Fraction and Simplification, Average and Mean

PrepBank · পাতা ৮ / ১০ · ৭০১–৮০০ / ৯৪৮

৭০১.

Find the value of ,

ক
3/4
খ
5/3
গ
5/4
ঘ
2

ব্যাখ্যা

Question: Find the value of ,

Solution:

৭০২.

In seven given numbers, the average of the first four numbers is 4 and the last four numbers is also 4. If the average of these given seven numbers is 3, the fourth number is -

ক
ক) 3
খ
খ) 4
গ
গ) 11
ঘ
ঘ) None of these

ব্যাখ্যা

Question: In seven given numbers, the average of the first four numbers is 4 and the last four numbers is also 4. If the average of these given seven numbers is 3, the fourth number is -

Solution:
Sum of first four numbers = 4 × 4 = 16
Sum of last four numbers = 4 × 4 = 16
Sum of first four numbers and last four numbers = 16 + 16 = 32

Again, Sum of seven numbers = 7 × 3 = 21

So, fourth number is = 32 - 21 = 11

৭০৩.

A batsman makes a score of 80 runs in the 16th innings and increases average by 3. What is his average after 16th innings?

ক
ক) 25
খ
খ) 29
গ
গ) 32
ঘ
ঘ) 35

ব্যাখ্যা

Question: A batsman makes a score of 80 runs in the 16th innings and increases average by 3. What is his average after 16th innings?

Solution:
Assume his initial average after 15 innings = x
His total runs after 15 innings = 15x

After scoring 80 runs his average got increased by 3 to x + 3
So his total runs after 16 innings= 16 × (x +3)

But it was given that the difference in the total scores after 15 innings and 16 innings =80
16×(x + 3) - 15X=80
16x + 48 - 15x = 80
x + 48 = 80
x = 32

His average after 16th innings is = 32 + 3 = 3 = 35

৭০৪.

The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?

ক
30
খ
25
গ
45
ঘ
35

ব্যাখ্যা

Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?

Solution:
(27 × 5) - (25 × 4)
= 135 - 100
= 35

৭০৫.

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

ক
30
খ
20
গ
60
ঘ
80
ঙ
None of these

ব্যাখ্যা

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

Solution:

Average of 4 terms = 20

Hence, the total sum of 4 terms = 80

Let terms be A, B, C, D

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

Given,
3A = B + C + D
3A + A = A + B + C + D
4A = A + B + C + D

So, 4A = 80,

A = 20

৭০৬.

The average height of girls in a class is 5 feet and that of boys is 5.7 feet. If the average height of the students in class is 5.5 feet. What could be the possible strength of boys and girls respectively in the class:

ক
ক) 50, 25
খ
খ) 30, 20
গ
গ) 20, 30
ঘ
ঘ) 60, 50
ঙ
ঙ) 50, 20

ব্যাখ্যা

The number of boys = B
The number of Girls = G
According to question, 5G + 5.7B = 5.5(B + G)
Or, 0.2B = 0.5G
Or, B:G = 5:2
Now, sum of the ratio= 7.
Sum of one option is divisible by 7 that is = 50 + 20
= 70

৭০৭.

The average of x numbers is y² and the average of y numbers is x². So the average of all the numbers taken together is

ক
(x³ + y³)/(x + y)
খ
(x² + y²)/(x + y)
গ
xy² + x²y
ঘ
xy

ব্যাখ্যা

Question: The average of x numbers is y² and the average of y numbers is x². So the average of all the numbers taken together is

Solution:
ATQ,
Average of x number is y²
∴ Sum of x number is = xy²

Average of y number is = x²
∴ Sum of y number is = yx²

Average of all number is = (xy²+ yx²)/(x + y)
= xy(y + x)/(x + y)
= xy

৭০৮.

Six times the average of six consecutive even integers is 18 more than the four times the largest integer. What is the average of the consecutive integers?

ক
ক) 19
খ
খ) 20
গ
গ) 21
ঘ
ঘ) 22

ব্যাখ্যা

Let the first even integer be y.
Therefore, 6(y + y + 2 + y + 4 + y + 6 + y + 8 + y + 10)/6 = 4(y + 10) + 18
⇒ 6y + 30 = 4y + 58
⇒ 2y = 28
⇒ y = 14
Therefore, the required average
= (6y + 30)/6
= (6 × 14 + 30)/6
= 114/6
= 19
----------------------------------------
৬ টি ক্রমিক জোড় পূর্ণ সংখ্যার গড়ের ৬ গুণ বৃহত্তম পূর্ণ সংখ্যার ৪ গুনের চেয়ে ১৮ বেশি হলে, সংখ্যা গুলোর গড় কত?

১ম জোড় পূর্ণ সংখ্যা y হলে,
6(y + y + 2 + y + 4 + y + 6 + y + 8 + y + 10)/6 = 4(y + 10) + 18
⇒ 6y + 30 = 4y + 58
⇒ 2y = 28
⇒ y = 14
অতএব, নির্ণেয় গড়
= (6y + 30)/6
= (6 × 14 + 30)/6
= 114/6
= 19

৭০৯.

The sum of Moni and Mimi's ages is 50 years and the difference between their ages is 6 years. What is the product of their ages?

ক
ক) 524 years
খ
খ) 616 years
গ
গ) 480 years
ঘ
ঘ) 300 years

ব্যাখ্যা

Question: The sum of Moni and Mimi's ages is 50 years and the difference between their ages is 6 years. What is the product of their ages?

Solution:
Let, Moni's age be = x years
and Mimi's age be = y years

ATQ,
x + y = 50.........(i)
x - y = 6.............(ii)

Now,
(i) + (ii),
x + y + x - y = 50 + 6
⇒ 2x = 56
⇒ x = 28

So, y = 50 - 28 = 22

∴ product of their ages = 28 × 22 = 616 years

৭১০.

The average of runs of a cricket player in 10 innings was 42. How many runes must be made in his next innings to increase his average of runs by 3?

ক
85
খ
75
গ
69
ঘ
68

ব্যাখ্যা

Question: The average of runs of a cricket player in 10 innings was 42. How many runes must be made in his next innings to increase his average of runs by 3?

Solution:
after increasing 3 runs the average will be 45

so, run required
= (45 × 11) - (42 × 10)
= 495 - 420
= 75

৭১১.

A, B, C and D are four consecutive even numbers respectively and their average is 75. What is the product of A and C?

ক
5472
খ
5078
গ
4476
ঘ
3464

ব্যাখ্যা

Question: A, B, C and D are four consecutive even numbers respectively and their average is 75. What is the product of A and C?

Solution:
Let's define the four consecutive even numbers as A, B, C, and D. The average of these numbers is given as 75.
Than the sum is,
75 × 4 = 300
Now let the 1^stnumber is x. The next three will be x + 2, x + 4, x + 6

According to the question,
⇒ x + x + 2 + x + 4 + x + 6 = 300
⇒ 4x + 12 = 300
⇒ 4x = 300 - 12
⇒ 4x = 288
⇒ x = 288/4
∴ x = 72
So the 1^st number is A = 72
The next three numbers are B = 72 + 2 = 74, C = 72 + 4 = 76, D = 72 + 6 = 78

∴ Finally, the product of A and C is,
A × C = 72 × 76 = 5472
So, the product of A and C is 5472.

৭১২.

Siddik has a new set of golf clubs. Using a club 8, 7, and 6 the ball travels an average distance of 100m, 108m, 114m respectively. How far will the ball go if he uses a club 5?

ক
ক) 122m
খ
খ) 120m
গ
গ) 118m
ঘ
ঘ) 116m

ব্যাখ্যা

এখানে,
দূরত্বকে একটি ধারা মনে করে পাই,
ধারাঃ 100m 108m 114m 118m
পার্থক্যঃ 8m 6m 4m
সুতরাং সঠিক উত্তর 118m

৭১৩.

The average of 15 numbers is zero. Of them, at the most, how many may be greater than zero?

ক
ক) 0
খ
খ) 1
গ
গ) 10
ঘ
ঘ) 14

ব্যাখ্যা

প্রশ্ন: The average of 15 numbers is zero. Of them, at the most, how many may be greater than zero?

