x = (1/6)x + (1/8)x - y
⇒ (1/4)x = (1/6 + 1/8)x - y
⇒ (1/4)x = (24/144 + 18/144)x - y
⇒ (36/144)x = (42/144)x - y
⇒ y = (42/144)x - (36/144)x
⇒ y = (6/144)x
∴ y = (1/24)x

Therefore, 1/24th of the total students know both English and Spanish.

৫০৮.

In a class there are 50 students, their average weight is 45 kg. When a student leaves the class, the average is reduced by 100 g. Find the weight of the student who left class.

ক
43.90
খ
44.90
গ
46.90
ঘ
49.90
ঙ
None of above

ব্যাখ্যা

Total weight = 45 × 50 = 2250 kg
New average = 45 - 0.1 = 44.9
The total weight of 49 = 49 × 44.9 = 2200.1
The weight of the student who left the class = (2250 - 2200.1) kg
= 49.9 kg

৫০৯.

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?

ক
77
খ
68
গ
58
ঘ
49
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

৫১০.

The average price of 10 books is Tk.12 while the average price of 8 of these books is Tk.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

ক
Tk. 5, Tk. 17
খ
Tk. 8.50, Tk. 12.75
গ
Tk. 16, Tk. 10
ঘ
Tk. 12, Tk. 14

ব্যাখ্যা

As per question,
Total cost of 10 books = Tk. 120
Total cost of 8 books = Tk. 94
∴ The cost of 2 books = Tk. 26

Let the price of one book is x TK.
∴ The other book must be 160% of x or 1.6x TK.

∴ x + 1.6x = 26
Or, x = 10.

∴ Cost of a book is = 10 TK
and cost of the other book is = 26 - 10 = 16 TK.

৫১১.

The average of the first five multiples of 7 is -

ক
ক) 20.5
খ
খ) 21
গ
গ) 25
ঘ
ঘ) 26.2

ব্যাখ্যা

Question: The average of the first five multiples of 7 is-

Solution:
the first five multiples of 7, 14, 21, 28, 35

the average is = (7 + 14 + 21 + 28 + 35)/5
= 21

৫১২.

The average of the first and the second of three numbers is 15 more than the average of the second and the third of these numbers. What is the difference between the first and the third of these three numbers?

ক
ক) 15
খ
খ) 45
গ
গ) 60
ঘ
ঘ) None of these

ব্যাখ্যা

Let 1st no = x
2nd no = y
and, 3rd no = z
ATQ,
(x + y)/2 = 15 + (y + z)/2
Or, x + y = 30 + y + z
Or, x - z = 30
So, Difference of 1st and 3rd no is 30

৫১৩.

Having scored 98 runs in the 19th innings a cricketer increase his average score by 4.what will be his average score after the 19th innings?

ক
ক) 24
খ
খ) 28
গ
গ) 26
ঘ
ঘ) 22

ব্যাখ্যা

Question: Having scored 98 runs in the 19th innings a cricketer increase his average score by 4.what will be his average score after the 19th innings?

Solution:
Let, his average score is x
His total score after 19th innings = 19x

ATQ,
(19x - 98)/18 = x - 4
⇒ 19x - 98 = 18x - 72
⇒ 19x - 18x = 98 - 72
∴ x = 26

His average score is 26

৫১৪.

In a group of 144 persons, 50% people contributed tk. 50 each, 25% contributed Tk. 60 each and the remaining persons contributed Tk. 70 each. Find the average contribution for the group?

ক
57.5
খ
58.5
গ
59.5
ঘ
60.5

ব্যাখ্যা

Question: In a group of 144 persons, 50% people contributed tk. 50 each, 25% contributed Tk. 60 each and the remaining persons contributed Tk. 70 each. Find the average contribution for the group?

Solution:
total people = 144

Since
50% of them contributed Tk. 50
∴ amount contributed by these 50% = (144/2) × 50 = 3600

Since 25% of them contributed TK. 60
∴ amount contributed by these 25% = (25/100) × (144) × 60 = 2160

and
remaining 25% of them contributed Tk. 70
∴ amount contributed by these 25% = (25/100) × 144 × 70 = 2520

∴ Total amount contributed = 3600 + 2160 + 2520 = 8280

∴ Average contribution = 8280/144 = 57.5

৫১৫.

If 12a + 3b = 1 and 7b – 2a = 9, what is the average of a and b ?

ক
ক) 0.1
খ
খ) 0.5
গ
গ) 1
ঘ
ঘ) 2.5

ব্যাখ্যা

Adding the given equations:
12a + 3b + 7b - 2a = 10
Or, 10a + 10b = 10
Or, 10(a + b) = 10
Or, a + b = 1
So, average of a and b is 0.5

৫১৬.

The average age of a group of 10 students was 20 years. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?

ক
ক) 29 years
খ
খ) 30 years
গ
গ) 31 years
ঘ
ঘ) 32 years

ব্যাখ্যা

The average age of a group of 10 students was 20
Therefore, the total age of a group of 10 students was 20 × 10 = 200

The average age increased by 2 years when two new students joined the group.
That means, the average age of a group of (10 + 2) students was (20 + 2) years
Therefore, the total age of a group of 12 students was 22 × 12 = 264 years

the total age of 2 students is (264 - 200) = 64 years
The average age is 64/2 = 32 years
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১০ জন ছাত্রের গড় বয়স ২০ বছর। নতুন ২ জন ছাত্র যোগ দিলে গড় বয়স ২ বছর বৃদ্ধি পায়। নতুন ২ জন ছাত্রের গড় বয়স কত?

১০ জন ছাত্রের গড় বয়স ২০ বছর। সুতরাং মোট বয়স = ২০ × ১০ = ২০০ বছর
নতুন ২ জন ছাত্র গ্রুপে যোগ দিলে গড় বয়স ২ বছর বৃদ্ধি পায়।
সুতরাং (১০ + ২০) বা ১২ জন ছাত্রের গড় বয়স = (২০ + ২) বা ২২ বছর। সুতরাং মোট বয়স = ২২ × ১২ বা ২৬৪ বছর
অতএব ২ জন নতুন ছাত্রের মোট বয়স = ২৬৪ - ২০০ = ৬৪ বছর। অতএব গড় বয়স = ৬৪/২ = ৩২ বছর

৫১৭.

The average of four numbers 13, 27, 35, and x is 25. Find the number x.

ক
25
খ
35
গ
45
ঘ
15

ব্যাখ্যা

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

৫১৮.

A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

ক
(4p/3) - 22
খ
(p/2) + 11
গ
(2p/3) - 22
ঘ
2p - 22

ব্যাখ্যা

Question: A number p equals 3/2 the average of 10, 12, and q. What is q in terms of p?

Solution:
Average = (10 + 12 + q)/3
= (22 + q)/3

Now, p is 3/2 the average
So, p = (3/2) × {(22 + q)/3}
⇒ p = (22 + q)/2
⇒ 22 + q = 2p
∴ q = 2p - 22

৫১৯.

In a football team of 11 members, the captain is 28 years old, and the goalkeeper is 4 years older. If we exclude their ages, the average age of the other players is 2 years below the team's overall average. What is the average age of the entire team?

ক
15 years
খ
17 years
গ
21 years
ঘ
None of the above

ব্যাখ্যা

Question: In a football team of 11 members, the captain is 28 years old, and the goalkeeper is 4 years older. If we exclude their ages, the average age of the other players is 2 years below the team's overall average. What is the average age of the entire team?

