Fraction and Simplification, Average and Mean

PrepBank · পাতা ৫ / ১০ · ৪০১–৫০০ / ৯৪৮

৪০১.

Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 48. Then the average mark obtained by the girls is:

ক
32
খ
35
গ
36
ঘ
38

ব্যাখ্যা

Question: Average mark in Math in a class of 40 students is 45. Average mark of all the 30 boys is 48. 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 48
Total mark of all the 30 boys is (48 × 30)
= 1440

∴ Total marks of all the 10 girls is (1800 - 1440) = 360
The average mark of all the 10 girls is 360/10 = 36

৪০২.

Before anybody could notice, Rifat took one-fourth of the chocolates from a box. Later, his four cousins arrived, and the remaining chocolates were distributed equally among the five of them. Rifat received a total of 40 chocolates. How many did each of his cousins receive?

ক
12
খ
15
গ
9
ঘ
10
ঙ
18

ব্যাখ্যা

Question: Before anybody could notice, Rifat took one-fourth of the chocolates from a box. Later, his four cousins arrived, and the remaining chocolates were distributed equally among the five of them. Rifat received a total of 40 chocolates. How many did each of his cousins receive?

Solution:
ধরি, মোট চকলেট ছিল x টি।
রিফাত প্রথমবার নিয়েছিল = x এর 1/4 অংশ = x/4 টি
বাকী চকলেট = x - x/4 = (4x - x)/4 = 3x/4 টি
এই বাকী চকলেট রিফাত এবং তার চারজন কাজিনের মধ্যে, অর্থাৎ মোট পাঁচজনের মধ্যে সমানভাবে ভাগ করা হয়েছিল।
∴ প্রত্যেকে পেয়েছে = (3x/4) × (1/5) = 3x/20 টি

প্রশ্ন অনুযায়ী, রিফাত মোট 40 টি চকলেট পেয়েছে।
∴ রিফাতের মোট চকলেট = (প্রথমবারের অংশ) + (সমানভাবে ভাগের অংশ)
⇒ (x/4) + (3x/20) = 40
⇒ (5x + 3x)/20 = 40
⇒ 8x/20 = 40
⇒ 2x/5 = 40
⇒ x = 40 × (5/2)
⇒ x = 100

সুতরাং, বাক্সে মোট চকলেট ছিল 100 টি।
প্রত্যেক কাজিন পেয়েছে = 3x/20 = (3 × 100)/20 = 300/20 = 15 টি
অতএব, তার প্রত্যেক কাজিন 15টি করে চকলেট পেয়েছিল।

৪০৩.

If 2a = 3b = 4c = 72, then what is the average (arithmetic mean) of a, b and c?

ক
ক) 39
খ
খ) 26
গ
গ) 24
ঘ
ঘ) 18

ব্যাখ্যা

Question: If 2a = 3b = 4c = 72, then what is the average (arithmetic mean) of a, b and c?

Solution:

2a = 72

বা, a = 36

একইভাবে, b = 24 এবং c = 18

সুতরাং, গাণিতিক গড় = (36+24+18) / 3 = 26

৪০৪.

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

ক
180
খ
210
গ
240
ঘ
420
ঙ
None of these

ব্যাখ্যা

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

Solution:
The sum of salary of officers will be = 30 × 120 = 3600
Let the number of labourers = X.
ATQ,
3600 + 40X = 50(30 + X)
⇒ 3600 + 40X = 1500 + 50X
⇒ 2100 = 10X
∴ X = 210

৪০৫.

A man has Tk. 640 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. Simplify this with equation and what is the total number of notes that he has?

ক
80
খ
100
গ
120
ঘ
140

ব্যাখ্যা

Question: A man has Tk. 640 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. Simplify this with equation and what is the total number of notes that he has?

Solution:
Let the number of notes of each denomination be x.

Then
x + 5x + 10x = 640
⇒ 16x = 640
∴ x = 40

Hence, the total number of notes = 3x = 120

৪০৬.

The value of is-

ক
1.04
খ
0.96
গ
0.86
ঘ
0.69
ঙ
None of these

ব্যাখ্যা

Question: The value of is-

Solution:

৪০৭.

The average of 60 numbers is 25. If two numbers 40 and 50 are discarded, find the average of the remaining numbers.

ক
20.17
খ
24.31
গ
25.17
ঘ
29.17

ব্যাখ্যা

Question: The average of 60 numbers is 25. If two numbers 40 and 50 are discarded, find the average of the remaining numbers.

Solution:
Given,
Average of 60 numbers = 25
Sum of 50 numbers = 25 × 60 = 1500
Sum of discarded numbers = 40 + 50 = 90
Sum of remaining numbers = 1500 - 90 = 1410
Now, total remaining numbers = 60 - 2 = 58

Average of remaining numbers = 1410/58 = 24.31

৪০৮.

A batsman in his 12th innings makes a score of 120, and thereby increases his average by 5. The average score after 12th innings is-

ক
65
খ
70
গ
75
ঘ
80
ঙ
85

ব্যাখ্যা

Question: A batsman in his 12th innings makes a score of 120, and thereby increases his average by 5. The average score after 12th innings is-

Solution:
Let, average runs after 12 innings = x
Average runs after 11 innings = x - 5

ATQ,
12x = (x - 5) × 11 + 120
⇒ 12x = 11x - 55 + 120
⇒ 12x - 11x = 65
∴ x = 65

৪০৯.

In a cricket team of 11 players, the captain is 25 years old, while the wicketkeeper is 3 years older. When these two are excluded, the average age of the remaining players drops by one year compared to the entire team. Find the team's average age.

ক
18 years
খ
22 years
গ
28 years
ঘ
32 years

ব্যাখ্যা

Question: In a cricket team of 11 players, the captain is 25 years old, while the wicketkeeper is 3 years older. When these two are excluded, the average age of the remaining players drops by one year compared to the entire team. Find the team's average age.

Solution:
Let the average age of the whole team by x years.
⇒ 11x - (25 + 28) = 9(x -1)
⇒ 11x - 53 = 9x - 9
⇒ 11x - 9x = 44
⇒ 2x = 44
⇒ x = 22.

So, the average age of the team is 22 years.

৪১০.

The average of five numbers is 32. The sum of the first three numbers is 75. If the fourth number is 28, what is the fifth number?

ক
50
খ
53
গ
57
ঘ
60

ব্যাখ্যা

Question: The average of five numbers is 32. The sum of the first three numbers is 75. If the fourth number is 28, what is the fifth number?

Answer:
Average of five numbers = 32
Total sum = 5 × 32
= 160

Sum of first three numbers = 75.
Fourth number = 28.

Sum of first four numbers = 75 + 28 = 103.

∴ Fifth number = total sum - sum of first four
= 160 - 103
= 57

So the fifth number is 57.

৪১১.