সমাধান: ধরি, সংখ্যাগুলি হল a₁, a₂, ..., a₁₅
দেয়া আছে, সংখ্যাগুলোর গড় শূন্য

তাহলে, (a₁ + a₂ +...+ a₁₅)/15 = 0
⇒ a₁ + a₂ +...+ a₁₅ = 0
⇒ a₁ + a₂ +...+ a₁₄= −a₁₅
∴ সর্বোচ্চ ১৪ টি সংখ্যার মান শুন্য থেকে বড় হতে পারে।

৭১৪.

If the average of p numbers is 2q² and the average of q numbers is 2p², what is the average of the combined (p + q) numbers?

ক
p + q
খ
2pq
গ
(p² + q²)/(p +q)
ঘ
2(p² + q²)/pq

ব্যাখ্যা

Question: If the average of p numbers is 2q² and the average of q numbers is 2p², what is the average of the combined (p + q) numbers?

Solution:
দেওয়া আছে,
p সংখ্যার গড় = 2q²
∴ p সংখ্যার সমষ্টি = p × 2q²

q সংখ্যার গড় = 2p²
∴ q সংখ্যার সমষ্টি = q × 2p²

∴ মোট সমষ্টি = (p × 2q²) + (q × 2p²)
= 2pq(q + p)

∴ তাদের গড় = মোট সমষ্টি / (p + q)
= 2pq(p + q)/(p + q)
= 2pq

৭১৫.

The average age a family consists of six members is 20 years. If one person is removed, the average becomes 15 years. Find the age of the person removed?

ক
45 years
খ
40 years
গ
42 years
ঘ
None of these

ব্যাখ্যা

Question: The average age a family consists of six members is 20 years. If one person is removed, the average becomes 15 years. Find the age of the person removed?

Solution:
The average age of a family consists of 6 members is 20 years.
The total age of all family members 20 × 6 = 120

one person is removed then the average becomes 15 years.
The sum of the age of 5 members 15 × 5 = 75 years.

The age of the person removed 120 - 75 = 45 years.
∴ The average age of the person removed is 45 years.

৭১৬.

The average age of a class of 29 students is 20 years. If the age of the teacher is included, then the average increases by 3 months. Find the age of the teacher.

ক
ক) 25.2 years
খ
খ) 27.5 years
গ
গ) 29 years
ঘ
ঘ) 31.5 years

ব্যাখ্যা

Average = Sum of Quantities/Number of Quantities

1) First calculate the total age of 40 students
Total age of 29 students = ( Average age x No. of students)
= (20 x 29) = 580 years

2) Average age of 29 students + 1 teacher = 20 years + 3 months = 81/4 years

3) Finally the total age of 29 students + 1 teacher = 81/4 × 30 = 607.5 years

Therefore, age of teacher = (Total age of 30 members - Total age of 29 students)
= (607.5 – 580)
= 27.5 years.

৭১৭.

What will come in the place of the question mark in the following question- 40% of 50% of 3/4 of 2400 = ?

ক
360
খ
280
গ
520
ঘ
300

ব্যাখ্যা

Question: What will come in the place of the question mark in the following question- 40% of 50% of 3/4 of 2400 = ?

Solution:
40% of 50% of 3/4 of 2400 = ?
⇒ 40% × 50% × (3/4) × 2400 = ?
⇒ (40/100) × (50/100) × 3/4 × 2400 = ?
⇒ (2/5) × (1/2) × (3/4) × 2400 = ?
⇒ (6/40) × 2400 = ?
⇒ ? = 360

∴ The value of ? is 360

৭১৮.

The monthly sales of a grocer for five months are Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562. How much must he sell in the sixth month to ensure his average over six months is exactly Tk. 6500?

ক
Tk. 4560
খ
Tk. 4991
গ
Tk. 6251
ঘ
Tk. 7135

ব্যাখ্যা

Question: The monthly sales of a grocer for five months are Tk. 6435, Tk. 6927, Tk. 6855, Tk. 7230 and Tk. 6562. How much must he sell in the sixth month to ensure his average over six months is exactly Tk. 6500?

Solution:
ধরি,
6-তম মাসে বিক্রির পরিমাণ = ক টাকা

প্রথম ৫ মাসে মোট বিক্রি = (6435 + 6927 + 6855 + 7230 + 6562) টাকা = 34009 টাকা

প্রশ্নমতে,
(34009 + ক)/6 = 6500
⇒ 34009 + ক = 6500 × 6
⇒ 34009 + ক = 39000
⇒ ক = 39000 - 34009
⇒ ক = 4991

∴ 6-তম মাসে বিক্রির পরিমাণ হতে হবে = 4991 টাকা

৭১৯.

If the average of 'a' numbers is b² and the average of 'b' numbers is a², what is the average of the combined (a + b) numbers?

ক
a - 1
খ
a + 1
গ
ab
ঘ
1

ব্যাখ্যা

Question: If the average of 'a' numbers is b² and the average of 'b' numbers is a², what is the average of the combined (a + b) numbers?

Solution:
দেওয়া আছে:
'a' সংখ্যার গড় = b²
∴ a সংখ্যার সমষ্টি = a × b²

'b' সংখ্যার গড় = a²
∴ 'b' সংখ্যার সমষ্টি = b × a²

∴ মোট সমষ্টি = (a × b²) + (b × a²)
= ab(a + b)

∴ তাদের গড় = মোট সমষ্টি/(a + b)
= ab(a + b)/(a + b)
= ab

৭২০.

A group of 30 employees of Cadre A has a mean age of 27. A different group of 70 employees of Cadre B has a mean age of 23. What is the mean age of the employees of the two groups together?

ক
26.2
খ
23.2
গ
24
ঘ
24.2

ব্যাখ্যা

Question: A group of 30 employees of Cadre A has a mean age of 27. A different group of 70 employees of Cadre B has a mean age of 23. What is the mean age of the employees of the two groups together?

Solution:
• Cadre A has a mean age = 27
- Total employees = 30
- Total age = 27×30 = 810 years

On the other hand,
• Cadre B has a mean age = 23
- Total employees = 70
- Total age = 1610 years

• From both the A and B cadre groups,
- Total employees = 100
- Total age = 2420 years
Now, Mean or Average = 2420/100 = 24.2 years.

৭২১.

Puja has 60 Tk more than Titu and 90 Tk more than Pavel. If their total is 330 Tk, what is Puja's share?

ক
100 Tk.
খ
160 Tk.
গ
180 Tk.
ঘ
190 Tk.

ব্যাখ্যা

Question: Puja has 60 Tk more than Titu and 90 Tk more than Pavel. If their total is 330 Tk, what is Puja's share?

Solution:
let,
Puja has x Tk.
Titu has (x - 60)Tk.
Pavel has (x - 90)Tk.

x + x - 60 + x - 90 = 330
or, 3x - 150 = 330
or, 3x = 330 + 150
or, x = 480/3
∴ x = 160

So, Puja's share is 160 Tk.

৭২২.

The average of the largest and smallest 3 digits numbers formed by 0, 2, and 4 would be:

ক
212
খ
303
গ
232
ঘ
312

ব্যাখ্যা

Question: The average of the largest and smallest 3 digits numbers formed by 0, 2, and 4 would be:

Solution:
ATQ,
Largest number = 420
Smallest number = 204

∴ Average = (420 + 204)/2
= 624/2
= 312

৭২৩.

ক
0.03
খ
0.3
গ
0.43
ঘ
None of these

ব্যাখ্যা

Question:

Solution:

৭২৪.

If (5x - 2y) ∶ (x - 2y) = 9 ∶ 17, then find the value of x/y = ?

ক
4/19
খ
5/17
গ
8/15
ঘ
9/17

ব্যাখ্যা

Question: If (5x - 2y) ∶ (x - 2y) = 9 ∶ 17, then find the value of x/y = ?

Solution:
Given that,
(5x - 2y) ∶ (x - 2y) = 9 ∶ 17

Now,
⇒ (5x - 2y)/(x - 2y) = 9/17
⇒ 17 × (5x - 2y) = 9 × (x - 2y)
⇒ 85x - 34y = 9x - 18y
⇒ 76x = 16y
⇒ x/y = 16/76
∴ x/y = 4/19

৭২৫.

Simplify it.

ক
2.03
খ
2.13
গ
2
ঘ
2.69

ব্যাখ্যা

Question: Simplify it.

Solution:

৭২৬.