Solution:
Let the average age of the whole team be x years.

ATQ,
11x - (28 + 32) = 9(x - 2)
⇒ 11x - 60 = 9(x - 2)
⇒ 11x - 60 = 9x - 18
⇒ 11x - 9x = 60 - 18
⇒ 2x = 42
∴ x = 21

৫২০.

The average of 6 numbers is 7. The average of the three number of them is 5. What will be the average of remaining numbers?

ক
ক) 8
খ
খ) 9
গ
গ) 10
ঘ
ঘ) 11

ব্যাখ্যা

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

৫২১.

45 - [38 - {60 ÷ 3 - (6 - 9 ÷ 3) ÷ 3}]. Simplify the expression.

ক
24
খ
25
গ
26
ঘ
27

ব্যাখ্যা

Question: 45 - [38 - {60 ÷ 3 - (6 - 9 ÷ 3) ÷ 3}]. Simplify the expression.

Solution:
45 - [38 - {60 ÷ 3 - (6 - 9 ÷ 3) ÷ 3}]
= 45 - [38 - {60 ÷ 3 - 3 ÷ 3}]
= 45 - [38 - {20 - 1}]
= 45 - [38 - 19]
= 45 - 19
= 26.

৫২২.

Find the value of x, if (x/7) - (x/9) = 2

ক
53
খ
75
গ
47
ঘ
63

ব্যাখ্যা

Question: Find the value of x, if (x/7) - (x/9) = 2

Solution:
Given that,
(x/7) - (x/9) = 2
⇒ (9x - 7x)/63 = 2
⇒ 2x = 2 × 63
∴ x = 63

৫২৩.

- 5x - [4y - {9x - (3y - 7x)}] simplifies to

ক
- 21x + 7y
খ
1
গ
11x - 7y
ঘ
21x - 7y

ব্যাখ্যা

Question: - 5x - [4y - {9x - (3y - 7x)}] simplifies to

Solution:
- 5x - [4y - {9x - (3y - 7x)}]
= - 5x - [4y - {9x - 3y + 7x}]
= - 5x - [4y - 9x + 3y - 7x]
= - 5x - [7y - 16x]
= - 5x - 7y + 16x
= 11x - 7y

৫২৪.

A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

ক
Tk. 1200
খ
Tk. 1250
গ
Tk. 1300
ঘ
Tk. 1400

ব্যাখ্যা

Question: A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

Solution:
১টি বইয়ে দাম কমে ৪ টাকা
∴ ৫০টি বইয়ে দাম কমে (৫০ × ৪) টাকা
= ২০০ টাকা

সে মোট বই কিনে (৫০ + ১০) টি
= ৬০টি

১০টি বইয়ের দাম ২০০ টাকা
∴ ৬০টি বইয়ের দাম (২০০ × ৬০)/১০ টাকা
= ১২০০ টাকা

∴ তার কাছে ১২০০ টাকা আছে।

৫২৫.

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 44° C, what was the temperature on Wednesday?

ক
41° C
খ
39° C
গ
42° C
ঘ
38° C
ঙ
None of these

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 44° C, what was the temperature on Wednesday?

Solution:
Average temperature for Wednesday, Thursday and Friday = 40° C
∴ Total temperature = 3 × 40 = 120° C

Average temperature for Thursday, Friday and Saturday = 41° C
∴ Total temperature = 41 × 3 = 123° C

And,
Temperature on Saturday = 44° C

Now,
(Thursday + Friday + Saturday) - (Wednesday + Thursday + Friday) = 123 - 120
⇒ Saturday - Wednesday = 3
∴ Wednesday = 44 - 3 = 41° C

৫২৬.

A boy rides his bicycle 10 km at an average speed of 12 km/hr. and again travels 12km at an average speed of 10km/hr. His average speed of for the entire trip is approximately -

ক
10 km/hour
খ
10.5 km/hour
গ
11.2 km/hour
ঘ
10.8 km/hour

ব্যাখ্যা

Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr. and again travels 12km at an average speed of 10km/hr. His average speed of for the entire trip is approximately -

Solution:
Total Distance = 10 + 12 = 22 km
Total time = (10/12) + (12/10)
= (5/6) + (6/5)
= (25 + 36)/30
= 61/30 hours

Average speed = 22/(61/30) = 660/61 = 10.8 km/hour

৫২৭.

The average of the first five multiples of 9 is:

ক
23
খ
25
গ
27
ঘ
30

ব্যাখ্যা

Question: The average of the first five multiples of 9 is:

Solution:
Required average = total sum of first five multiples s of 9/5
= (9 + 18 + 27 + 36 + 45)/5
= 135/5
= 27

৫২৮.

The average of x and y is 45, and the average of y and z is 50. If y = 42, then find the value of (x + z).

ক
68
খ
84
গ
96
ঘ
106

ব্যাখ্যা

Question: The average of x and y is 45, and the average of y and z is 50. If y = 42, then find the value of (x + z).

Solution:
Given y = 42

Average of x and y = 45
∴ x + y = 45 × 2
⇒ x + y = 90
⇒ x + 42 = 90
⇒ x = 90 - 42
⇒ x = 48

Average of y and z = 50
∴ y + z = 50 × 2
⇒ y + z = 100
⇒ 42 + z = 100
⇒ z = 100 - 42
⇒ z = 58

Now, x + z = 48 + 58 = 106

৫২৯.

If the average of x and y is 70 and the average of y and z is 90. What is the value of z - x?

ক
30
খ
40
গ
60
ঘ
55

ব্যাখ্যা

Question: If the average of x and y is 70 and the average of y and z is 90. What is the value of z - x?

Solution:
(x + y)/2 = 70
∴ x + y = 140 .........(1)

Again,
(y + z)/2 = 90
∴ y + z = 180 .........(2)

From (2) - (1) we get,
y + z - x - y = 180 - 140
∴ z - x = 40

৫৩০.

A batsman has a certain average of runs for 12 innings. In the 13th inning, he scores 96 runs thereby increasing his average by 5 runs. what is his average after the 13 innings ?

ক
ক) 36
খ
খ) 48
গ
গ) 24
ঘ
ঘ) 31

ব্যাখ্যা

Let original average be x

then (12x+ 96) / 13 = x + 5
⇒ 12x + 96 = 13x + 65
⇒ x = 96 - 65 = 31
∴ His average after 13 innings = 31 + 5 = 36

৫৩১.

Tamim 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:

ক
22 runs
খ
28 runs
গ
32 runs
ঘ
38 runs

ব্যাখ্যা

Question: Tamim 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 Tamim's average be x for 9 innings.
So, Tamim scored 9x runs 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.

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

New average = (x + 8) = 28 runs.

৫৩২.

Having scored 117 runs in the 19th innings Tamim increase his average score by 5. What will be his average score after the 19th innings?

ক
ক) 23
খ
খ) 25
গ
গ) 27
ঘ
ঘ) 29

ব্যাখ্যা

Question: Having scored 117 runs in the 19th innings Tamim increase his average score by 5. What will be his average score after the 19th innings?

Solution:
Let,
Tamim's average score after the 19th innings is x
∴ Tamim's total score after 19th innings = 19x

Tamim's Total score after 18th innings = 19x - 117
∴ Tamim's average score after the 18th innings was (19x - 117)/18

ATQ,
(19x - 117)/18 = x - 5
⇒ 19x - 117 = 18x - 90
⇒ 19x - 18x = 117 - 90
∴ x = 27

His average score is 27

৫৩৩.