The average of 7 consecutive numbers is n. If the next two numbers are included, the average will-

ক
increased by 2.5
খ
remains the same
গ
increased by 1
ঘ
increased by 2
ঙ
None of these

ব্যাখ্যা

Question: The average of 7 consecutive numbers is n. If the next two numbers are included, the average will-

Solution:

The average of 7 consecutive numbers is n implies that the 4th term is equal to n.

Now if we include next two terms then the average of 9 terms will be the 5th term. Now as the terms are consecutive, so the 5th term will be n + 1.

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

(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)/9 = 45/9 = 5

৪১২.

A cake is divided into 18 pieces. If Mohiuddin takes 1/3 of the cake and Morshed takes 1/3 of the rest that are left, how many pieces are still left?

ক
4
খ
8
গ
6
ঘ
10
ঙ
None of these

ব্যাখ্যা

Question: A cake is divided into 18 pieces. If Mohiuddin takes 1/3 of the cake and Morshed takes 1/3 of the rest that are left, how many pieces are still left?

Solution:
Mohiuddin takes 1/3 of cake
Left after Mohiuddin takes = (1 - 1/3) of cake
= 2/3 of cake

Morshed takes (1/3) × (2/3) = 2/9 of cake

Mohiuddin and Morshed takes = (1/3 + 2/9) = (3 + 2)/9 = 5/9 of cake
Left after both take = (1 - 5/9) = 4/9 of cake

full cake divided into 18 pieces
∴ 4/9 of cake divided into (18 × 4)/9 pieces = 8 pieces

৪১৩.

The average age of all the students in a class is 22 years. The average age of the boys in the class is 25 years, and that of the girls is 18 years. If the number of girls in the class is 24, find the number of boys in the class.

ক
30
খ
32
গ
36
ঘ
40

ব্যাখ্যা

Question: The average age of all the students in a class is 22 years. The average age of the boys in the class is 25 years, and that of the girls is 18 years. If the number of girls in the class is 24, find the number of boys in the class.

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

Then,
22 (x + 24) = 25x + (18 × 24)
⇒ 22x + 528 = 25x + 432
⇒ 3x = 96
⇒ x = 32

∴ The number of boys in the class is 32

৪১৪.

A box contains 200 marbles, 25% of them are blue and the rest are black. From the box you gave your brother a certain number of marbles of which 60% are black. You then found that among the remaining marbles, only 20% are blue. How many marbles did you give to your brother?

ক
40
খ
50
গ
60
ঘ
70
ঙ
None

ব্যাখ্যা

Question: A box contains 200 marbles, 25% of them are blue and the rest are black. From the box you gave your brother a certain number of marbles of which 60% are black. You then found that among the remaining marbles, only 20% are blue. How many marbles did you give to your brother?

Solution:
বাক্সে মার্বেল আছে = 200 টি
Blue মার্বেল আছে = 200 এর 25%
= 200 এর 25/100 = 50 টি
Black মার্বেল আছে = (200 - 50)টি = 150টি

ধরি, ভাইকে দেওয়া হয়েছিলো = a টি

প্রশ্নমতে,
(200 - a)20% + a . 40% = 50
⇒ 0.2 (200 - a) + 0.4a = 50
⇒ 40 - 0.2a + 0.4a = 50
⇒ 0.2a = 10
∴ a = 50

ভাইকে দেওয়া হয়েছিলো 50টি

৪১৫.

The average marks obtained by 22 candidates in an examination are 45. The average marks of the first ten are 55 and that last eleven are 40. The number of marks obtained by the 11^th candidate is

ক
ক) 0
খ
খ) 45
গ
গ) 48
ঘ
ঘ) 52

ব্যাখ্যা

Total marks scored by 22 candidates = 22 × 45
= 990
Total marks scored by first 10 candidates =10 × 55
= 550
Total marks scored by last 11 candidates =11 × 40
=440
∴ Marks scored by 11th candidate = 990 - (550 + 440)
= 0

৪১৬.

A car owner buys petrol at Tk.17, TK. 19 and TK. 20 per liter for three consecutive years. Compute the average cost per liter. If he spends Tk. 6460 per year.

ক
Tk. 12.28
খ
Tk. 18.58
গ
Tk. 20
ঘ
None of these

ব্যাখ্যা

Question: A car owner buys petrol at Tk.17, TK. 19 and TK. 20 per liter for three consecutive years. Compute the average cost per liter. If he spends Tk. 6460 per year.

Solution:
Total quantity of petrol consumed in 3 years
= (6460/17 + 6460/19 + 6460/20) litres
= (380 + 340 + 323) litres
= 1043 litres

Total amount spent
= Tk. (3 × 6460)
= Tk. 19380

∴ Average cost
= Tk. (19380/1043)
= Tk. 18.58

৪১৭.

ক
38.4
খ
35.84
গ
35.52
ঘ
None of the above

ব্যাখ্যা

Question:

Solution:

৪১৮.

In the first 20 over's of a cricket game, the run rate was only 3.5. What should be the run rate in remaining 30 over's to reach the target of 289 runs?

ক
ক) 7.1
খ
খ) 7.2
গ
গ) 7.3
ঘ
ঘ) 7.4

ব্যাখ্যা

The run rate in remaining 30 over's to reach the target of 289 runs = {289 - (20×3.5)}/30 = 7.3

৪১৯.

ক
4
খ
6
গ
8
ঘ
12

ব্যাখ্যা

Question:

Solution:

৪২০.

The average age of all the students of a class in 18 years. The average age of the boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.

ক
30
খ
35
গ
36
ঘ
None

ব্যাখ্যা

Question: The average age of all the students of a class in 18 years. The average age of the boys of the class is 20 years and that of the girls is 15 years. If the number of girls in the class is 20, then find the number of boys in the class.

Solution:
Let,
the number of boys in the class be x.
Then, 18 × (x + 20) = 20x + (15 × 20)
⇒ 18x + 360 = 20x + 300
⇒ 20x + 300 = 18x + 360
⇒ 20x -18x = 360 -300
⇒ 2x = 60
⇒ x = 30

∴ The number of boys in the class is 30.

৪২১.

Find

ক
2
খ
4
গ
321
ঘ
12

ব্যাখ্যা

Question: Find

Solution:

৪২২.

ক
- 2
খ
4
গ
- 3
ঘ
2
ঙ
None of these

ব্যাখ্যা

Question:

Solution:

৪২৩.

A, B, C, D and E are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers was deleted?

ক
B
খ
A
গ
D
ঘ
C

ব্যাখ্যা

Question: A, B, C, D and E are five consecutive numbers in increasing order of size. Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%. Which one of the following numbers was deleted?