Average of 60 numbers are 42. When 5 more numbers are included, the average of 65 numbers become 45. Find the average of 5 numbers.

ক
78
খ
80
গ
81
ঘ
82

ব্যাখ্যা

Question: Average of 60 numbers are 42. When 5 more numbers are included, the average of 65 numbers become 45. Find the average of 5 numbers.

Solution:
Total of 60 numbers = 60 × 42 = 2520
Now, total of 65 numbers = 65 × 45 = 2925

Hence, sum of 5 numbers = 2925 - 2520 = 405

∴ Average of five numbers = 405/5
= 81

৭২৭.

The daughter's age is mean proportional to age of the father and son. The age of the father and son is 50 years and 8 years respectively. What is the age of the daughter?

ক
ক) 10 years
খ
খ) 16 years
গ
গ) 20 years
ঘ
ঘ) None of these

ব্যাখ্যা

Question: The daughter's age is mean proportional to age of the father and son. The age of the father and son is 50 years and 8 years respectively. What is the age of the daughter?

Solution:
Let,
1st proportional = Father's age
and 3rd proportional = Son's age

We know,
Mean Proportional = √(1st proportional × 3rd proportional)

So, daughter's age = √(50 × 8) years
= √400 years
= 20 years

৭২৮.

After 3 semesters in college, Jim has a 3.0 GPA. What GPA must Jim attain in his fourth semester if he wishes to raise his GPA to a 3.1?

ক
ক) 2.7
খ
খ) 3.1
গ
গ) 3.3
ঘ
ঘ) 3.4
ঙ
ঙ) 3.5

ব্যাখ্যা

Question: After 3 semesters in college, Jim has a 3.0 GPA. What GPA must Jim attain in his fourth semester if he wishes to raise his GPA to a 3.1?

Solution:
After 3 semesters in college, Jim has a 3.0 GPA.

Jim's Total points after 3 semester = 3.0 × 3 = 9.0

Let,
He must attain X point in his fourth semester.

ATQ,
(9.0 + X)/4 = 3.1
⇒ 9.0 + X = 12.4
⇒ X = 12.4 - 9.0
∴ X = 3.4

৭২৯.

X's marks are 70, 90, 65, 85 and 75. What marks he must get on the next test to raise her average to 80?

ক
ক) 80
খ
খ) 85
গ
গ) 90
ঘ
ঘ) 95

ব্যাখ্যা

Question: X's marks are 70, 90, 65, 85 and 75. What marks he must get on the next test to raise her average to 80?

Solution:
X এর প্রাপ্ত নম্বর ৭০, ৯০, ৬৫, ৮৫, ৭৫
ধরি, পরবর্তী পরীক্ষায় y নম্বর পেলে গড় ৮০ হবে।

৭০ + ৯০ + ৬৫ + ৮৫ + ৭৫ + y / ৬ = ৮০
⇒ ৩৮৫ + y = ৪৮০
∴ y = ৪৮০ - ৩৮৫
= ৯৫

৭৩০.

Rahim's average score in 4 tests was 80 out of a possible 100. If his scores in two of the tests were 60 and 70, what is the lowest that either of his other scores could have been?

ক
ক) 70
খ
খ) 80
গ
গ) 85
ঘ
ঘ) 90

ব্যাখ্যা

Question: Rahim's average score in 4 tests was 80 out of a possible 100. If his scores in two of the tests were 60 and 70, what is the lowest that either of his other scores could have been?

Solution:
Total marks of 4 tests = 4 x 80 = 320

Marks of the other two subjects = (320 - 60 - 70) = 190 marks
He can get the highest 100 marks in one of the subjects.

∴ The lowest mank = 190 - 100 = 90 marks

৭৩১.

The average weight of 50 students in a class is 55 kg. If three students weighing 60 kg, 65 kg, and 70 kg leave the class, what is the new average weight of the remaining students?

ক
54.4 kg
খ
47.7 kg
গ
49.3 kg
ঘ
40.2 kg

ব্যাখ্যা

Question: The average weight of 50 students in a class is 55 kg. If three students weighing 60 kg, 65 kg, and 70 kg leave the class, what is the new average weight of the remaining students?

Solution:
Total weight = 50 × 55 = 2750 kg

Students leaving = 60 kg + 65 kg + 70 kg = 195 kg
Remaining total weight = 2750 - 195 = 2555 kg

Remaining students = 50 - 3 = 47 students
New average = 2555/47
= 54.4 kg

Therefore, the new average weight is approximately 54.4 kg

৭৩২.

The average of four consecutive odd integers is 24. Then which will be the lowest of them?

ক
21
খ
25
গ
28
ঘ
24

ব্যাখ্যা

Let the x, x + 2, x + 4 and x + 6 be the 4 consecutive odd integers.
We have to find the lowest integer x.
It is given that the average of these numbers is 24.
i,e., (x + x + 2 + x + 4 + x + 6)/4 = 24
⇒ 4x + 12 = 24x4
⇒ 4x = 84
⇒ x = 84/4
= 21
Hence, the answer is 21.

৭৩৩.

The average of 8 numbers is 8. If 4 is subtracted from each of 6 of these numbers, what is the new average?

ক
3.5
খ
5
গ
4
ঘ
6.5

ব্যাখ্যা

Question: The average of 8 numbers is 8. If 4 is subtracted from each of 6 of these numbers, what is the new average?

Solution:
দেওয়া আছে,
8 টি নম্বরের গড় = 8
∴ 8 টি নম্বরের সমষ্টি = (8 × 8) = 64

8 টি নম্বরের মধ্যে 6 টি নম্বরের প্রতিটি থেকে 4 বিয়োগ করা হলে নতুন সমষ্টি,
= 64 - (6 × 4)
= 64 - 24
= 40

সুতরাং 8 টি সংখ্যার নতুন গড় হবে,
= 40/8
= 5

৭৩৪.

What is the average of odd numbers from 1 to 40?

ক
20
খ
21
গ
31
ঘ
41

ব্যাখ্যা

Question: What is the average of odd numbers from 1 to 40?

Solution:
sum of odd numbers from 1 to 40 = 1 + 3 + 5 + ... + 39
= 20 (1 + 39)/2
= 20 × 40/2
= 400

Average = 400/20
= 20

৭৩৫.

Gita and Raju got their marks in 4 subjects i.e English, Science, Maths and Social. The average marks obtained by Raju is 38. The ratio of marks obtained by Raju and Gita in Maths is 5 ∶ 6 and the average marks obtained by Gita is 41. If the marks scored by both of them in English and Science is same and in Social Raju got 5 marks less than Gita. What is the marks scored by them in English and Science if Raju scored 40 marks in Social?

ক
42
খ
36.5
গ
38.5
ঘ
40

ব্যাখ্যা

Question: Gita and Raju got their marks in 4 subjects i.e English, Science, Maths and Social. The average marks obtained by Raju is 38. The ratio of marks obtained by Raju and Gita in Maths is 5 ∶ 6 and the average marks obtained by Gita is 41. If the marks scored by both of them in English and Science is same and in Social Raju got 5 marks less than Gita. What is the marks scored by them in English and Science if Raju scored 40 marks in Social?

Solution:
Total marks scored by Raju = 38 × 4 = 152
Total marks scored by Gita = 41 × 4 = 164
Ratio of marks obtained by Raju and Gita in Maths = 5 ∶ 6
Let the marks obtained by Raju and Gita in Maths be 5x and 6x

Marks scored by Raju in Social = 40
∴ Marks scored by Gita in Social = 45

Let the marks scored by them in English and Science = y

∴ The difference in marks scored by them
(6x + y + y + 45) - (5x + y + y + 40) = 164 - 152
⇒ x + 5 = 12
∴ x = 7

∴ Marks scored by Raju in Maths = 7 × 5 = 35
∴ Marks obtained by Raju in English and Science = y + y = 152 - 40 - 35 = 77
⇒ 2y = 77
⇒ y = 77/2
∴ y = 38.5

∴ The marks scored by Gita and Raju in English and Science is 38.5

৭৩৬.

The mean weight of three club members is 42 kg. If none of them weighs less than 40 kg, what is the maximum possible weight of one of the members?

ক
41 kg
খ
44 kg
গ
46 kg
ঘ
48 kg

ব্যাখ্যা

Question: The mean weight of three club members is 42 kg. If none of them weighs less than 40 kg, what is the maximum possible weight of one of the members?