Of the four numbers, whose average is 80, the first is one-fourth of the sum of the last three. What is the value of the first number?

ক
ক) 43
খ
খ) 44
গ
গ) 54
ঘ
ঘ) 64

ব্যাখ্যা

Question: Of the four numbers, whose average is 80, the first is one-fourth of the sum of the last three. What is the value of the first number?

Solution:
Average of four numbers is 80
The sum of four numbers is = (4 × 80) = 320

let, the first number is x
then sum of last three is 4x

x + 4x = 320
⇒ 5x = 320
∴ x = 64

৫৩৪.

The average of the first six prime numbers is-

ক
ক) 6.83
খ
খ) 5.83
গ
গ) 7.83
ঘ
ঘ) 8.83

ব্যাখ্যা

First 6 prime numbers.= 2, 3, 5, 7, 11, 13
Average = Sum of all numbers / Total numbers.
= (2 + 3 + 5 + 7 + 11 + 13)/6
= 41/6
= 6.83
Therefore the avg of first 9 prime numbers is 6.83

৫৩৫.

An amount of money was divided among 3 boys in such a way that the first boy was given twice the third boy and the second boy was given equal to third boy. If the average is 400 Taka. How much was the first boy given?

ক
ক) 500 Tk.
খ
খ) 800 Tk.
গ
গ) 600 Tk.
ঘ
ঘ) 400 Tk.

ব্যাখ্যা

Question: An amount of money was divided among 3 boys in such a way that the first boy was given twice the third boy and the second boy was given equal to third boy. If the average is 400 Taka. How much was the first boy given?

Solution:
ধরি,
তৃতীয় বালক পায় = ক টাকা
∴ প্রথম বালক পায় = ২ক টাকা

প্রশ্নমতে,
(২ক + ক + ক)/৩ = ৪০০
৪ক/৩ = ৪০০
ক = ৩০০ টাকা

∴ প্রথম বালক পায় = ২ × ৩০০ = ৬০০ টাকা।

৫৩৬.

For 8 innings, Miraz has an average of 60 runs. In the 9th inning, he scored 6 runs, thus decrease his average. How much does his average decrease?

ক
6
খ
8
গ
11
ঘ
12

ব্যাখ্যা

Question: For 8 innings, Miraz has an average of 60 runs. In the 9th inning, he scored 6 runs, thus decrease his average. How much does his average decrease?

Solution:
Total score for 8 innings = 60 × 8 = 480
Total score after 9th innings = 480 + 6 = 486

∴ the new average is = 486/9 = 54

So, his average decrease = 60 - 54 = 6

৫৩৭.

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?

ক
A = B +C
খ
3A = B +C
গ
2A = B +C
ঘ
2B = (A/2) +C

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 other the numbers = 3C

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

৫৩৮.

If 2 is added to the numerator of a fraction, the fraction becomes 1. If 9 is added to the denominator, the fraction becomes 1/2. Find the fraction.

ক
11/14
খ
11/13
গ
1/11
ঘ
9/11
ঙ
11/15

ব্যাখ্যা

Question: If 2 is added to the numerator of a fraction, the fraction becomes 1. If 9 is added to the denominator, the fraction becomes 1/2. Find the fraction.

Solution:
ধরি,
লব x, হর y
শর্তমতে,
(x +2)/y = 1
⇒ x + 2 = y ................(1)

আবার,
x/(y + 9) = 1/2
⇒ 2x = y + 9
⇒ 2x - 9 = y ..................(2)

(1) ও (2) হতে পাই,
2x - 9 = x + 2
⇒ x = 11

x এর মান (1) নং এ বসিয়ে পাই,
11 + 2 = y
⇒ y = 13

∴ ভগ্নাংশটি 11/13

৫৩৯.

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than him. 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?

ক
ক) 23
খ
খ) 24
গ
গ) 25
ঘ
ঘ) None

ব্যাখ্যা

Given, Captain's age 26 years and Wicketkeeper's age 29 years.
Let, Average age be X years

ATQ,
9(x - 1) + 26 + 29 = 11x
⇒ 9x - 9 + 26 + 29 = 11x
⇒ 2x = 46
⇒ x = 23

৫৪০.

A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70. Then how many horses are there?

ক
16
খ
14
গ
12
ঘ
10

ব্যাখ্যা

Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70. Then how many horses are there?

Solution:
Let, the number of horses be x.
Then, the number of men = x
Number of man walking = x/2

ATQ,
4x + (x/2) . 2 = 70
⇒ 5x = 70
∴ x = 14

৫৪১.

একজন শিক্ষার্থী বিদ্যালয়ের তিনটি পরীক্ষায় ইংরেজিতে গড়ে ৬২ নম্বর পেয়েছে। বার্ষিক পরীক্ষায় কত নম্বর পেলে তাঁর নম্বরের গড় ৬৫ হবে?

ক
৭০ নম্বর
খ
৭৪ নম্বর
গ
৮১ নম্বর
ঘ
৮৫ নম্বর
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: একজন শিক্ষার্থী বিদ্যালয়ের তিনটি পরীক্ষায় ইংরেজিতে গড়ে ৬২ নম্বর পেয়েছে। বার্ষিক পরীক্ষায় কত নম্বর পেলে তাঁর নম্বরের গড় ৬৫ হবে?

সমাধান:
তিনটি পরীক্ষায় গড় নম্বর = ৬২
∴ তিনটি পরীক্ষায় মোট নম্বর = (৬২ × ৩)
= ১৮৬

ধরি,
বার্ষিক পরীক্ষায় ক নম্বর পেলে তাঁর নম্বরের গড় ৬৫ হবে।

প্রশ্নমতে,
(১৮৬ + ক)/৪ = ৬৫
⇒ ১৮৬ + ক = ২৬০
⇒ ক = ২৬০ - ১৮৬
∴ ক = ৭৪

৫৪২.

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?

ক
p²q²
খ
3pq
গ
3(p + q)
ঘ
2pq/(p + q)

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 + 3qp²
= 3pq(q + p)

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

৫৪৩.

The mean weight of a class of 20 students is 48 kg. Two more students weighing 60 kg and 58 kg respectively join the class. What is the mean weight of the class now?

ক
32 kg
খ
36 kg
গ
48 kg
ঘ
49 kg

ব্যাখ্যা

Question: The mean weight of a class of 20 students is 48 kg. Two more students weighing 60 kg and 58 kg respectively join the class. What is the mean weight of the class now?

Solution:
The mean Weight of 20 students = 48
∴ Total weight = 20 × 48 = 960

Add two students weighing 60, 58 to 960 = 960 + 60 + 58 = 1078

Therefore, Mean = 1078/22
= 49 kg

So the new mean weight of the class is 49 kg.

৫৪৪.

1 - [2 - {3 - (4 - 5) + 6} + 7] =?

ক
- 2
খ
0
গ
1
ঘ
2

ব্যাখ্যা

Question: 1 - [2 - {3 - (4 - 5) + 6} + 7] =?

Solution:
1 - [2 - {3 - (4 - 5) + 6} + 7]
= 1 - [2 - {3 - (-1) + 6} + 7]
= 1 - [2 - {3 + 1 + 6} + 7]
= 1 - [2 - {10} + 7]
= 1 - [2 - 10 + 7]
= 1- [-1]
= 1 + 1
= 2

৫৪৫.