Solution:
Let, the numbers are A = x, B = x + 1, C = x + 2, D = x + 3, E = x + 4

sum = x + x + 1 + x + 2 + x + 3 + x + 4 = 5x + 10

Deleting one of the five numbers from the set decreased the sum of the remaining numbers in the set by 20%.

new sum = sum - 0.2 sum
= 0.8 sum
= 0.8 (5x + 10)
= 4x + 8

deleted number = 5x + 10 - 4x - 8 = x + 2 = C

৪২৪.

The average of 25 results is 18. The average of the first 12 of those is 14 and the average of the last 12 is 17. What is the 13th result?

ক
74
খ
78
গ
76
ঘ
72

ব্যাখ্যা

Question: The average of 25 results is 18. The average of the first 12 of those is 14 and the average of the last 12 is 17. What is the 13th result?

Solution:
Sum of 1st 12 results = 12 × 14 = 168
Sum of last 12 results = 12 × 17 = 204
Let,
13th result = x

ATQ,
168 + 204 + x = (25 × 18)
⇒ 372 + x = 450
⇒ x = 450 - 372
∴ x = 78

৪২৫.

An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job. How much wire doesn't he need to cut?

ক
1/2
খ
3/16
গ
21/16
ঘ
55/16
ঙ
13/16

ব্যাখ্যা

Question: An electrician has three and seven-sixteenths cm of wire. He needs only two and five-eighths cm of wire for a job. How much wire doesn't he need to cut?

Solution:

৪২৬.

Four friends planned to rent a car for a trip and spilt the cost equally. If at the last minute, two of the friends do not attend the trip, the remaining people will each have to pay 40 taka more to rent the car. How much did each person originally have to pay to rent the car?

ক
20
খ
40
গ
60
ঘ
120

ব্যাখ্যা

Question: Four friends planned to rent a car for a trip and spilt the cost equally. If at the last minute, two of the friends do not attend the trip, the remaining people will each have to pay 40 taka more to rent the car. How much did each person originally have to pay to rent the car?

Solution:
ধরি,
গাড়ি ভাড়া x টাকা
4 জনকে দেওয়া লাগত x/4 টাকা
2 জনকে দেওয়া লাগত x/2 টাকা

প্রশ্নমতে,
(x/2) - (x/4) = 40
বা, (2x - x)/4 = 40
বা, x/4 = 40
∴ x = 160

4 জনকে দেওয়া লাগত 160/4 টাকা
= 40 টাকা করে

৪২৭.

Tk. 850 was distributed among P, Q, R, S, T in ascending order forming an arithmetic progression. T received Tk. 60 more than P. How much did R receive?

ক
Tk. 140
খ
Tk. 150
গ
Tk. 170
ঘ
Tk. 180

ব্যাখ্যা

Question: Tk. 850 was distributed among P, Q, R, S, T in ascending order forming an arithmetic progression. T received Tk. 60 more than P. How much did R receive?

Solution:
Given that, P + Q + R + S + T = Tk. 850
And, T - P = 60

Now, Arithmetic progression: a, a + d, a + 2d, a + 3d, a + 4d
∴ Amount of T is = (a + 4d) and Amount of P is = a

According to the question,
⇒ a + 4d - a = 60
⇒ 4d = 60
⇒ d = 60/4
⇒ d = 15

Also,
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 850
⇒ 5a + 10d = 850
⇒ 5a + 10 × 15 = 850
⇒ 5a + 150 = 850
⇒ 5a = 700
⇒ a = 140

So, amount R = a + 2d
= 140 + 2 × 15
= 140 + 30
= Tk. 170

৪২৮.

In a family of 8, the men eat on average 72 kg of food and women eat on an average 50 kg of food. The men and women are equal in number. A hungry woman named Akhi joined the family for dinner and the average consumption became 67. How much did Akhi eat (in kgs)?

ক
115
খ
80
গ
90
ঘ
85
ঙ
None of these

ব্যাখ্যা

Question: In a family of 8, the men eat on average 72 kg of food and women eat on an average 50 kg of food. The men and women are equal in number. A hungry woman named Akhi joined the family for dinner and the average consumption became 67. How much did Akhi eat (in kgs)?

Solution:

As men and women are equal so , there are 4 women and 4 men so, total consumption will be 72 × 4 = 288(by men) and 50 × 4 = 200(by women)

Total consumption = 488.

But after including Akhi the average consumption for 9 people is given to be 67.
So the total consumption will be 67 × 9 = 603.
So, Neetu’s consumption will be = 603 - 488 = 115

৪২৯.

৮ জন ছাত্রের গড় বয়স ২০ বছর। প্রথম ২ জন ছাত্রের গড় বয়স ১৯ বছর এবং পরবর্তী ৩ জন ছাত্রের গড় বয়স ২১ বছর। যদি ৬ষ্ঠ ছাত্রের বয়স ৭ম ছাত্রের চেয়ে ২ বছর কম এবং ৮ম ছাত্রের চেয়ে ৩ বছর কম হয়, তবে ৮ম ছাত্রের বয়স কত?

ক
২১ বছর
খ
১৮ বছর
গ
২৪ বছর
ঘ
৩০ বছর
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: ৮ জন ছাত্রের গড় বয়স ২০ বছর। প্রথম ২ জন ছাত্রের গড় বয়স ১৯ বছর এবং পরবর্তী ৩ জন ছাত্রের গড় বয়স ২১ বছর। যদি ৬ষ্ঠ ছাত্রের বয়স ৭ম ছাত্রের চেয়ে ২ বছর কম এবং ৮ম ছাত্রের চেয়ে ৩ বছর কম হয়, তবে ৮ম ছাত্রের বয়স কত?

সমাধান:
৮ জনের গড় বয়স = ২০ বছর
∴৮ জনের মোট বয়স = ৮ × ২০ = ১৬০ বছর

প্রথম ২ জন ছাত্রের গড় বয়স ১৯ বছর
∴প্রথম ২ জনের মোট বয়স = ২ × ১৯ = ৩৮ বছর

পরবর্তী ৩ জন ছাত্রের গড় বয়স ২১ বছর
∴ পরবর্তী ৩ জনের মোট বয়স = ৩ × ২১ = ৬৩ বছর

ধরি, ৬ষ্ঠ ছাত্রের বয়স = x বছর
∴ ৭ম ছাত্রের বয়স = x + ২ বছর
∴ ৮ম ছাত্রের বয়স = x + ৩ বছর

প্রশ্নমতে,
মোট বয়স = প্রথম ৫ জনের বয়স + শেষ ৩ জনের বয়স
⇒ ১৬০ = ৩৮ + ৬৩ + x + (x + ২) + (x + ৩)
⇒ ১৬০ = ১০১ + ৩x + ৫
⇒ ৩x + ১০৬ = ১৬০
⇒ ৩x = ১৬০ - ১০৬
⇒ ৩x = ৫৪
∴ x = ১৮

∴ ৮ম ছাত্রের বয়স = x + ৩ বছর
= ১৮ + ৩ = ২১ বছর

৪৩০.