Solution:
Given,
the mean weight of three members is 42 kg
Total weight of three members = (42 × 3) kg = 126 kg

According to the question,
Minimum weight of any member = 40 kg
So, Minimum weight of 2 members = (40 × 2) = 80 kg

∴ Maximum weight of any of three members = (126 - 80) kg = 46 kg

৭৩৭.

A sum of Tk. 3300 is divided among A, B and C such that A gets 2/5 of what B gets and B gets 1/3 of what C gets. B’s share is:

ক
700 Tk.
খ
750 Tk.
গ
800 Tk.
ঘ
900 Tk.

ব্যাখ্যা

Question: A sum of Tk. 3300 is divided among A, B and C such that A gets 2/5 of what B gets and B gets 1/3 of what C gets. B’s share is:

Solution:
Let,
C’s share = Tk. x
Then,
B’s share = Tk. x/3
A’s share = Tk. (2/5) × (x/3) = Tk. 2x/15

∴ 2x/15 + x/3 + x = 3300
⇒ (2x + 5x + 15x)/15 = 3300
⇒ 22x/15 = 3300
⇒ 22x = 3300 × 15
⇒ 22x = 49500
⇒ x = 49500/22
⇒ x = 2250

∴ B’s share = 2250/3 = 750 Tk.

৭৩৮.

The average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age become 15.5 years. The number of persons initially going for tour is -

ক
40
খ
20
গ
10
ঘ
5

ব্যাখ্যা

Question: The average age of a group of persons going for tour is 16 years. Twenty new persons with an average age of 15 years join the group on the spot due to which their average age become 15.5 years. The number of persons initially going for tour is -

Solution:
The number of persons initially going for tour is x
initial total age = 16x

new age added = 20 × 15 = 300 years

(16x + 300)/(x + 20) = 15.5
⇒ 16x + 300 = 15.5 (x + 20)
⇒ 16x + 300 = 15.5x + 310
⇒ 0.5x = 10
∴ x = 10/0.5 = 20

৭৩৯.

The average age of a group of 20 employees is 30 years. If 10 more employees join the group, the average age increases by 3 years. Find the average age of the new employees?

ক
35 years
খ
36 years
গ
39 years
ঘ
42 years

ব্যাখ্যা

Question: The average age of a group of 20 employees is 30 years. If 10 more employees join the group, the average age increases by 3 years. Find the average age of the new employees?

Solution:
Here,
Total age of the 20 employees,
= 20 × 30=600 years

After joining 10 new employees, average age increases by 3 years.
So, New average age = 30 + 3 = 33 years

Total age of the 30 employees,
= 30 × 33 = 990 years

∴ Total age of the 10 new employees = (990 - 600) years
= 390 years

∴ Average age of the 10 new employees = 390/10 = 39 years

৭৪০.

The average monthly income of P and Q is Tk. 5000. The average monthly income of Q and R is Tk. 6050 and the average monthly income of P and R is Tk. 5400. Calculate the monthly income of Q.

ক
TK. 6450
খ
TK. 5650
গ
TK. 4350
ঘ
TK. 3550

ব্যাখ্যা

Question: The average monthly income of P and Q is Tk. 5000. The average monthly income of Q and R is Tk. 6050 and the average monthly income of P and R is Tk. 5400. Calculate the monthly income of Q.

Solution:
Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5000 x 2) = 10000 .... (i)
Q + R = (6050 x 2) = 12100 .... (ii)
P + R = (5400 x 2) = 10800 .... (iii)

Adding (i), (ii) and (iii), we get:
2(P + Q + R) = 32900
∴ P + Q + R = 16450 .... (iv)

Subtracting (iii) from (iv),
We get Q = 5650

∴ Q's monthly income = TK. 5650

৭৪১.

Out of three numbers, the first is twice the second and is half of the third. If the average of the three number is 56, then the difference of first and third number is:

ক
30
খ
32
গ
40
ঘ
48

ব্যাখ্যা

Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three number is 56, then the difference of first and third number is:

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

∴ 2x + x + 4x = 56 × 3
⇒ 7x = 168
⇒ x = 168/7
⇒ x = 24

Required difference:
= 4x - 2x
= 2x
= 2 × 24
= 48.

৭৪২.

If 3x + 2y = 8 and 2x - y = 3. Find the value of 3x - 4.

ক
4
খ
- 2
গ
- 3
ঘ
2

ব্যাখ্যা

Question: If 3x + 2y = 8 and 2x - y = 3. Find the value of 3x - 4.

Solution:
Given that,
3x + 2y = 8 .......... (1)
2x - y = 3 ............(2)

Now,
(1) + (2) × 2 ⇒ 3x + 2y + 2(2x - y) = 8 + 6
⇒ 3x + 2y + 4x - 2y = 14
⇒ 7x = 14
⇒ x = 14/7
∴ x = 2
Now puting the value of x = 2 into equation = 3x - 4
= 3(2) - 4
= 6 - 4
= 2

৭৪৩.

Hasan's average on 4 tests is 85. Assuming he can earn no more than 100 on any test, what is the least he can earn on his 5^th test and still have a chance for an 87 average after seven tests?

ক
ক) 75
খ
খ) 69
গ
গ) 72
ঘ
ঘ) 70

ব্যাখ্যা

Question: Hasan's average on 4 tests is 85. Assuming he can earn no more than 100 on any test, what is the least he can earn on his 5^th test and still have a chance for an 87 average after seven tests?

Solution:
হাসান 4টি পরীক্ষায় মোট পায় = 4 × 85 = 340 নম্বর
হাসান 7টি পরীক্ষায় মোট পায় = 7 × 87 = 609 নম্বর

হাসান 3টি পরীক্ষায় মোট পায় = 609 - 340 = 269 নম্বর

৬ষ্ঠ ও ৭ম পরীক্ষায় সর্বোচ্চ নম্বর পায় = 100 + 100 = 200
৫ম পরীক্ষায় সর্বনিম্ন নম্বর পায় = 269 - 200 = 69

৭৪৪.

A man earns N dollars a month and spends S dollars a month on rent. If he then spends 3/8 of the remainder on food, how much, in dollars, is left over for other expenses, in terms of N and S?

ক
(3/8) (N - S)
খ
(3/8) (N + S)
গ
(5/8) (N - S)
ঘ
(5/8) (N + S)
ঙ
(1/8) (N - S)

ব্যাখ্যা

Question: A man earns N dollars a month and spends S dollars a month on rent. If he then spends 3/8 of the remainder on food, how much, in dollars, is left over for other expenses, in terms of N and S?

Solution:
Given that,
Monthly income = N dollars
Rent = S dollars

∴ Remaining after rent = N - S

And, He spends 3/8 of the remainder on food.
∴ Food expense = (3/8)(N - S)

∴ Left for other expenses = Remaining after rent - Food expense
= (N - S) - {(3/8)(N - S)}
= (8/8)(N - S) - {(3/8)(N - S)}
= {(8 - 3)/8}(N - S)
= (5/8)( N - S)

৭৪৫.

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

ক
30 kg
খ
31 kg
গ
32 kg
ঘ
34 kg

ব্যাখ্যা

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

Solution:
Let P, Q, C 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),
P + 2Q + R = 80 + 86
P + 2Q + R = 166 ........... (iv)

Subtracting (i) from (iv),
P + 2Q + R = 166
P + Q + R = 135
Q = 31

∴ Q's weight = 31 kg.

৭৪৬.

Find the average of numbers 87, 84, 86, 90, 82, 88, 78.

ক
86
খ
85
গ
84
ঘ
83
ঙ
82

ব্যাখ্যা

Question: Find the average of numbers 87, 84, 86, 90, 82, 88, 78.

Solution:

The sum of all the observations here is 87 + 84 + 86 + 90 + 82 + 88 + 78 = 595

Number of observations = 7

So, Average = 595/7 = 85

৭৪৭.

Of the three numbers, the first is twice the second is half of the third. If the average of the three numbers is 63, then difference of first and third numbers is-

ক
36
খ
42
গ
48
ঘ
54

ব্যাখ্যা

Question: Of the three numbers, the first is twice the second is half of the third. If the average of the three numbers is 63, then difference of first and third numbers is-

Solution:
Let,
the second number be = a
Then, first number is = 2a
And third number is = 4a

ATQ,
(2a + a + 4a)/3 = 63
⇒ 7a = (63 × 3)
⇒ 7a = 189
∴ a = 27

∴ Requried difference = 4a - 2a
= (4 × 27) - (2 × 27)
= 54

৭৪৮.