ক
25
খ
59
গ
100
ঘ
116
ঙ
170

ব্যাখ্যা

Question:

Solution:

৫৪৬.

a, b, c, d, e, f are five consecutive odd numbers, their average is-

ক
ক) 5(a+4)
খ
খ) abcde/5
গ
গ) 5(a+b+c+d+e)
ঘ
ঘ) a+b+c+f
ঙ
ঙ) None of these

ব্যাখ্যা

পাঁচটি ধারাবাহিক বেজোর সংখ্যার প্রথমটি a হলে পরের চারটি হবে a+2, a+4, a+6, a+8। এদের যোগফলঃ a + a+2 + a+4 + a+6 + a+8 = 5a + 20 = 5(a+4)। সুতরাং এদের গড় = 5(a+4)/5 = (a+4)

৫৪৭.

On simplification √{(0.65)² - (0.16)²} reduces to-

ক
0.63
খ
0.54
গ
0.65
ঘ
None of these

ব্যাখ্যা

Question: On simplification √{(0.65)² - (0.16)²} reduces to-

Solution:
Given that,
√{(0.65)² - (0.16)²}
Since, a² - b² = (a - b)( a + b)
= √{(0.65 + 0.16)(0.65 - 0.16)}
= √{(0.81)(0.49)}
= √{(0.9)(0.9)×(0.7)(0.7)}
= 0.9 × 0.7
= 0.63

৫৪৮.

A batsman scored 45, 68, 52, 71, and 59 runs in five innings. How many runs must he score in the sixth innings to have an average of exactly 60 runs?

ক
58
খ
61
গ
65
ঘ
73

ব্যাখ্যা

Question: A batsman scored 45, 68, 52, 71, and 59 runs in five innings. How many runs must he score in the sixth innings to have an average of exactly 60 runs?

Solution:
ধরি, 6-তম ইনিংসে রান = x
প্রথম 5টি ইনিংসে মোট রান = (45 + 68 + 52 + 71 + 59) = 295

প্রশ্নমতে,
(295 + x)/6 = 60
⇒ 295 + x = 60 × 6
⇒ 295 + x = 360
⇒ x = 360 - 295
⇒ x = 65

∴ 6-তম ইনিংসে 65 রান করতে হবে।

৫৪৯.

The average of two numbers x and y is 16. If x, y, z are non-negative integers such that x < z < y, what is the minimum possible average of x, y, z.

ক
11
খ
11.5
গ
12
ঘ
10.5

ব্যাখ্যা

Question: The average of two numbers x and y is 16. If x, y, z are non-negative integers such that x < z < y, what is the minimum possible average of x, y, z.

Solution:
According to the questions,
(x + y)/2 = 16
x + y = 32
As x, y, z are non-negative integers and x < z < y.

The minimum possible value of these integers are,
X = 0
Z = 1
Y = 32

∴ Average = (0 + 32 + 1)/3
= 11

৫৫০.

The average age of the 20 persons is 19.2 years. After some time two more persons join them and then average is increased by 0.3 years. Find the difference between the age of new persons.

ক
ক) 45 years
খ
খ) 32 years
গ
গ) 22 years
ঘ
ঘ) None of these

ব্যাখ্যা

The average age of the 20 persons is 19.2 years. Therefore, total age = 20 × 19.2 = 384 years
After some time two more persons join them and then average is increased by 0.3 years.
So, average age of (20 + 2) or 22 persons = (19.2 + 0.3) years. Therefore, the total age = 22 × 19.5 = 429 years
Total age of 2 new persons = 429 - 384) = 45 years
It is possible to calculate to find the total age of two new persons but not difference.
--------------------------------------------------------------------------------------------------------------------
২০ জন ব্যক্তির গড় বয়স ১৯.২ বছর। কিছু দিন পর ২ জন নতুন ব্যক্তি যোগ দেওয়ায় গড় বয়স ০.৩ বছর বেড়ে গেলো। তাদের বয়সের বিয়োগফল কত?

২০ জন ব্যক্তির গড় বয়স ১৯.২ বছর হলে মোট বয়স ২০ × ১৯.২ = ৩৮৪ বছর
২ জন নতুন ব্যক্তি যোগ দেওয়ায় (২০ + ২) বা ২২ জনের গড় বয়স ০.৩ বছর বৃদ্ধি পেল। অতএব মোট বয়স = ২২ × (১৯.২ + ০.৩) = ২২ × ১৯.৫ = ৪২৯ বছর
২ জন নতুন ব্যক্তির মোট বয়স = ৪২৯ - ৩৮৪ = ৪৫ বছর
২ জন নতুন ব্যক্তির মোট বয়স বের করা সম্ভব কিন্তু পর্যাপ্ত ডেটা না থাকায় তাদের বয়সের বিয়োগফল বের করা সম্ভব নয়।

৫৫১.

What is the simple average of 3³⁰, 3³¹ and 3³²?

ক
3²⁹
খ
13 × (3³⁰)
গ
3³⁰
ঘ
13 × (3²⁹)

ব্যাখ্যা

Question: What is the simple average of 3³⁰, 3³¹ and 3³²?

Solution:
the simple average of 3³⁰ , 3³¹ and 3³² = (3³⁰ + 3³¹ + 3³²)/3
= (3³⁰/3) + (3³¹/3) + (3³²/3)
= 3²⁹ + 3³⁰ + 3³¹
= 3²⁹ (1 + 3 + 32)
= 3²⁹ (1 + 3 + 9)
= 13 × (3²⁹)

৫৫২.

Find the Arithmetic mean of 3, 6, 7, and 4.

ক
5.5
খ
6
গ
4
ঘ
5

ব্যাখ্যা

Question: Find the Arithmetic mean of 3, 6, 7, and 4.

Solution:
The mean is calculated first by taking the sum of all the values 3+6+7+4 = 20
- and then dividing it by, 4 (as we have a total of 4 terms.)
∴ Arithmetic mean = 20/4 = 5
Thus, the arithmetic mean of the given value is 5.

৫৫৩.

A man has Tk. 480 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

ক
60
খ
80
গ
120
ঘ
90

ব্যাখ্যা

Question: A man has Tk. 480 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

Solution:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
⇒ 16x = 480
∴ x = 30.

Hence, total number of notes = 3x = 90

৫৫৪.

The average of 10 numbers is 52. Later it is found that two numbers have been wrongly added. The first one is 20 greater than the actual number and the second number added is 15 instead of 31. Find the correct average-

ক
51.1
খ
51.6
গ
52.2
ঘ
52.5

ব্যাখ্যা

Question: The average of 10 numbers is 52. Later it is found that two numbers have been wrongly added. The first one is 20 greater than the actual number and the second number added is 15 instead of 31. Find the correct average -

Solution:
১০টি সংখ্যার প্রকৃত সমষ্টি = (52 × 10 - 20 + 31 - 15)
= 516

∴ প্রকৃত গড় = (516/10) = 51.6

৫৫৫.

The average score of a class of 90 students in an exam was 40. The average score of the students who had passed is 50, and the average score of the students who had failed is 30. How many students failed in the exam?

ক
15
খ
20
গ
33
ঘ
45
ঙ
None

ব্যাখ্যা

Question: The average score of a class of 90 students in an exam was 40. The average score of the students who had passed is 50, and the average score of the students who had failed is 30. How many students failed in the exam?

Solution:
Let
Total number of students who had failed = x
So, the total number of students who had passed = 90 - x

ATQ,
50(90 - x) + 30x = 90 × 40
⇒ 4500 - 50x + 30x = 3600
⇒ 20x = 4500 - 3600
⇒ 20x = 900
∴ x = 45

৫৫৬.