The average age of father and son is 30 years. After 6 years, the ratio of the age of them is 5 : 1. The present age of son is

ক
ক) 4
খ
খ) 6
গ
গ) 12
ঘ
ঘ) 14

ব্যাখ্যা

The average age of father and son is 30 years.
The total age of father and son is 30 × 2 = 60 years.
Suppose, after 6 years, the age of father and son are 5x and x years respectively.
5x - 6 + x - 6 = 60
⇒ 6x = 72
∴ x = 12
present age of son is 12 - 6 = 6 years.
------------------------------------------------------
পিতা ও পুত্রের বয়সের গড় ৩০ বছর। ৬ বছর পরে তাদের বয়সের অনুপাত ৫ঃ১ হলে, পুত্রের বর্তমান বয়স কত?

পিতা ও পুত্রের বয়সের গড় ৩০ বছর হলে, তাদের মোট বয়স = ৩০ × ২ = ৬০ বছর
মনে করি, ৬ বছর পরে, পিতার বয়স 5x ও পুত্রের বয়স x বছর
5x - 6 + x - 6 = 60
⇒ 6x = 72
∴ x = 12
পুত্রের বর্তমান বয়স ১২ - ৬ = ৬ বছর

৪৩১.

5 - [4 - {3 - (3 - 3 - 6)}] is equal to:

ক
10
খ
18
গ
6
ঘ
0

ব্যাখ্যা

Question: 5 - [4 - {3 - (3 - 3 - 6)}] is equal to:

Solution:
Given that,
5 - [4 - {3 - (3 - 3 - 6)}]
= 5 - [4 - {3 - (-6)}]
= 5 - [4 - {3 +6}]
= 5 - [4 - {9}]
= 5 - [4 - 9]
= 5 - [-5]
= 5 + 5
= 10

৪৩২.

The average of the first six multiples of 4 is-

ক
14
খ
12
গ
11
ঘ
16
ঙ
18

ব্যাখ্যা

Question: The average of the first six multiples of 4 is-

Solution:
The first six multiples of 4 are = 4, 8, 12, 16, 20, 24

Average = (4 + 8 + 12 + 16 + 20 + 24)/6
= 14

৪৩৩.

The average of 7 consecutive numbers is a. If the next two numbers are included, the average will be-

ক
ক) increase by 1
খ
খ) increase by 2
গ
গ) increase by 3
ঘ
ঘ) remain same

ব্যাখ্যা

Question: The average of 7 consecutive numbers is a. If the next two numbers are included, the average will be-

Answer:
let first number is n
so, the numbers are n, n+1, n+2,......, n+6
(n + n + 1 + .... + n + 6)/7 = a
⇒ 7n + (1 + 2 + 3 +....+ 6) = 7a
⇒ 7n + (6 × 7)/2 = 7a
⇒ 7n + 21 = 7a
⇒ 7n = 7a - 21
⇒ n = (7a - 21)/7
∴ n = 7(a - 3)/7 = a - 3

If the next two numbers are included, the average will be
= (n + n + 1 + .... + n + 8)/9
= {9n +(1 + 2 + 3 +.....+8)}/9
= (9n + 36)/9
= n + 4
= a - 3 + 4
= a + 1

So, the average will increase by 1

৪৩৪.

The average age of a husband and his wife was 25 years at the time of their marriage. After five years they have a three-year old child. What is the average age of the family now?

ক
ক) 20 years
খ
খ) 21 years
গ
গ) 22 years
ঘ
ঘ) 23 years

ব্যাখ্যা

Question: The average age of a husband and his wife was 25 years at the time of their marriage. After five years they have a three-year old child. What is the average age of the family now?

solution:
The average age of a husband and his wife was 25 years at the time of their marriage
Sum of age = 25 × 2 = 50

After five years, sum of their age = 50 + 5 + 5 = 60
Sum of age of the family = 60 + 3 = 63 years

∴the average age of the family is = 63/3 = 21 years

৪৩৫.

Which of the following fractions is equal to 0.16?

ক
1/4
খ
4/25
গ
5/8
ঘ
8/5

ব্যাখ্যা

Question: Which of the following fractions is equal to 0.16?

Solution:
1/4 = 0.25
4/25 = 0.16
5/8 = 0.625
8/5 = 1.6

৪৩৬.

The average of 4 terms is 30 and the last term is 1/3 of the remaining terms. What will be the last number?

ক
ক) 20
খ
খ) 30
গ
গ) 40
ঘ
ঘ) 50

ব্যাখ্যা

Question: The average of 4 terms is 30 and the last term is 1/3 of the remaining terms. What will be the last number?

Solution:
The average of 4 terms is 30
total sum = (4 × 30) = 120

let, last term is x
remaining terms is 3x

3x + x = 120
⇒ 4x = 120
∴ x = 30
The last number is 30

৪৩৭.

The average of five consecutive integers is X. If the next two numbers are added, how shall the average vary?

ক
It shall increase by 1
খ
It shall increase by 1.4
গ
It shall increase by 2
ঘ
It shall remain the same

ব্যাখ্যা

Question: The average of five consecutive integers is X. If the next two numbers are added, how shall the average vary?

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

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

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

So, the average increased by 1

৪৩৮.

Ajit has a certain average for 9 innings. In the 10th innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:

ক
ক) 20
খ
খ) 25
গ
গ) 28
ঘ
ঘ) 29

ব্যাখ্যা

Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings.

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

Now,
9x + 100 = 10(x + 8)
⇒ x = 20

New average
= x + 8
= 20 + 8
= 28

৪৩৯.

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

ক
ক) 9
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 13

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

৪৪০.

Solve: (73.48 + 126.52) ÷ 5² = 1.6 × 3 + ?

ক
3.2
খ
- 3.5
গ
2.8
ঘ
3.9

ব্যাখ্যা

Question: Solve: (73.48 + 126.52) ÷ 5² = 1.6 × 3 + ?

Solution:
Given that, (73.48 + 126.52) ÷ 5² = 1.6 × 3 + ?
⇒ 200 ÷ 25 = 1.6 × 3 + ?
⇒ 8 = 4.8 + ?
⇒ ? = 8 - 4.8
∴ ? = 3.2

৪৪১.

A group of 8 boxes has its average weight increased by 3 kg after replacing a 50 kg box with a new one. What is the weight of the new box?

ক
54 kg
খ
74 kg
গ
62 kg
ঘ
57 kg

ব্যাখ্যা

Question: A group of 8 boxes has its average weight increased by 3 kg after replacing a 50 kg box with a new one. What is the weight of the new box?

Solution:
Let the weight of the new box be x kg.
Let the total weight of the original 8 boxes = W.
Original average = W/8.

After replacing the 50 kg box with a box weighing x kg,
The total weight becomes = W - 50 + x.
∴ The new average = (W - 50 + x)/8.