The average height of girls in a class is 5ft and that of boys is 5.7ft. If the average height of the students in class is 5.5 ft what could be the possible strength of boys and girls respectively in the class:

ক
ক) 50,20
খ
খ) 30,20
গ
গ) 20,30
ঘ
ঘ) 60,50

ব্যাখ্যা

ধরি,
ছাত্র সংখ্যা= x জন
ছাত্রী সংখ্যা = y জন

প্রশ্নমতে,
5.7x + 5y = 5.5 (x + y)
57x + 50y =55x + 55y
57x - 55x = 55y - 50y
2x = 5y
x/y = 5/2
x : y = 5 : 2
অনুপাতের যোগফল = 5 + 2 = 7
যা দ্বারা 50 + 20 = 70 বিভাজ্য
সম্ভাব্য ছাত্র ছাত্রী সংখ্যা হতে পারে = 50,20

৭৪৯.

The average salary of 65 workers is Rs. 5680 out of which average salary of 31 workers is Rs. 2356 and that of 23 workers is Rs. 4589. What is the average salary of remaining workers?

ক
ক) Tk. 19832.25
খ
খ) Tk. 19732.50
গ
গ) Tk. 17328.81
ঘ
ঘ) Tk. 18734.47

ব্যাখ্যা

Total salary of 65 workers = 65 × 5680 = Tk. 369200
Total salary of 31 workers = 31 × 2356 = Tk. 73036
Total salary of 23 workers = 23 × 4589 = Tk. 105547
No. of remaining workers = 65 - 31 – 23 = 65 – 54 = 11
Total Salary of 11 workers = 369200 – 73036 – 105547
= 369200 – 178583
= Tk. 190617
Required average = 190617/11
= Tk. 17328.81
Hence, the required average is Tk. 17328.81

৭৫০.

If , then x = ?

ক
9
খ
4
গ
1
ঘ
6

ব্যাখ্যা

Question: If , then x = ?

Solution:

৭৫১.

The average of two numbers is 6.5 and the square root of their product is 6. What are the numbers?

ক
ক) 11 and 2
খ
খ) 8 and 5
গ
গ) 10 and 3
ঘ
ঘ) 9 and 4
ঙ
ঙ) 9 and 5

ব্যাখ্যা

According to the question,
(x + y)/2 = 6.5,
or, x + y = 13 and
xy = 36,
Now substitute the value of x and y from the option and find the answer.

৭৫২.

A grocer has a sale of Tk. 6430, Tk. 6932, Tk. 6850, Tk. 7235 and Tk. 6560 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
5469
খ
4993
গ
5989
ঘ
6455

ব্যাখ্যা

Question: A grocer has a sale of Tk. 6430, Tk. 6932, Tk. 6850, Tk. 7235 and Tk. 6560 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. (6430 + 6932 + 6850 + 7235 + 6560) = Tk. 34007.

Required sale = Tk. [(6500 × 6) - 34009]
= Tk. (39000 - 34007)
= Tk. 4993

৭৫৩.

The average age of all the students in a driving class is 22 years. The average age of the boys is 24 years and that of the girls is 18 years. If there are 15 girls in the class, find the number of boys.

ক
30
খ
25
গ
24
ঘ
20

ব্যাখ্যা

Question: The average age of all the students in a driving class is 22 years. The average age of the boys is 24 years and that of the girls is 18 years. If there are 15 girls in the class, find the number of boys.

Solution:
Let the number of boys in the class be x.

According to the question,
22 × (x + 15) = 24x + (18 × 15)
⇒ 22x + 330 = 24x + 270
⇒ 24x + 270 = 22x + 330
⇒ 24x - 22x = 330 - 270
⇒ 2x = 60
⇒ x = 30

∴ The number of boys in the class is 30.

৭৫৪.

Simplify the expression,

ক
14
খ
12
গ
8
ঘ
16

ব্যাখ্যা

Question: Simplify the expression,

Solution:

৭৫৫.

The average of a, b, c is 8 and a - b = 4, ab = 60, what is the value of c?

ক
ক) 7
খ
খ) 8
গ
গ) 9
ঘ
ঘ) 10

ব্যাখ্যা

দেয়া আছে,
(a + b + c)/3 = 8
a + b + c = 24 ............ (1)

a - b = 4,
ab = 60

আমরা জানি
(a + b)² = (a - b)² + 4ab
(a + b)² = (4)² + 4 × 60
(a + b)²= 16 + 240
(a + b)² = 256
a + b = 16
(1) নং এ a + b এর মান বসিয়ে পাই,
a + b + c = 24
16 + c = 24
c = 24 - 16
c = 8

৭৫৬.

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?

ক
19
খ
21
গ
17
ঘ
23

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)

We can say,
11x - (26 + 29) = 9(x - 1)
⇒ 11x - 55 = 9x - 9
⇒ 11x - 9x = - 9 + 55
⇒ 2x = 46
∴ x = 23 Years.

৭৫৭.

The average attendance of a college for the first three days of a week is 327 and the first four days is 321. How many were present on the fourth day?

ক
ক) 310
খ
খ) 320
গ
গ) 303
ঘ
ঘ) 307

ব্যাখ্যা

প্রশ্ন : The average attendance of a college for the first three days of a week is 327 and the first four days is 321. How many were present on the fourth day?
সমাধান :
Total attendance for first 3 days = 327×3 = 981
Total attendance for first 4 days = 321×4 = 1284
∴ Present on the 4th day = 1284 - 981 = 303

৭৫৮.

If 7x + 3y = 17 and 3x + 7y = 19, what is the average of x and y?

ক
1.55
খ
2.05
গ
1.8
ঘ
3.6
ঙ
None

ব্যাখ্যা

প্রশ্ন: If 7x + 3y = 17 and 3x + 7y = 19, what is the average of x and y?

সমাধান:
দেওয়া আছে,
7x + 3y = 17 .......... (1)
3x + 7y = 19 ......... (2)

(1) নং + (2) নং ⇒
7x + 3y + 3x + 7y = 17 + 19
⇒ 10x + 10y = 36
⇒ 10(x + y) = 36
⇒ x + y = 36/10
⇒ x + y = 3.6

অতএব, গড় = (x + y)/2
= 3.6/2
= 1.8

৭৫৯.

A batsman makes a score of 87 runs in the 17th innings and thus increases his average by 3. What is his average after 17th innings?

ক
35
খ
40.5
গ
39
ঘ
42

ব্যাখ্যা

Let average of 17 innings = x
Total runs scored in 17 innings = 17x
Average of 16 innings = (x - 3)
Total runs scored in 16 innings = 16 (x -3)
Total runs scored in 16 innings + 87 = Total runs scored in 17 innings
⇒ 16(x - 3) + 87 = 17x
⇒ 16x - 48 + 87 = 17x
⇒ x = 39.

৭৬০.

If the number of quantities in group A is 10 and in group B is 8, and their individual average is 24 and 16 respectively, find the combined average of the two groups.

ক
18.22
খ
20.44
গ
16.22
ঘ
18.66

ব্যাখ্যা

Question: If the number of quantities in group A is 10 and in group B is 8, and their individual average is 24 and 16 respectively, find the combined average of the two groups.

Solution:
The sum of group A = 10 × 24 = 240
The sum of group B = 8 × 16 = 128

∴ Combined Average of the two groups = (240 + 128)/(10 + 8)
= 368/18
= 20.44

৭৬১.

When 35 - [30 - {35 - (15 - x)}] = 60, then x is equal to-

ক
- 19
খ
35
গ
20
ঘ
- 29

ব্যাখ্যা

Question: When 35 - [30 - {35 - (15 - x)}] = 60, then x is equal to-

Solution:
35 - [30 - {35 - (15 - x)}] = 60
⇒ 35 - [30 - {35 -15 + x}] = 60
⇒ 35 - [30 - {20 + x}] = 60
⇒ 35 - [30 - 20 - x] = 60
⇒ 35 - [10 - x] = 60
⇒ 35 - 10 + x = 60
⇒ 25 + x = 60
∴ x = 60 - 25 = 35

৭৬২.