A straight pipe 1 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?

ক
1/6 and 1/4 only
খ
1/4 and 1/3 only
গ
1/6, 1/4, and 1/3
ঘ
1/12, 1/6 and 1/4
ঙ
1/12, 1/6, and 1/3

ব্যাখ্যা

Question: A straight pipe 1 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard?

Solution:
LCM of 3 & 4 = 12, marking the lengths accordingly

Lengths possible are 3/12 = 1/4, (4/12 - 3/12) = 1/12, (6/12 - 4/12) = 2/12 = 1/6, (8/12 - 6/12) = 2/12 = 1/6, (9/12 - 8/12) = 1/12, (12/12 - 9/12) = 3/12 = 1/4

The answer is D.

৫৫৭.

The sum of five consecutive odd numbers is 260 more than the average of the numbers. What is the smallest number?

ক
ক) 55
খ
খ) 58
গ
গ) 61
ঘ
ঘ) 69

ব্যাখ্যা

Let the five consecutive odd numbers be x, x + 2, x + 4, x + 6, x + 8
x + x + 2 + x + 4 + x + 6 + x + 8 = 260 + (x + x + 2 + x + 4 + x + 6 + x + 8)/5
⇒ 5x + 20 = 260 + (5x + 20)/5
⇒ 5x + 20 - 260 = (5x + 20)/5
⇒ 5x - 240 = (5x + 20)/5
⇒ 25x - 1200 = 5x + 20
⇒ 20x = 1200 + 20
∴ x = 61
-----------------------------------------------------------------------
৫টি ক্রমিক বিজোড় সংখ্যার সমষ্টি সংখ্যাগুলোর গড় অপেক্ষা ২৬০ বেশি। ক্ষুদ্রতম সংখ্যাটি কত?

মনে করি, ৫টি ক্রমিক বিজোড় সংখ্যাগুলি x, x + 2, x + 4, x + 6, x + 8
প্রশ্নানুসারে,
x + x + 2 + x + 4 + x + 6 + x + 8 = 260 + (x + x + 2 + x + 4 + x + 6 + x + 8)/5
⇒ 5x + 20 = 260 + (5x + 20)/5
⇒ 5x + 20 - 260 = (5x + 20)/5
⇒ 5x - 240 = (5x + 20)/5
⇒ 25x - 1200 = 5x + 20
⇒ 20x = 1200 + 20
∴ x = 61

৫৫৮.

The average of 5 consecutive number integers starting with m as the first integer is n. Then n =?

ক
ক) 5m
খ
খ) m + 3
গ
গ) m + 2
ঘ
ঘ) nm + 2

ব্যাখ্যা

দেয়া আছে,
প্রথম সংখ্যাটি = m

প্রশ্নমতে
m + (m +1) + (m + 2) + (m + 3) + (m + 4)/5 = n
m + m + 1 + m + 2 + m + 3 + m + 4 = 5n
5m + 10 = 5n
5n = 5(m + 2)
n = m + 2

৫৫৯.

The average of 6 consecutive numbers (integers) is 19.5. What is the largest of these numbers?

ক
21
খ
22
গ
22.5
ঘ
21.5

ব্যাখ্যা

Question: The average of 6 consecutive numbers (integers) is 19.5. What is the largest of these numbers?

Solution:
Let the 6 consecutive integers be:
x, x+1, x+2, x+3, x+4, x+5.

Their sum is:
Sum=x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)=6x+15
To calculate the average, we use the average formula
Average: Summation/ total number
= 6x+15 / 6 = 19.5

We multiply both sides by 6:
6x+15=117
⇒6x=102
⇒x=17

So the numbers are:
17, 18, 19, 20, 21, 22
- Largest number = 22.

৫৬০.

The average weight of 15 girls in a group is 24 kg when a new girl included the average weight increases by 3. What is the weight of the new girl?

ক
56 kg
খ
68 kg
গ
72 kg
ঘ
78 kg

ব্যাখ্যা

Average weight of 15 girls = 24 kg
Total weight of 15 girls = 24 x 15 = 360 kg
Average after including a new girl = 24 + 3 = 27 kg
Total weight of 16 girls = 27 x 16 = 432 kg
Weight of the new girl = Total weight of 16 girls - Total weight of 15 girls = 432 - 360 = 72 kg
Hence the required answer is 72 kg.

৫৬১.

The average of 4 consecutive numbers is 10.5. The largest of these numbers is:

ক
9
খ
10
গ
11
ঘ
12

ব্যাখ্যা

প্রশ্ন: The average of 4 consecutive numbers is 10.5. The largest of these numbers is:

সমাধান:
৪ টি ক্রমিক সংখ্যার গড় ১০.৫
৪ টি সংখ্যার সমষ্টি = ১০.৫ × ৪ = ৪২

ধরি, সংখ্যাগুলি হল a, a + ১, a + ২, a + ৩
প্রশ্নমতে,
a + a + ১ + a + ২ + a + ৩ = ৪২
⇒ ৪a + ৬ = ৪২
⇒ ৪a = ৪২ - ৬
⇒ ৪a = ৩৬
⇒ a = ৯

∴ বড় সংখ্যাটি হল a + ৩
= ৯ + ৩
= ১২

৫৬২.

The average of ten numbers is 7. What will be the new average if each of the numbers is multiplied by 8?

ক
ক) 45
খ
খ) 52
গ
গ) 56
ঘ
ঘ) 55

ব্যাখ্যা

10 টি সংখ্যার সমষ্টি = 10 × 7 = 70
8 দ্বারা ওই দশটি সংখ্যার প্রত্যেককে গুণ করার পর সমষ্টি হবে = 70 × 8 = 560
∴ নতুন গড় = 560/10 = 56

৫৬৩.

If 2x² + 12x + 18 = 0, what is the value of x?

ক
2
খ
3
গ
- 3
ঘ
- 2

ব্যাখ্যা

Question: If 2x² + 12x + 18 = 0, what is the value of x?

Solution:
2x² + 12x + 18 = 0
or, 2(x² + 6x + 9) = 0
or, (x)² + 2.x.3 + (3)² = 0
or, (x + 3)² = 0
or, x + 3 = 0
∴ x = - 3

৫৬৪.

Find the average of all the numbers between 6 and 34 which are divisible by 5

ক
ক) 15
খ
খ) 16
গ
গ) 18
ঘ
ঘ) 20

ব্যাখ্যা

Numbers between 6 and 34 divisible by 5 are 10, 15, 20, 25, 30.
Required average =(10 + 15 + 20 + 25 + 30)/5
= 100/5
= 20

৫৬৫.

In a hostel, 52 students are living. If 18 students are joined in this hostel then the average expenditure will be 3 tk. less whenever the total expenditure is 510 tk. will be increased. What is the total expenditure initially?

ক
Tk. 2080
খ
Tk. 1080
গ
Tk. 8020
ঘ
Tk. 2280

ব্যাখ্যা

Question: In a hostel, 52 students are living. If 18 students are joined in this hostel then the average expenditure will be 3 tk. less whenever the total expenditure is 510 tk. will be increased. What is the total expenditure initially?

Solution:
Let, the average expenditure of initial students be x,

ATQ,
52x + 510 = (52 + 18) × (x - 3)
⇒ 52x + 510 = 70x - 210
⇒ 70x - 52x = 510 + 210
⇒ 18x = 720
∴ x = 40

Hence, the total expenditure of 52 students = 52 × 40 = 2080 tk.