ATQ,
New average = Old average + 3
(W - 50 + x)/8 = W/8 + 3
⇒ W - 50 + x = W + 24
⇒ x = 24 + 50
⇒ x = 74

∴ The weight of the new box is 74 kg.

৪৪২.

A motorist travels to a place 150 km away at an average speed of 50 km and returns at 30 km per hour. His average speed for the whole journey in km per hour is-

ক
ক) 35
খ
খ) 37
গ
গ) 37.5
ঘ
ঘ) 40

ব্যাখ্যা

Average speed
= (2xy / x+y) km/hr
= (2×50×30 / 50+30) km/hr
= 37.5 km/hr

৪৪৩.

Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.

ক
ক) 93
খ
খ) 112
গ
গ) 115
ঘ
ঘ) 119

ব্যাখ্যা

Sum of 80 numbers
= 80 × 42 = 3360
Now, sum of 85 numbers
= 85 × 45 = 3825
Hence, sum of 5 numbers
= 3825 - 3360 = 465
Average of five numbers
= 465/5
= 93

৪৪৪.

The average of 20 numbers is 35. If two numbers, 40 and 50 are discarded, then the average of the remaining numbers is nearly -

ক
ক) 32.89
খ
খ) 33.89
গ
গ) 34.59
ঘ
ঘ) 33.1

ব্যাখ্যা

Question: The average of 20 numbers is 35. If two numbers, 40 and 50 are discarded, then the average of the remaining numbers is nearly -

Solution:
Sum of 20 numbers = (20 × 35) = 700

after discarding 2 numbers of 40 and 50 the new average is = (700 - 40 - 50)/18
= 33.89

৪৪৫.

In a group of five men, no two men have the same age. The oldest man is 50 years old, and the youngest is 30 years old. If X is the average age of the men in the group, which of the following best indicates all and only possible values of X? (All ages are in whole numbers)

ক
30 < X < 50
খ
31 < X < 49
গ
32 < X < 48
ঘ
35 < X < 45

ব্যাখ্যা

Question: In a group of five men, no two men have the same age. The oldest man is 50 years old, and the youngest is 30 years old. If X is the average age of the men in the group, which of the following best indicates all and only possible values of X? (All ages are in whole numbers)

Solution:
Here,
Oldest man = 50 years
Youngest man = 30 years
Average age = X

Since no two people are the same age, the minimum average = (30 + 31 + 32 + 33 + 50)/5
= 176/5
= 35.2
and the maximum average = (30 + 47 + 48 + 49 + 50)/5
= 224/5
= 44.8

That is, the value of X is greater than 35 and less than 45.
i.e. 35 < X < 45

৪৪৬.

Average of ten positive numbers is x. If each number increases by 10%, then x-

ক
remains unchanged
খ
may increase or decrease
গ
will increase
ঘ
is increased by 10%

ব্যাখ্যা

Question: Average of ten positive numbers is x. If each number increases by 10%, then x-

Solution:
Let the ten positive numbers be n₁, n₂,..., n₁₀
Then, n₁ + n₂+ n₃ + ........... + n₁₀ = 10x ............(1)

According to the question,
each number is increased by 10%
10% = 10/100 = 0.1
Suppose the average of the ten numbers = X₁
Therefore, X₁ =( 1.1n₁ + 1.1n₂+ 1.1n₃+ ........... + 1.1n₁₀)/10
⇒ X₁ = 1.1(n₁ + n₂ + n₃ + ........... + n₁₀)/10
⇒ X₁ = 1.1X [We get from equation (1)]
⇒ X₁/ X = 1.1
⇒ X₁/X = (1.1 x 100)%
⇒ X₁/X = 110%

Total percentage gains = (110 - 100)% = 10%

∴ The new average increases by 10%.

৪৪৭.

If 5x + 7y = 41 and 7x + 5y = 43, what is the average of x and y?

ক
2.8
খ
3
গ
3.5
ঘ
4.6

ব্যাখ্যা

Question: If 5x + 7y = 41 and 7x + 5y = 43, what is the average of x and y?

Solution:
দেয়া আছে,
5x + 7y = 41 ...........(1)
7x + 5y = 43 ...........(2)

(1) ও (2) যোগ করে পাই,
5x + 7y + 7x + 5y = 41 + 43
⇒ 12x + 12y = 84
⇒ 12(x + y) = 84
⇒ x + y = 84/12
∴ x + y = 7

∴ গড় = (x + y) /2
= 7/2
= 3.5

৪৪৮.

A school has only four classes that contain 10, 20, 30 and 40 students respectively. The pass percentage of these classes are 20%, 30%, 60% and 100% respectively. Find the pass % of the entire school.

ক
72%
খ
78%
গ
66%
ঘ
62%

ব্যাখ্যা

Question: A school has only four classes that contain 10, 20, 30 and 40 students respectively. The pass percentage of these classes are 20%, 30%, 60% and 100% respectively. Find the pass % of the entire school.

Solution:
Here,
10 of 20% = 2
20 of 30% = 6
30 of 60% = 18
40 of 100% = 40

The number of pass candidates are 2 + 6 + 18 + 40 = 66 out of total 100.

Hence, Pass percentage = 66%

৪৪৯.

What is the average of the first six multiples of 4?

ক
16
খ
18
গ
14
ঘ
24
ঙ
12

ব্যাখ্যা

Question: What is the average of the first six multiples of 4?

Solution:
First six multiples of 4 is 4, 8, 12, 16, 20, 24

Average = (4 + 8 + 12 + 16 + 20 + 24)/6

= 84/6

= 14

৪৫০.

Rina bought 40 shares at Tk 75 each. After 3 months, she bought 20 more shares at Tk 70 each. At what price should she buy 40 additional shares so that the average price per share becomes Tk 72?

ক
68
খ
70
গ
72
ঘ
75

ব্যাখ্যা

Question: Rina bought 40 shares at Tk 75 each. After 3 months, she bought 20 more shares at Tk 70 each. At what price should she buy 40 additional shares so that the average price per share becomes Tk 72?

Solution:
Let,
She wants to buy 40 more shares at = Tk x
∴ Total = 40 × x = Tk 40x

First,
40 shares at Tk 75
∴ Total = 40 × 75 = Tk 3000

Then,
20 shares at Tk 70
∴ Total = 20 × 70 = Tk 1400

Here, total shares = 40 + 40 + 20 = 100
∴ Total cost = 100 × 72 = Tk 7200

ATQ,
40x + 3000 + 1400 = 7200
⇒ 40x + 4400 = 7200
⇒ 40x = 7200 - 4400
⇒ 40x = 2800
⇒ x = 2800 ÷ 40
∴ x = 70

৪৫১.

The average of 9 numbers is 40. If 60 is added, what is the new average?

ক
ক) 40
খ
খ) 41
গ
গ) 42
ঘ
ঘ) 43

ব্যাখ্যা

Question: The average of 9 numbers is 40. If 60 is added, what is the new average?