In a room, if 4 students sit in each bench, there are 3 empty benches, but 6 students have to stand if 3 students sit each bench. How many students are there in that room?

ক
80
খ
70
গ
60
ঘ
50
ঙ
None

ব্যাখ্যা

Question: In a room, if 4 students sit in each bench, there are 3 empty benches, but 6 students have to stand if 3 students sit each bench. How many students are there in that room?

Solution:
ধরি,
বেঞ্চ সংখ্যা ক টি

একটি রুমের প্রতি বেঞ্চে ৪ জন করে ছাত্র বসলে ৩ টি বেঞ্চ খালি থাকে।
∴ ছাত্রসংখ্যা= (ক - ৩) × ৪ জন

প্রতি বেঞ্চে ৩ জন করে ছাত্র বসালে ৬ জন ছাত্রকে দাঁড়িয়ে থাকতে হয়।
∴ ছাত্রসংখ্যা = ৩ক + ৬ জন

প্রশ্নমতে,
(ক - ৩) × ৪ = ৩ক + ৬
⇒ ৪ক - ১২ = ৩ক + ৬
∴ ক = ১৮

ছাত্রসংখ্যা = (ক - ৩) × ৪ জন
= (১৮ - ৩) × ৪ জন
= ১৫ × ৪ জন
= ৬০ জন

৭৬৩.

Four numbers are in the ratio 1 : 2 : 3 : 4 and their HCF 12. The average of four numbers is -

ক
28
খ
25
গ
24
ঘ
30

ব্যাখ্যা

Question: Four numbers are in the ratio 1 : 2 : 3 : 4 and their HCF 12. The average of four numbers is -

Solution:
Let the four numbers are x, 2x, 3x, 4x respectively
Their HCF = x

ATQ,
x = 12

So, the four numbers are 12, 24, 36 and 48 respectively
The average of the four number = (12 + 24 + 36 + 48)/4 = 30

৭৬৪.

The average salary of all the workers in a workshop is Tk. 8,000. The average salary of 7 technicians is Tk. 12,000 and the average salary of the rest is Tk. 6,000. The total number of workers in the workshop is:

ক
17
খ
20
গ
21
ঘ
27

ব্যাখ্যা

Question: The average salary of all the workers in a workshop is Tk. 8,000. The average salary of 7 technicians is Tk. 12,000 and the average salary of the rest is Tk. 6,000. The total number of workers in the workshop is:

Solution:
Let the number of rest workers = x

Now, According to the question,
(7 + x) × 8000 = 12000 × 7 + 6000x
⇒ 56000 + 8000x = 84000 + 6000x
⇒ 2000x = 28000
⇒ x = 14

So the total number of worker
= 14 + 7
= 21

৭৬৫.

Which of the following numbers does not lie between 4/5 and 7/13?

ক
2/3
খ
3/4
গ
1/2
ঘ
5/7

ব্যাখ্যা

Question: Which of the following numbers does not lie between 4/5 and 7/13?

Solution:
4/5 = 0.8, and 7/13 = 0.53

Now checking the options,

1/2 = 0.5
2/3 = 0.66
3/4 = 0.75
5/7 = 0.714

Clearly, 0.5 does not lie between 0.53 and 0.8

∴ 1/2 does not lie between 4/5 and 7/13.

৭৬৬.

Average score of a class of 70 students, in an exam, was 43. Average score of the students who had passed is 50 and average score of students who had failed is 15. How many students failed in the exam?

ক
ক) 10
খ
খ) 14
গ
গ) 16
ঘ
ঘ) 18

ব্যাখ্যা

Question: Average score of a class of 70 students, in an exam, was 43. Average score of the students who had passed is 50 and average score of students who had failed is 15. How many students failed in the exam?

Solution:
Let total number of students fail = x
So, total number of student passed = 70 -x
Then,
50(70 - x) + 15x = 70 × 43
⇒ 3500 - 50x + 15x = 3010
⇒ 35x = 3500 - 3010
⇒ 35x = 490
∴ x = 14

৭৬৭.

If the average (arithmetic mean) of five distinct positive integers is 10, what is the differe between the largest possible value of the greatest integer and the least possible value of greatest of the five integers?

ক
ক) 5
খ
খ) 28
গ
গ) 12
ঘ
ঘ) 40

ব্যাখ্যা

Question: If the average (arithmetic mean) of five distinct positive integers is 10, what is the difference between the largest possible value of the greatest integer and the least possible value of greatest of the five integers?

Solution:
Let the five numbers be v, w, x, y and z such that v > w> x > y > z; it is given that none of them are equal.

Let us first find the largest possible value of the largest integer among the five, i.e. v.
We must aim to keep the integers (w, y, x and z) as small as possible such that they are distinct.
Thus, z=1, (smallest possible positive integer), x = 2, y = 3 and w = 4.
Since the average of the five integers =10,
the sum of the integers =5 × 10 = 50

⇒ v = (Sum of the five numbers) - (Sum of the four numbers)
⇒ v = 50 - (1 + 2 + 3 + 4) = 40
Thus, the largest possible value of the greatest of the five numbers = 40.

Let us now find the least possible value of the greatest among the five, i.e. v.
We must aim to keep all the five integers as close to each other as possible.
Let us assume that the middle-most integer x=10, because the average is 10.
Let's make y less than x by the minimum possible positive value, i.e., 1, thus y=10 - 1= 9; similarly, z = 9 -1 = 8.
w=10 + 1 = 11 and v= 11 + 1 = 12.

Thus, we get the values:
v=12, w=11, x=10, y=9, and z=8.
Thus, the least possible value of the greatest of the five numbers =12.

Thus, the difference between the largest possible value of the greatest integer and the least possible value of the greatest of the five integers
= 40 - 12 = 28

৭৬৮.

Among 80 students, the average marks in Mathematics is 65. If the 50 girls scored an average of 68, determine the average score of the remaining boys.

ক
40
খ
46
গ
52
ঘ
60

ব্যাখ্যা

Question: Among 80 students, the average marks in Mathematics is 65. If the 50 girls scored an average of 68, determine the average score of the remaining boys.

Solution:
Let,
the average marks of the boys = k
Total marks of 80 students = 80 × 65 = 5200
Total marks of 50 girls = 50 × 68 = 3400

According to the question,
3400 + (80 − 50) × k = 5200
⇒ 3400 + 30k = 5200
⇒ 30k = 5200 − 3400
⇒ 30k = 1800
⇒ k = 1800 / 30
⇒ k = 60

∴ Average marks of the remaining 30 boys = 60

৭৬৯.

The average of 50 numbers is 30. If two numbers, 35 and 40, are discarded, then the average of the remaining numbers is nearly.

ক
28.32
খ
28.78
গ
29.27
ঘ
29.68

ব্যাখ্যা

Question: The average of 50 numbers is 30. If two numbers, 35 and 40, are discarded, then the average of the remaining numbers is neraly.

Solution:
The average of 50 numbers is 30
Sum of all the numbers =30 × 50 = 1500

Sum of 48 numbers =1500 - (35 + 40)
= 1425

New average =1425/48 = 29.69

৭৭০.

A cricketer has a mean score of 58 runs in nine innings. Find out how many runs are to be scored by him in the tenth innings to raise the mean score to 61.

ক
80
খ
84
গ
85
ঘ
88

ব্যাখ্যা

Question: A cricketer has a mean score of 58 runs in nine innings. Find out how many runs are to be scored by him in the tenth innings to raise the mean score to 61.

Solution:
Mean score of 9 innings = 58 runs.
Total score of 9 innings = (58 × 9) runs = 522 runs.

Required mean score of 10 innings = 61 runs.
Required total score of 10 innings = (61 × 10) runs = 610 runs.

Number of runs to be scored in the 10th innings
= (total score of 10 innings) - (total score of 9 innings)
= (610 - 522) = 88.

Hence, the number of runs to be scored in the 10th innings = 88.

৭৭১.

555.05 + 55.5 + 5.55 + 5 + 0.55 =?

ক
621.55
খ
634.65
গ
621.65
ঘ
655.45

ব্যাখ্যা

Question: 555.05 + 55.5 + 5.55 + 5 + 0.55 =?

Solution:

৭৭২.