৫৬৬.

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is -

ক
1/12
খ
5/12
গ
7/12
ঘ
11/12
ঙ
None of these

ব্যাখ্যা

Question: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is -

Solution:
Let, the fraction is a/b

Now, (a - 1)/b = 1/3
⇒ b = 3a - 3

Again, a/(b + 8) = 1/4
⇒ b + 8 = 4a
⇒ b = 4a - 8

∴ 3a - 3 = 4a - 8
⇒ 4a - 3a = 8 - 3
⇒ a = 5

And, b = (3 × 5) - 3
= 15 - 3
= 12

∴ The fraction = a/b = 5/12

৫৬৭.

The average weight of 16 boys in a class is 50.25kg and that of the remaining 8 boys is 45.15kg. Find the average weight of all the boys in the class.

ক
ক) 47.55kg
খ
খ) 48kg
গ
গ) 48.55kg
ঘ
ঘ) 49.25kg

ব্যাখ্যা

Question: The average weight of 16 boys in a class is 50.25kg and that of the remaining 8 boys is 45.15kg. Find the average weight of all the boys in the class.

Solution:
Required average = (50.25 × 16 + 45.15 × 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.2/24
= 48.55

৫৬৮.

The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.

ক
36
খ
38
গ
40
ঘ
42

ব্যাখ্যা

Question: The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.

Solution:
Mean of 5 numbers = 28.
Sum of these 5 numbers = (28 × 5) = 140.

Mean of the remaining 4 numbers = (28 - 2) =26.
Sum of these remaining 4 numbers = (26 × 4) = 104.

Excluded number
= (sum of the given 5 numbers) - (sum of the remaining 4 numbers)
= (140 - 104)
= 36.

Hence, the excluded number is 36.

৫৬৯.

The average age of 8 men is increased by 4 years when one of them whose age is 30 years is replaced by a new man. What is the age of a new man?

ক
65 years
খ
57 years
গ
62 years
ঘ
76 years
ঙ
72 years

ব্যাখ্যা

Let, the average age of 8 men be x
Sum of the age of 8 men = 8x
Let, age of new man be y
According to question,
8x + y - 30 = 8 (x + 4)
8x + y - 30 = 8x + 32
y = 8x + 32 + 30 - 8x
y = 62 years

So, Age of the new man is 62 years.

৫৭০.

What is the meaning of the word 'Trepidation'?

ক
An uncomfortable feeling of nervousness.
খ
Very comfortable situation.
গ
Find a solution.
ঘ
Always being confident.

ব্যাখ্যা

Trepidation (noun)
- English Meaning: An uncomfortable feeling of nervousness or worry about something that is happening or might happen in the future.
- Bangla Meaning: সচকিত উত্তেজিত মনোভাব।

Synonyms:
• Anxiety - ভবিষ্যৎ বিষয়ে ভয় ও অনিশ্চয়তাবোধ; উদ্বেগ; দুশ্চিন্তা।

• Apprehension - আশঙ্কা; ভবিষ্যৎ বিষয়ে উৎকণ্ঠার অনুভূতি; উপলব্ধি; চেতনা; বোধ।

• Disquietude - মানসিক অস্থিরতা বা উদ্বেগ।

Antonyms:
• Calmness - শান্ততা, বিশ্রান্ততা।

• Equanimity - মনমেজাজের প্রশান্তি।

• Composure - শান্তি; স্থৈর্য; আত্মসংবরণ।

Other options:
খ) Very comfortable situation.
- Translations: খুবই আরামদায়ক অবস্থা।

গ) Find a solution.
- Translations: সমাধান বের করা।

ঘ) Always being confident.
- Translations: সবসময় আত্মবিশ্বাসী।

Source: Live MCQ Lecture.

৫৭১.

= ?

ক
1.25
খ
1
গ
12.5
ঘ
25

ব্যাখ্যা

Question: = ?

Solution:

৫৭২.

ক
(42 - 5√11)/19
খ
(42 + 5√11)/19
গ
(49 - 5√11)/19
ঘ
None of the these

ব্যাখ্যা

Question:

Solution:

৫৭৩.

Out of 8 people in a lift, a person weighing 65 kg gets off, and a new person enters. As a result, the average weight of the 8 people increases by 2.5 kg. What is the weight of the new person?

ক
82 kg
খ
84 kg
গ
85 kg
ঘ
70 kg

ব্যাখ্যা

Question: Out of 8 people in a lift, a person weighing 65 kg gets off, and a new person enters. As a result, the average weight of the 8 people increases by 2.5 kg. What is the weight of the new person?

Solution:
ধরি,
লিফটে থাকা 8 জন ব্যাক্তির গড় ওজন = x kg
তাহলে, মোট ওজন = 8x
65 কেজি ওজনের ব্যক্তি বের হয়ে যাওয়ার পর মোট ওজন = 8x − 65

আবার, মনে করি, নতুন ব্যাক্তির ওজন= y kg
তাহলে নতুন ব্যক্তি প্রবেশ করার পর নতুন মোট ওজন হবে = (8x − 65 + y) kg
এবং নতুন গড় হবে = x + 2.5

প্রশ্নমতে,
(8x − 65 + y) /8 = x + 2.5
⇒ 8x − 65 + y = 8x + 20
⇒ 8x + y - 8x = 20 + 65
⇒ y = 85

সুতরাং, নতুন ব্যাক্তির ওজন 85 kg ।

৫৭৪.

The average of 20, 70 and x is 40. If the average of 20, 70, x and y is 50, then y = ?

ক
100
খ
80
গ
70
ঘ
60

ব্যাখ্যা

Question: The average of 20, 70 and x is 40. If the average of 20, 70, x and y is 50, then y = ?

Solution:
The average of 20, 70 and x is 40

(x + 20 + 70)/3 = 40
⇒ x + 20 + 70 = (3 × 40) = 120
⇒ x + 90 = 120
⇒ x = 120 - 90 = 30

the average of 20, 70, x and y is 50

(20 + 70 + x + y)/4 = 50
⇒ 90 + x + y = (4 × 50)
⇒ 90 + 30 + y = 200
⇒ 120 + y = 200
⇒ y = 200 - 120
∴ y = 80

৫৭৫.

There are 71 members in group A, 18 members in group B and 53 members in group C. All the members of these groups went to a restaurant. The average amount spent on each member of group A, B and C is Tk.397, Tk.421 and Tk.137 respectively. The total average amount (in Tk.) spent per member is-

ক
Tk. 295
খ
Tk. 335
গ
Tk. 402
ঘ
Tk. 303

ব্যাখ্যা

Question: There are 71 members in group A, 18 members in group B and 53 members in group C. All the members of these groups went to a restaurant. The average amount spent on each member of group A, B and Cis Tk.397, Tk.421 and Tk.137 respectively. The total average amount (in Tk.) spent per member is-

Solution:
Given that,

Members in A = 71, B = 18, C = 53

Average spent per member: A = Tk. 397, B = Tk. 421 and C = Tk. 137

Now,
Total amount by A = 71 × 397 = 28187
Total amount by B = 18 × 421 = 7578
Total amount by C = 53 × 137 = 7261

∴ Total amount = 28187 + 7578 + 7261 = 43026

∴ Total members = 71 + 18 + 53 = 142

∴ Average = 43026/142 = 303

Total average amount spent per member = Tk. 303

৫৭৬.