Solution:
৯ টি সংখ্যার গড় = ৪০
সমষ্টি = (৪০ × ৯) = ৩৬০

৬০ যোগ করার পর মোট = ৩৬০ + ৬০ = ৪২০

গড় = ৪২০/ ১০ = ৪২

৪৫২.

If b = 9d - c and d = (a/6), what is the average (arithmetic mean) of a, b, c and d?

ক
2d
খ
3d
গ
4d
ঘ
none

ব্যাখ্যা

Question: If b = 9d - c and d = (a/6), what is the average (arithmetic mean) of a, b, c and d?

Solution:
d = a/6
∴ 6d = a

b = 9d - c
⇒ b + c = 9d

Average of the four values = (a + b + c + d)/4
Substitute to get: average = (6d + 9d + d)/4 = 16d/4 = 4d

৪৫৩.

If the fractions 7/13, 2/3, 4/11, 5/9 are arranged in ascending order, then the correct sequence is ?

ক
2/3, 7/13, 4/11, 5/9
খ
7/13, 4/11, 5/9, 2/3
গ
4/11, 7/13, 5/9, 2/3
ঘ
5/9, 4/11, 7/13, 2/3
ঙ
None of these

ব্যাখ্যা

Question: If the fractions 7/13, 2/3, 4/11, 5/9 are arranged in ascending order, then the correct sequence is ?

Solution:
Given that,
(7/13) = 0.538
(2/3) = 0.666
(4/11) = 0.3636
(5/9) = 0.5555

Out of 2/3, 7/13, 4/11, 5/9

2/3 is the largest number followed by 5/9 then 7/13 and the smallest is 4/11.

∴ The ascending order will be 4/11, 7/13, 5/9, 2/3.

৪৫৪.

The average weight of the women in a group is 55 kg and that of the men is 70 kg. If the average weight of the group is 65 kg, what is the ratio of women to men in the group?

ক
2 : 3
খ
1 : 3
গ
1 : 2
ঘ
2 : 5

ব্যাখ্যা

Question: The average weight of the women in a group is 55 kg and that of the men is 70 kg. If the average weight of the group is 65 kg, what is the ratio of women to men in the group?

Solution:
Average weight of women = 55 kg
Average weight of men = 70 kg
Average weight of the entire group = 65 kg

Let,
the number of men = M.
and, the number of women = W.
Then, the total number of people in the group is (M + W)

ATQ,
55W + 70M = 65(M + W)
Or, 55W + 70M = 65M + 65W
Or, 70M - 65M = 65W - 55W
Or, 5M = 10W
Or, W : M = 1 : 2

∴ The ratio of women to men in the group is 1 : 2.

৪৫৫.

The sum of the three consecutive even numbers is 60 more than the average of these numbers. Which of the following is the largest of these numbers?

ক
28
খ
32
গ
44
ঘ
46

ব্যাখ্যা

Question: The sum of three consecutive even numbers is 60 more than the average of these numbers. Which of the following is the largest of these numbers?

Solution:
Let,
the numbers be x, x + 2 and x + 4.

Then,
(x + x + 2 + x + 4) - (x + x + 2 + x + 4)/3 = 60
⇒ (3x + 6) - (3x + 6)/3 = 60
⇒ {3(3x + 6) - (3x + 6)}/3 = 60
⇒ (9x + 18 - 3x - 6) = 180
⇒ (6x + 12) = 180
⇒ x = 168/6
∴ x = 28

∴ Largest number = x + 4
= 28 + 4 = 32.

৪৫৬.

The average marks of four subjects is 120. If in one subject 33 was misread as 13 during the calculation, what would be the correct average?

ক
ক) 125
খ
খ) 130
গ
গ) 135
ঘ
ঘ) 140

ব্যাখ্যা

Question: The average marks of four subjects is 120. If in one subject 33 was misread as 13 during the calculation, what would be the correct average?

Solution:
The average given is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to the total.
Then the average of is and so must be added to average, i.e.
Correct average = 120 + 5 = 125

৪৫৭.

In a quiz, a student gets 5 marks for each correct answer and loses 3 marks for each wrong answer. He attempts 50 questions and scores 170 marks. How many questions did he answer correctly?

ক
45
খ
30
গ
35
ঘ
40

ব্যাখ্যা

Question: In a quiz, a student gets 5 marks for each correct answer and loses 3 marks for each wrong answer. He attempts 50 questions and scores 170 marks. How many questions did he answer correctly?

Solution:
Let,
the number of correct answers be x,
and the number of wrong answers is (50 - x).

ATQ,
5x - 3(50 - x) = 170
⇒ 5x - 150 + 3x = 170
⇒ 8x - 150 = 170
⇒ 8x = 170 + 150
⇒ x = 320/8
∴ x = 40

∴ He attempted 40 questions correctly.

৪৫৮.

The average weight of A, B, and C is 60 kg, and that of B and C is 62 kg. A’s present weight is-

ক
48 kg
খ
50 kg
গ
56 kg
ঘ
52 kg

ব্যাখ্যা

Question: The average weight of A, B, and C is 60 kg, and that of B and C is 62 kg. A’s present weight is-

Solution:
The average of A, B and C is 60

So, the sum of their weights = 180
The sum of the weights of B and C is = 62 × 2 = 124

So, A’s present weight is = 180 - 124 = 56 kg

৪৫৯.

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

ক
50 kg
খ
52 kg
গ
54 kg
ঘ
55 kg

ব্যাখ্যা

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

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

Total weight of 6 boys = (52 + 57 + 55 + 60 + 59 + 55) kg
= 338 kg.

Weight of the 7th boy = (total weight of 7 boys) - (total weight of 6 boys)
= (392 - 338) kg
= 54 kg.

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

৪৬০.

A sprinter runs 100 meters in 9.58 seconds. What decimal of a kilometer per second is this speed (approximate)?

ক
0.01044 km/s
খ
0.02044 km/s
গ
0.00144 km/s
ঘ
None of the above

ব্যাখ্যা

Question: A sprinter runs 100 meters in 9.58 seconds. What decimal of a kilometer per second is this speed?

Solution:
Distance = 100 meters
Time = 9.58 seconds

Converting meters to kilometers
100/1000 = 0.1 kilometers

Speed = Distance/Time
= 0.1 km/9.58 s
≈ 0.01044 km/s

The sprinter's speed is approximately 0.01044 kilometers per second (decimal fraction).

৪৬১.

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

ক
18
খ
20
গ
24
ঘ
30

ব্যাখ্যা

Question: Find the average of all the number between 6 and 34 which are divisible by 5.

Solution:
Numbers between 6 and 34 divisible by 5 are: 10, 15, 20, 25, 30
Sum of these numbers = 10 + 15 + 20 + 25 + 30 = 100
Count of numbers = 5
Average = 100/5 = 20

So the average is 20.