If a = 4, b = 6 and c = 3, then a(b - c)/b(a + b + c) =?

ক
2/15
খ
3/8
গ
1/11
ঘ
2/13

ব্যাখ্যা

Question: If a = 4, b = 6 and c = 3, then a(b - c)/b(a + b + c) =?

Solution:
Given that,
a = 4, b = 6 and c = 3

Now,
a(b - c)/b(a + b + c)
= 4(6 - 3)/6(4 + 6 + 3)
= 12/78
= 2/13

৭৭৩.

The average monthly salary of 40 employees in a company is Tk. 9000. If three employees with monthly salaries of Tk. 12,500, Tk. 15,000, and Tk. 14,300 leave the company, what will be the new average monthly salary of the remaining employees?

ক
Tk. 6,250
খ
Tk. 7,680
গ
Tk. 8,600
ঘ
Tk. 8,750

ব্যাখ্যা

Question: The average monthly salary of 40 employees in a company is Tk. 9000. If three employees with monthly salaries of Tk. 12,500, Tk. 15,000, and Tk. 14,300 leave the company, what will be the new average monthly salary of the remaining employees?

Solution:
Here,
The average monthly salary of 40 employees = Tk. 9000
∴ Total monthly salary of 40 employees = 9000 × 40 = Tk. 3,60,000

three employees with monthly salaries of Tk. 12,500, Tk. 15,000, and Tk. 14,300 leave the company
∴ Total monthly salary of 3 employees = (12,500 + 15,000 + 14,300) = Tk. 41,800

Remaining total salary = (3,60,000 - 41,800) = Tk. 3,18,200

Remaining number of employees = (40 - 3) = 37 employees

∴ New average = 3,18,200/37
= Tk. 8,600

Therefore, the new average monthly salary of the remaining employees = Tk. 8,600

৭৭৪.

Find the average of all the numbers between 10 and 50 which are divisible by 4.

ক
27
খ
30
গ
34
ঘ
32

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

৭৭৫.

What is the average of the first five multiples of 12?

ক
24
খ
32
গ
36
ঘ
48

ব্যাখ্যা

Average = 12 × (1 + 2 + 3 + 4 + 5) × (1/2)
= 12 × 15 × (1/2)
= 12 × 3
= 36.

∴ The first five multiples of 12 is 36.

৭৭৬.

The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is:

ক
12 years
খ
10 years
গ
9 years
ঘ
8 years

ব্যাখ্যা

Question: The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is:

Solution:

The sum of the ages of three boys = 45 years

Now, (3x + 5x + 7x) = 45

⇒ 15x = 45

⇒ x = 3

So, the age of the youngest boy = 3x

= (3 × 3) years

= 9 years

৭৭৭.

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
11 km/hour
খ
10.8 km/hour
গ
11.2 km/hour
ঘ
10.5 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

৭৭৮.

Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 50. Then the average mark obtained by the girls is:

ক
ক) 30
খ
খ) 35
গ
গ) 25
ঘ
ঘ) 40
ঙ
ঙ) 33

ব্যাখ্যা

Question: Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 50. Then the average mark obtained by the girls is:

Solution:
Average mark of 40 students is 45
Total mark of 40 students is (45 × 40)
= 1800

Average mark of all the 30 boys is 50
Total mark of all the 30 boys is (50 × 30)
= 1500

∴ Total marks of all the 10 girls is (1800 - 1500) = 300
The average mark of all the 10 girls is 300/10 = 30

৭৭৯.

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
5
খ
4
গ
3
ঘ
2

ব্যাখ্যা

Question: 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?

Solution:
let, old number of exams be n

ATQ,
(80n + 92)/(n + 1) = 84
⇒ 80n + 92 = 84n + 84
⇒ 4n = 8
⇒ n = 2

total exam = 2 + 1 = 3

৭৮০.

Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then the average of the first and the third number is -

ক
ক) 48
খ
খ) 72
গ
গ) 80
ঘ
ঘ) 96

ব্যাখ্যা

Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, then the average of the first and the third number is -

Solution:
Let, the second number be = x
So, the first number is = 2x
and the third number is = 2x × 2 = 4x

According to the question,
2x + x + 4x = 56 × 3
⇒ 7x = 168
⇒ x = 24

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

Then, the average of the first and the third number is = (48 + 96)/2 = 72

৭৮১.

A batsman makes a score of 82 runs in the 15th innings and thus increases his average by 2. Find his average after the 15th innings.

ক
ক) 42
খ
খ) 48
গ
গ) 52
ঘ
ঘ) 54

ব্যাখ্যা

Question: A batsman makes a score of 82 runs in the 15th innings and thus increases his average by 2. Find his average after the 15th innings.

Solution:
Let, the average after the 15th innings be = x
Then, average after 14th innings = (x - 2)

ATQ,
14 × (x - 2) + 82 = 15x
⇒ 14x - 28 + 82 = 15x
⇒ x = 54

৭৮২.

The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. What is the number?

ক
65
খ
71
গ
82
ঘ
68

ব্যাখ্যা

Question: The sum of the digits of a two-digit number is 8. If the digits are reversed, the number is decreased by 54. What is the number?

Solution:
Let the two-digit number be 10x + y, where x = tens digit and y = ones digit.

Given,
1st condition: x + y = 8
⇒ x = 8 - y .......(1)

2nd condition:
(10x + y) - (10y + x) = 54
⇒ 9x - 9y = 54
⇒ 9(8 - y) - 9y = 54
⇒ 72 - 9y - 9y = 54
⇒ 72 - 18y = 54
⇒ - 18y = 54 - 72
⇒ - 18y = - 18
⇒ y = 1

From equation (1) we get,
x = 8 - y = 8 - 1 = 7

So the number is:
10x + y = 10(7) + 1 = 71

৭৮৩.

There are six numbers 30, 72, 53, 68, x and 87 out of which x is unknown. The average value of the numbers is 60. What is the value of x?

ক
ক) 48
খ
খ) 50
গ
গ) 51
ঘ
ঘ) 55

ব্যাখ্যা

According to the question,
(30 + 72 + 53 + 68 + x + 87)/6 = 60
310 + x = 360
x = 360 - 310
x = 50

৭৮৪.

Three years ago, the average age of Anik, Pritom, and Varsha was 27 years. If five years ago, the average age of Pritam and Varsha was 20 years, find the present age of Anik.

ক
30
খ
40
গ
60
ঘ
25

ব্যাখ্যা

Question: Three years ago, the average age of Anik, Pritom, and Varsha was 27 years. If five years ago, the average age of Pritam and Varsha was 20 years, find the present age of Anik.

Solution:
Sum of the present ages of Anik, Pritam and Varsha = (27 × 3 + 3 × 3) years = 90 years.
Sum of the present ages of Pritam and Varsha = (20 × 2 + 5 × 2) years = 50 years.
Anik's present age = (90 - 50) years = 40 years.

৭৮৫.

A student scored 70, 80, 75, and 85 in four subjects. What score must he get in the fifth subject to have an average of 80?

ক
90
খ
80
গ
85
ঘ
88

ব্যাখ্যা

Question: A student scored 70, 80, 75, and 85 in four subjects. What score must he get in the fifth subject to have an average of 80?

Solution:
- If the average is 80, then
- Total marks needed = 80 × 5 = 400
- Marks so far obtained in 4 subjects = 70 + 80 + 75 + 85 = 310
- Marks Required to obtain desired average = 400 - 310 = 90

৭৮৬.

The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?

ক
ক) 6.5
খ
খ) 4
গ
গ) 3
ঘ
ঘ) 3.5
ঙ
ঙ) None of these

ব্যাখ্যা

Question: The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?

Solution:
The average of 5 quantities is 6
The sum of 5 quantities = 6 × 5
= 30

The average of 3 of them is 8
The sum of 3 = (3 × 8)
= 24

The sum of the remaining two numbers = 30 - 24
= 6
∴ the average of the remaining two numbers is = 6/2
= 3

৭৮৭.

What is the average of natural numbers from 1 to 67?

ক
33.5
খ
33
গ
35
ঘ
34
ঙ
36.5

ব্যাখ্যা

Question: What is the average of natural numbers from 1 to 67?

Solution:
Given, natural numbers 1 to 67.