The average of 20, 70 and x is 40. If the average of 20, 70, x and y is 50, then y =?

ক
100
খ
80
গ
70
ঘ
60

ব্যাখ্যা

Question: The average of 20, 70 and x is 40. If the average of 20, 70, x and y is 50, then y =?

Solution:
The average of 20, 70 and x is 40
(x + 20 + 70)/3 = 40
⇒ x + 20 + 70 = (3 × 40) = 120
⇒ x + 90 = 120
⇒ x = 120 - 90 = 30

the average of 20, 70, x and y is 50

(20 + 70 + x + y)/4 = 50
⇒ 90 + x + y = (4 × 50)
⇒ 90 + 30 + y = 200
⇒ 120 + y = 200
⇒ y = 200 - 120
∴ y = 80

৫৭৭.

The average weight of 12 students in a class is 45.5 kg. What should be the weight of a 13th student so that the average weight of all 13 students becomes 47.2 kg?

ক
65 kg
খ
68 kg
গ
67.6 kg
ঘ
70 kg
ঙ
66.5 kg

ব্যাখ্যা

Question: The average weight of 12 students in a class is 45.5 kg. What should be the weight of a 13th student so that the average weight of all 13 students becomes 47.2 kg?

Solution:
Average weight of 12 students = 45.5 kg
∴ Total weight of 12 students = (45.5 × 12) kg
= 546 kg

Again,
Average weight of 13 students = 47.2 kg
Total weight of 13 students = (47.2 × 13) kg
= 613.6 kg

∴ Weight of the 13th student = (613.6 - 546) kg
= 67.6 kg

Therefore, the weight of the 13th student should be 67.6 kg.

৫৭৮.

The value of 12 ÷ (1/2) + {(35 ÷ 7) of 40} + 20 - 15 of 10 is-

ক
80
খ
88
গ
94
ঘ
99

ব্যাখ্যা

Question: The value of 12 ÷ (1/2) + {(35 ÷ 7) of 40} + 20 - 15 of 10 is-

Solution:
12 ÷ (1/2) + {(35 ÷ 7) of 40} + 20 - 15 of 10
= 12 ÷ (1/2) + {(5) of 40} + 20 - 15 of 10
= 12 ÷ (1/2) + 5 × 40 + 20 - 150
= 12 × 2 + 200 + 20 - 150
= 244 - 150
= 94

∴ The required answer is 94.

৫৭৯.

The average of 60 numbers is 25. If two numbers, namely 30 and 40, are discarded, what is the average of the remaining numbers?

ক
22.84
খ
23.42
গ
24.66
ঘ
26.50

ব্যাখ্যা

Question: The average of 60 numbers is 25. If two numbers, namely 30 and 40, are discarded, what is the average of the remaining numbers?

Solution:
ATQ,
The average of 60 numbers is = 25
The sum of 60 numbers is = 25 × 60 = 1500
The two numbers discarded = 30 + 40 = 70
The sum of the remaining 58 numbers = 1500 - 70 = 1430

∴ The new average = 1430/58 = 24.66 (approximately)

৫৮০.

The average of ten numbers is 7. What will be the new average if each of the numbers is multiplied by 8?

ক
51
খ
63
গ
56
ঘ
48
ঙ
41

ব্যাখ্যা

10 টি সংখ্যার সমষ্টি = 10 × 7 = 70

8 দ্বারা ওই দশটি সংখ্যার প্রত্যেককে গুণ করার পর সমষ্টি হবে = 70 × 8 = 560

∴ নতুন গড় = 560/10 = 56

৫৮১.

The average of several exam scores is 80. One make-up exam was given. Included with the other scores, the new average was 84. If the score on the make up exam was 92, how many total exams were given?

ক
ক) 3
খ
খ) 2
গ
গ) 4
ঘ
ঘ) 5

ব্যাখ্যা

Let, there was x exams (excluding the makeup exam)
ATQ, 80x + 92 = 84(x + 1)
Or, 80x + 92 = 84x + 84
Or, x = 2
So, total number of exams including the makeup exam = 2 + 1 = 3

৫৮২.

A student find the average of ten 2 digit numbers, and while copying numbers by mistake, he writes one number with its digit interchanged, as a result of that his average is 3.6 less that the correct answer, then find the difference of the digits of the number in which he made the mistake.

ক
2
খ
3
গ
4
ঘ
5

ব্যাখ্যা

Question: A student find the average of ten 2 digit numbers, and while copying numbers by mistake, he writes one number with its digit interchanged, as a result of that his average is 3.6 less that the correct answer, then find the difference of the digits of the number in which he made the mistake.

Solution:
The number = 10x + y
After interchanging the digit, the number becomes 10y + x
The difference in average after interchanging the digits = 3.6
As there are 10 numbers,
The difference between the numbers will be = 3.6 × 10 = 36

Now
10x + y - (10y + x) = 36
9x - 9y ⇒ 36
9(x - y) = 36
x - y = 4

Difference in digits, (x - y) = 4

∴ The difference of the digits of the number in which he made the mistake is 4.

৫৮৩.

If 39/x = √(169/289), then what is the value of x?

ক
51
খ
58
গ
68
ঘ
70

ব্যাখ্যা

Question: If 39/x = √(169/289), then what is the value of x?

Sol:
39/x = √(169/289)
⇒ 39/x = 13/17
⇒ x = (39 × 17)/13
∴ x = 51

৫৮৪.

The average of 9 consecutive odd numbers is 33. What is the average of the first two and last two numbers?

ক
35
খ
33
গ
31
ঘ
29

ব্যাখ্যা

Question: The average of 9 consecutive odd numbers is 33. What is the average of the first two and last two numbers?

Solution:
The middle number is = 33
So, the other numbers are = 25, 27, 29, 31, 33, 35, 37, 39, 41

The average of the first two and last two numbers is = (25 + 27 + 39 + 41)/4 = 132/4 = 33

৫৮৫.

Of four numbers whose average is 70, the first is one-fourth of the sum of the last three. The first number is-

ক
ক) 54
খ
খ) 55
গ
গ) 56
ঘ
ঘ) 57

ব্যাখ্যা

Let
The four numbers be a, b, c and d
According the question
a = (1/4)(b + c + d)
b + c + d = 4a

again
a + b + c + d = 70 × 4
a + 4a = 280
5a = 280
a = 280/5
a = 56

৫৮৬.

The average of six consecutive numbers A, B, C, D, E and F is 62. What is the sum of B and F?

ক
120
খ
125
গ
134
ঘ
140

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

৫৮৭.

What is the average (arithmetic mean) of the values 39, 40, 39, 45, 42, 35, 47?

ক
ক) 39
খ
খ) 41
গ
গ) 45
ঘ
ঘ) 47

ব্যাখ্যা

Question: What is the average (arithmetic mean) of the values 39, 40, 39, 45, 42, 35, 47?

Solution:
সংখ্যাগুলোর গড় = (39 + 40 + 39 + 45 + 42 + 35 + 47)/7
= 287/7
= 41

৫৮৮.

One of 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:

ক
ক) 16, 8, 4
খ
খ) 24, 12, 6
গ
গ) 20, 10, 5
ঘ
ঘ) 28, 14, 7

ব্যাখ্যা

Let
the third number be x
Then Second number =2x and 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 = 6

Therefore, the three numbers are 4 × 6 = 24 , 2 × 6 = 12 , 6

৫৮৯.

The average monthly income of P and Q is Tk. 6,000; that of Q and R is 5,250; and, that P and R are Tk. 5,500. What is P’s monthly income?