৪৬২.

The average age of parents is 38 years. The average age of parents and a child is 30 years. What is the age is the child?

ক
ক) 10 years
খ
খ) 12 years
গ
গ) 14 years
ঘ
ঘ) 15 years

ব্যাখ্যা

Question: The average age of parents is 38 years. The average age of parents and a child is 30 years. What is the age is the child?

Solution:
Total age of parents = 38 × 2 = 76 years
Total age of parents and the child = 30 × 3 = 90 years

So, Child's age = 90 - 76 = 14 years

৪৬৩.

If 6 students have an average (arithmetic mean) score of 88 on an exam, and one of those students scored a 93 on the exam, what is the average score on this exam for the other 5 students ?

ক
ক) 84
খ
খ) 85
গ
গ) 86
ঘ
ঘ) 87

ব্যাখ্যা

Question: If 6 students have an average (arithmetic mean) score of 88 on an exam, and one of those students scored a 93 on the exam, what is the average score on this exam for the other 5 students ?

Solution:
6 জন শিক্ষার্থীর গড় নম্বর = 88
6 জন শিক্ষার্থীর মোট নম্বর = 88 × 6 = 528

5 জন শিক্ষার্থীর মোট নম্বর = 528 - 93 = 435

5 জন শিক্ষার্থীর গড় নম্বর = 435/5= 87

৪৬৪.

A man earns the same amount every day, but on Sunday he earns three times as much as on the other days. What fraction of his total weekly earnings does he earn on Sunday?

ক
1/2
খ
1/6
গ
1/4
ঘ
1/3

ব্যাখ্যা

Question: A man earns the same amount every day, but on Sunday he earns three times as much as on the other days. What fraction of his total weekly earnings does he earn on Sunday?

Solution:
Let us assume that on each day except Sunday, he earns x taka.

Then,
Earnings on the other 6 days = 6x taka
Earnings on Sunday = 3x taka (since it is three times the usual daily amount)

∴ Total earnings in a week = 6x + 3x = 9x taka

Therefore, the fraction of the total weekly earnings that he earns on Sunday is,
= Sunday’s earnings/Total weekly earnings
= 3x/9x
= 1/3

So he earns 1/3 (one-third) of his total weekly earnings on Sunday.

৪৬৫.

The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers ?

ক
ক) 4
খ
খ) 5
গ
গ) 8
ঘ
ঘ) 6

ব্যাখ্যা

Question: The greatest of the 21 positive integers in a certain list is 16. The median of the 21 integers is 10. What is the least possible average (arithmetic mean) of the 21 integers?

Solution:

তালিকায় 21টি সংখ্যা রয়েছে এবং সংখ্যাগুলিকে ঊর্ধ্বক্রম সাজালে মধ্যমাটি হবে 11 তম সংখ্যা।

ধরি,

প্রথম ১০টি সংখ্যার প্রতিটির মানে হলো = 1,

শেষ ১০টি সংখ্যার প্রতিটির মানে হলো = 10,

এবং শেষ সংখ্যা হলো = 16.

অতএব, গড় হলো = (10 x 1 + 10 x 10 + 16)/21 = 126/21 = 6.

৪৬৬.

The average of a family of 6 members is 25 years. After a 45 year old member leaves the family, what is the average age (in years) of the family?

ক
ক) 22
খ
খ) 21
গ
গ) 20
ঘ
ঘ) 19

ব্যাখ্যা

6 জন সদস্যের বয়সের গড় 25 বছর
6 জন সদস্যের বয়সের সমষ্টি = (25 × 6) বছর
= 150 বছর

5 জন সদস্যের বয়সের সমষ্টি = (150 - 45) বছর
= 105 বছর

5 জন সদস্যের বয়সের গড় = 105/5 বছর
= 21 বছর

৪৬৭.

The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?

ক
2
খ
4
গ
70
ঘ
76

ব্যাখ্যা

Question: The average of runs of a cricket player of 10 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4?

Solution:
Total runs =32 × 10 = 320
Now increase in average is 4 runs
so,
New average = 32 + 4 = 36 runs
Total runs = 36 × 11 = 396
Runs made in the 11th inning = 396 - 320 = 76

৪৬৮.

Which of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?

ক
4
খ
5
গ
0
ঘ
9

ব্যাখ্যা

Question: Which of the following numbers can be removed from the set S = {0, 2, 4, 5, 9} without changing the average of set S?

Solution:
The average of the elements in the original set S is (0 + 2 + 4 + 5 + 9)/5
= 20/5
= 4

If we remove an element that equals the average, then the average of the new set will remain unchanged.
The new set after removing 4 is {0, 2, 5, 9}.

∴ The average of the elements is (0 + 2 + 5 + 9)/4
= 16/4
= 4

৪৬৯.

The average salary of five employees is Tk. 23200. If one of them is excluded the average decreases by 200. The slary of the excluded employee is:

ক
Tk. 24000
খ
Tk. 25000
গ
Tk. 23500
ঘ
Tk. 24500

ব্যাখ্যা

Question: The average salary of five employees is Tk. 23200. If one of them is excluded the average decreases by 200. The slary of the excluded employee is:

Solution:
The average salary of five employees is Tk. 23200
Total salary = 23200 × 5 = 116000

After excluding one person,
The new average is become = 23200 - 200 = 23000

Total salary of remaining 4 employees = 23000 × 4 = 92000

Then,
The salary of excluded employee = 116000 - 92000
= 24000

৪৭০.

Find

ক
0.009
খ
1
গ
0.9
ঘ
0.09

ব্যাখ্যা

Question: Find

Solution:

৪৭১.

Three numbers have an arithmetic mean of 3x + 2. If one of them is x, determine the average of the other two.

ক
4x + 3
খ
7x + 3
গ
5x + 7
ঘ
2x + 3

ব্যাখ্যা

Question: Three numbers have an arithmetic mean of 3x + 2. If one of them is x, determine the average of the other two.

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

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

∴ The average of the other two numbers is = (8x + 6)/2 = 4x + 3

৪৭২.

What is the arithmetic mean of the first 100 natural numbers?

ক
ক) 50
খ
খ) 50.5
গ
গ) 51
ঘ
ঘ) 51.5

ব্যাখ্যা

আমরা জানি,
n সংখ্যক স্বাভাবিক সংখ্যার যোগফল = {n(n + 1)/2}
∴ 100 টি স্বাভাবিক সংখ্যার যোগফল = {100(100 + 1)/2} = 5050
সুতরাং, এদের গড় = 5050/100 = 50.5

৪৭৩.

One half of the students in a school are girls, 3/5 of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

ক
1/10
খ
1/5
গ
3/10
ঘ
1/4
ঙ
None of these

ব্যাখ্যা

Question: One half of the students in a school are girls, 3/5 of these girls are studying in lower classes. What fraction of girls are studying in lower classes?