Average of n natural numbers = (n + 1)/2

Here, n = 67

Average = (67 + 1)/2 = 68/2 = 34

৭৮৮.

- 6m - 2n - [3n - {8m - (4n - 10m)}] - 6m simplifies to

ক
12m - 9n
খ
12m - 7n
গ
6m - 9n
ঘ
12m + 9n

ব্যাখ্যা

Question: - 6m - 2n - [3n - {8m - (4n - 10m)}] - 6m simplifies to

Solution:
- 6m - [3n - {8m - (4n - 10m)}] - 6m
= - 6m - 2n - [3n - {8m - 4n + 10m}] - 6m
= - 6m - 2n - [3n - 8m + 4n - 10m] - 6m
= - 6m - 2n - 3n + 8m - 4n + 10m - 6m
= 6m - 9n

৭৮৯.

If X + Y = 174, and X is half of Y, then find the value of X.

ক
116
খ
114
গ
57
ঘ
58

ব্যাখ্যা

Question: If X + Y = 174, and X is half of Y, then find the value of X.

Solution:
Given that,
X + Y = 174 …… (i)
Y = 2X …… (ii)
On solving (i) and (ii), we get,
⇒ X + 2X = 174
⇒ 3X = 174
⇒ X = 174/3
∴ X = 58

৭৯০.

The average age of a group of men is increased by 5 year when an 18 year old man is replaced by a 38 year old person. How many men were there in the group?

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6
ঙ
ঙ) 7

ব্যাখ্যা

Let N be the no. of persons in the group.
Required number of person is given by;
Member in group × aged increased = difference of replacement
N × 5 = 38 - 18
Or, 5N = 20
Or, N = 4

৭৯১.

The average of 21 numbers is 16. The average of the first 10 of those is 14 and the average of last 10 numbers is 17. What is the 11th number?

ক
ক) 16
খ
খ) 22
গ
গ) 24
ঘ
ঘ) 26

ব্যাখ্যা

Question: The average of 21 numbers is 16. The average of the first 10 of those is 14 and the average of last 10 numbers is 17. What is the 11th number?

Solution:
Total sum of result = (21 × 16) = 336
sum of first 10 results = (10 × 14) = 140
sum of last 10 results = (10 × 17) = 170

11th number= 336 - 140 - 170
= 26

৭৯২.

Arib's Toyota Cross averages 25 km/liter inside city and 40 km/liter on highway. Yesterday, he drove to his Gulshan office from the factory which is 105 km away. If the Google Maps showed that he drove 25 km of this distance inside Dhaka, what was his average mileage?

ক
25
খ
28
গ
30
ঘ
33
ঙ
35

ব্যাখ্যা

Question: Arib's Toyota Cross averages 25 km/liter inside city and 40 km/liter on highway. Yesterday, he drove to his Gulshan office from the factory which is 105 km away. If the Google Maps showed that he drove 25 km of this distance inside Dhaka, what was his average mileage?

Solution:
দেওয়া আছে,
শহরের ভিতরে গড় জ্বালানি খরচ = ২৫ কি.মি./লিটার
হাইওয়ে পথে গড় জ্বালানি খরচ = ৪০ কি.মি./লিটার

তার মোট অতিক্রান্ত দূরত্ব = ১০৫ কি.মি

গুগল ম্যাপ অনুসারে,
সে শহরের ভিতরে অতিক্রম করে = ২৫ কি.মি.
∴ ২৫ কি.মি. পথের জন্য জ্বালানি খরচ হয় = ২৫/২৫ = ১ লিটার

∴ হাইওয়ে পথে অতিক্রম করে = (১০৫ - ২৫) কি.মি.
= ৮০ কি.মি.

∴ ৮০ কি.মি. পথের জন্য জ্বালানি খরচ হয় = ৮০/৪০ = ২ লিটার

∴ মোট জ্বালানি খরচ হয় = (১ + ২) = ৩ লিটার

∴ তার গড় জ্বালানি খরচ = ১০৫/৩ = ৩৫ কি.মি./লিটার

৭৯৩.

A cricketer’s average after 20 innings is 45 runs. If he scores 108 runs in the next innings, what is his new average?

ক
46 runs
খ
47 runs
গ
48 runs
ঘ
50 runs

ব্যাখ্যা

Question: A cricketer’s average after 20 innings is 45 runs. If he scores 108 runs in the next innings, what is his new average?

Solution:
Average after 20 innings = 45
Total runs after 20 innings:
= 20 × 45
= 900 runs.

Runs scored in the 21st innings = 108.
Total runs after 21 innings:
= 900 + 108
= 1008 runs.

New average = Total runs / Number of innings
= 1008 / 21
= 48 runs.

৭৯৪.

The average of eight numbers is 14. The average of six of these numbers is 16. The average of the remaining two numbers is –

ক
ক) 4
খ
খ) 8
গ
গ) 16
ঘ
ঘ) Data inadequate

ব্যাখ্যা

Total sum of remaining two
= (8 × 14 – 6 × 16) = 16
∴ Average of these two numbers is = 16 / 2 = 8

৭৯৫.

The cube root of .000216 is-

ক
0.6
খ
0.06
গ
77
ঘ
87

ব্যাখ্যা

Question: The cube root of .000216 is-

Solution:

৭৯৬.

Among 90 students, the average marks in science is 72. If the 60 girls scored an average of 75, determine the average score of the remaining 30 boys.

ক
54
খ
60
গ
66
ঘ
56

ব্যাখ্যা

Question: Among 90 students, the average marks in science is 72. If the 60 girls scored an average of 75, determine the average score of the remaining 30 boys.

Solution:
Let, the average marks of the boys = k
Total marks of 90 students = 90 × 72 = 6480
Total marks of 60 girls = 60 × 75 = 4500

According to the question,
4500 + 30k = 6480
⇒ 30k = 6480 - 4500
⇒ 30k = 1980
⇒ k = 1980/30
⇒ k = 66

∴ Average marks of the remaining 30 boys = 66.

৭৯৭.

On Sundays, a museum attracts around 510 visitors, while on weekdays, it has about 240. Calculate the average daily visitors in a 30-day month starting on a Sunday.

ক
280
খ
285
গ
290
ঘ
300

ব্যাখ্যা

Question: On Sundays, a museum attracts around 510 visitors, while on weekdays, it has about 240. Calculate the average daily visitors in a 30-day month starting on a Sunday.

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

Total visitors in Sundays = 5 × 510 = 2550
Total visitors in other days = 25 × 240 = 6000

∴ Total visiotors in the whole month = (2550 + 6000) = 8550

∴ Average number of visitors per day of the month = 8550/30 = 285

৭৯৮.

If 9 batsman have an average score of 56 on a match, and one of those batsman scored a 88 on the match, what is the average score on this match for the other 8 batsman?

ক
ক) 51
খ
খ) 52
গ
গ) 53
ঘ
ঘ) 54

ব্যাখ্যা

Question: If 9 batsman have an average score of 56 on a match, and one of those batsman scored a 88 on the match, what is the average score on this match for the other 8 batsman?

Solution:
9 জন ব্যাটসম্যানের গড় রান = 56
9 জন ব্যাটসম্যানের মোট রান = 56 × 9 = 504

8 জন ব্যাটসম্যানের মোট রান = 504 - 88 = 416

8 জন ব্যাটসম্যানের গড় রান = 416/8 = 52

৭৯৯.

The first term in a sequence is 1 and second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 21th term in the sequence?

ক
ক) 2
খ
খ) 3
গ
গ) 1
ঘ
ঘ) 5

ব্যাখ্যা

Question: The first term in a sequence is 1 and second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 21th term in the sequence?

Solution:
The first term = 1
Second term = 5
Third term =(1 + 5)/2 = 3
Fourth term =(1 + 5 + 3)/4 = 3
Fifth term =(1 + 5 + 3 + 3)/4 = 3

We always get an average of 3 for all the sum of all precedings terms.
So, the 21th term would be 3 and the sequence would be
1, 5, 3, 3, 3, 3, 3,.............3.

৮০০.

Which of the following is the largest?

ক
14/18
খ
15/25
গ
3/4
ঘ
12/14

ব্যাখ্যা

Question: Which of the following is the largest?

Solution:
14/18 = 7/9 = 0.78
15/25 = 3/5 = 0.6
3/4 = 0.75
12/14 = 6/7 = 0.86