ক
ক) Tk. 3,500
খ
খ) Tk. 4,500
গ
গ) Tk. 6,250
ঘ
ঘ) Tk. 4,800

ব্যাখ্যা

Question: The average monthly income of P and Q is Tk. 6,000; that of Q and R is 5,250; and, that P and R are Tk. 5,500. What is P’s monthly income?

Solution:
Average monthly income of P and Q = Tk. 6000
Average monthly income of Q and R = Tk. 5250
Average monthly income of P and R = Tk. 5500

Total income of P + Q = Tk. 2 × 6000 = Tk. 12000 .........(i)
Total income of Q + R = Tk. 2 × 5250 = Tk. 10500 .........(ii)
Total income of P + R = Tk. 2 × 5500 = Tk. 11000 ...........(iii)

On adding equation (i) + (ii) + (iii), we get
2 (P +Q + R) = 12000 + 10500 + 11000
P + Q + R = 33500/2
P + Q + R = Tk 16750 ........(iv)
by equation (iv) - (ii)
P's income = (16750 - 10500) = Tk. 6250.

৫৯০.

Simplify

ক
8
খ
10
গ
12
ঘ
14

ব্যাখ্যা

Question: Simplify

Solution:

= 22 - [9 - {6 - (10 - 1)}]
= 22 - [ 9 - { 6 - 9}]
= 22 - [9 - {-3}]
= 22 - [9 + 3]
= 22 - [12]
= 22 - 12
= 10

৫৯১.

If the Average of 7 consecutive positive odd integers is P, then what is the average of next seven consecutive odd integers in terms of P?

ক
ক) p+7
খ
খ) p+12
গ
গ) p+14
ঘ
ঘ) p+25
ঙ
ঙ) None

ব্যাখ্যা

7 টি পরপর ধনাত্মক বিজোড় সংখ্যার গড় p
ধরি, সংখ্যাগুলোঃ p-6, p-4, p-2, p, p+2, p+4, p+6

এবং এর পরবর্তি 7 টি ধনাত্মক বিজোড় সংখ্যা হবেঃ p+8, p+10, p+12, p+14, p+16, p+18, p+20
সুতরাং পরবর্তি 7 টি ধনাত্মক বিজোড় সংখ্যার গড় হবে = (7p+98) / 7 = p+14

৫৯২.

What is the average of 1², 2², 3², 4², 5², 6^2, 7²?

ক
ক) 20
খ
খ) 25
গ
গ) 30
ঘ
ঘ) 40

ব্যাখ্যা

Question: What is the average of 1², 2², 3², 4², 5², 6^2, 7²?

Solution:
Average = (1² + 2² + 3² + 4² + 5²+6²+7²)/7
= (1 + 4 + 9 +16 + 25 + 36 + 49)/7
= 140/7
= 20

Alternative Solution:
Sum = {n(n + 1)(2n + 1)}/6
= {7(7 + 1)(14 + 1)}/6
= (7 × 8 × 15)/6
= 140

Average = 140/7 = 20

৫৯৩.

In a primary school the average weight of male students is 65.9 kg and the average weight of female students is 57 kg. If the average weight of all the students (both male and female) is 60.3 kg and the number of male students in the school is 66, what is the number of female students in the school?

ক
ক) 162
খ
খ) 168
গ
গ) 180
ঘ
ঘ) 112

ব্যাখ্যা

Let the number of female students be x
Let the weight of female students = 57x
Number of male students = 66
Total weights of male students = 65.9 × 66
The average weight of all the students = 60.3 kg
Total weights of all the students = 60.3 (66 + x)

According to the given information,
Then,
⇒ 60.3 (66 + x) = 66 × 65.9 + 57x
⇒ 60.3 × 66 + 60.3x = 66 × 65.9 + 57x
⇒ 60.3x - 57x = 66 (65.9 - 60.3)
⇒ 3.3x = 66 × 5.6

∴ x = (66 × 5.6)/3.3
⇒ x = 2 × 56
⇒ x = 112

৫৯৪.

Find the average of the first 24 consecutive natural numbers.

ক
11.5
খ
14.5
গ
12.5
ঘ
13.5

ব্যাখ্যা

Question: Find the average of the first 24 consecutive natural numbers.

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

So, average = (24 + 1)/2 [Here, n=24]
= 25/2
= 12.5

৫৯৫.

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?

ক
Tk. 4991
খ
Tk. 5991
গ
Tk. 6001
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 × 6) - 34009 ]

= Tk. (39000 - 34009)

= Tk. 4991

৫৯৬.

In the first 15 overs of a cricket game, the run rate was only 3.4. What should be the rate in the remaining 35 overs to reach the target of 256 runs?

ক
5.47
খ
5.86
গ
6.14
ঘ
4.98

ব্যাখ্যা

Question: In the first 15 overs of a cricket game, the run rate was only 3.4. What should be the rate in the remaining 35 overs to reach the target of 256 runs?

Solution:
First 15 overs total run was = (3.4 × 15) = 51

Required run rate = (256 - 51)/35
= 205/35
= 5.86

৫৯৭.

If a/b = 5/4, then (4a + 3b)/(4a - 3b) =?

ক
4
খ
8
গ
2
ঘ
12

ব্যাখ্যা

Question: If a/b = 5/4, then (4a + 3b)/(4a - 3b) =?

Solution:

৫৯৮.

Among three numbers, the first is twice the second and thrice the third. If the average of the three numbers is 49.5, then the difference between the first and the third number is

ক
48
খ
45.5
গ
54
ঘ
38

ব্যাখ্যা

Question: Among three numbers, the first is twice the second and thrice the third. If the average of the three numbers is 49.5, then the difference between the first and the third number is-

Solution:
Let, the second number be = x
First number = 2x
∴ Third number = 2x/3

∴ 2x + x + (2x/3) = 49.5 × 3
⇒ 6x + 3x + 2x = 49.5 × 9
⇒ 11x = 445.5
⇒ x = 445.5/11
∴ x = 40.5

∴ Required difference = 2x - (2x/3)
= 4x/3
= (4 × 40.5)/3
= 54

৫৯৯.

a, b and c are all positive integers such that a + b + c = 150 and none of these values are equal to each other. What is the smallest possible value for the median of a, b and c?

ক
ক) 5
খ
খ) 4
গ
গ) 3
ঘ
ঘ) 2

ব্যাখ্যা

Question: a, b and c are all positive integers such that a + b + c = 150 and none of these values are equal to each other. What is the smallest possible value for the median of a, b and c?

Solution :
ধরি,
a = 1 , b = 2

a + b + c = 150
1 + 2 + c = 150
c = 150 - 3
c = 147

ক্রমানুসারে সংখ্যাগুলো হলো 1,2,147

সর্বনিম্ন মধ্যক হলো: 2

৬০০.

The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?

ক
32
খ
65
গ
67
ঘ
31

ব্যাখ্যা

Question: The average weight of P, Q and R is 45 kg. If the average weight of P and Q is 40 kg and that of Q and R is 43 kg, what is the weight of Q?

Solution:
Let
P, Q, R represent their respective weights. Then, we have:
P + Q + R = (45 × 3) = 135 ........ (i)
P + Q = (40 × 2) = 80 ....... (ii)
Q + R = (43 × 2) = 86 ....... (iii)

Adding (ii) and (iii), we get: P + 2Q + R = 166 ...... (iv)
Subtracting (i) from (iv), we get: Q = 31