Solution:

৪৭৪.

180 oranges are distributed among 70 boys and girls such that each boy gets 2 and each girls gets 3 oranges. The number of boys are -

ক
25
খ
30
গ
40
ঘ
60

ব্যাখ্যা

Question: 180 oranges are distributed among 70 boys and girls such that each boy gets 2 and each girls gets 3 oranges. The number of boys are -

Solution:
Let, the number of boys be x.
The number of girls = 70 - x

ATQ,
2x + 3(70 - x) = 180
⇒ 2x + 210 - 3x = 180
⇒ x = 210 - 180
∴ x = 30

∴ The number of boys 30.

৪৭৫.

Which one of the following numbers can be removed from the set S = {1, 2, 3, 4, 5, 6, 7} without changing the average of set S?

ক
4.5
খ
7
গ
6
ঘ
5.5
ঙ
4

ব্যাখ্যা

Question: Which one of the following numbers can be removed from the set S = {1, 2, 3, 4, 5, 6, 7} without changing the average of set S?

Solution:
Given the set is S = {1, 2, 3, 4, 5, 6, 7}
Sum of elements = 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28

There are 7 numbers in the set.
Average = Sum of elements/Number of elements
= 28/7 = 4

And,
Removing a number that is equal to the current average will not change the average of the remaining numbers. The average of the set is 4, which is an element in the set S.

If 4 is removed, the new set is {1, 2, 3, 5, 6, 7}
∴ New sum = 1 + 2 + 3 + 5 + 6 + 7 = 24
And New number of elements = 6

∴ New average = 24/6 = 4

The number that can be removed from the set S = {1, 2, 3, 4, 5, 6, 7} without changing the average of the set is 4.

৪৭৬.

Bangladesh need 282 runs against Australia. In the first 10 overs the run rate is only 3.2, What should be the run rate in the remaining 40 overs to reach the target?

ক
ক) 5.00
খ
খ) 5.50
গ
গ) 6.00
ঘ
ঘ) 6.25

ব্যাখ্যা

Question: Bangladesh need 282 runs against Australia. In the first 10 overs the run rate is only 3.2, What should be the run rate in the remaining 40 overs to reach the target?

Solution:
In the first 10 overs the run rate is 3.2
∴ After 10 overs the total run is = (3.2 × 10) runs
= 32 runs

Remaining = (282 - 32) runs
= 250 runs

The run rate in the remaining 40 overs to reach the target should be =(250 ÷ 40)
= 6.25

৪৭৭.

The average of 50 numbers is 40. When 5 more numbers are included, the average becomes 60. Find the average of the last 5 numbers.

ক
50
খ
130
গ
260
ঘ
85

ব্যাখ্যা

Question: The average of 50 numbers is 40. When 5 more numbers are included, the average becomes 60. Find the average of the last 5 numbers.

Solution:
Total of 50 numbers = (50 × 40)
= 2000

Now,
total of 55 numbers = (55 × 60)
= 3300

Hence, sum of the last 5 numbers = (3300 - 2000)
= 1300

∴ Average of the last five numbers = 1300/5
= 260

৪৭৮.

The average of 5 numbers is 24. If 3 more numbers, with an average of 18 are added to these numbers, what will be the average of the combined 8 numbers?

ক
21.75
খ
22
গ
23.65
ঘ
20.5

ব্যাখ্যা

Question: The average of 5 numbers is 24. If 3 more numbers, with an average of 18 are added to these numbers, what will be the average of the combined 8 numbers?

Solution:
The average of 5 numbers is 24
∴ The total of 5 numbers is 24 × 5 = 120

The average of 3 numbers is 18
∴ The total of 3 numbers is 18 × 3 = 54

The sum of 8 numbers is = 120 + 54 = 174
∴ The average of 8 numbers is 174/8 = 21.75

৪৭৯.

The total salary of Jasim, Younus and Zaved is Tk. 90,000. Jasim earns twice of what Zaved earns, and Younus earns 1.5 times of what Zaved earns. What is the salary of Zaved?

ক
Tk. 15,000
খ
Tk. 20,000
গ
Tk. 25,000
ঘ
Tk. 30,000

ব্যাখ্যা

Question: The total salary of Jasim, Younus and Zaved is Tk. 90,000. Jasim earns twice of what Zaved earns, and Younus earns 1.5 times of what Zaved earns. What is the salary of Zaved?

Solution:

Zaved এর আয় = a টাকা

Jasim এর আয় = 2a টাকা

Younus এর আয় = 1.5a টাকা

প্রশ্নমতে

a + 2a + 1.5a = 90000

⇒ 4.5a = 90000

⇒ a = 90000/4.5

∴ a = 20000

∴ Zaved এর আয় =20000 টাকা

৪৮০.

The average of 2, 7, 6, and P is 5 and the average of 18, 1, 6, P and Q is 10. What is the value of Q?

ক
30
খ
25
গ
20
ঘ
10

ব্যাখ্যা

Question: The average of 2, 7, 6, and P is 5 and the average of 18, 1, 6, P and Q is 10. What is the value of Q?

Solution:
Given that
average of 2, 7, 6, P is 5

Therefore,
5 = (2 + 7 + 6 + P)/4
⇒ 20 = 15 + P
⇒ P = 20 - 15
∴ P = 5

Therefore,
10 = (18 + 1 + 6 + P + Q)/5
⇒ 50 = 25 + 5 + Q
⇒ Q = 50 - 30
∴ Q = 20

৪৮১.

The average weight of P, Q and R is 55 kg. If the average weight of P and Q is 50 kg and that of Q and R is 53 kg, then the weight of Q is-

ক
41 kg
খ
52 kg
গ
43 kg
ঘ
49 kg
ঙ
38 kg

ব্যাখ্যা

Question: The average weight of P, Q and R is 55 kg. If the average weight of P and Q is 50 kg and that of Q and R is 53 kg, then the weight of Q is-

Solution:
Given that,
The average weight of P, Q and R= 55 Kg
The average weight of P and Q = 50 Kg
The average weight of Q and R = 53 Kg

Now,
Sum of weight(P + Q + R) = 55 × 3 = 165 kg ..........(1)
Sum of weight(P + Q) = 50 × 2 = 100 kg ........... (2)
Sum of weight(Q + R) = 53 × 2= 106 kg ..............(3)

Now,
(2) + (3) ⇒ P + Q + Q + R = 100 + 106
⇒ P + 2Q + R = 206 ............ (4)

And,
(4) - (1) ⇒ P + 2Q + R - (P + Q + R) = 206 - 165
∴ Q = 41

So the weight of Q is 41 kg.

৪৮২.

A pizza is divided into 36 slices. If Rahim takes 1/4 of the pizza and Karim takes 1/3 of the remaining slices, how many slices are still left?

ক
9
খ
18
গ
15
ঘ
12

ব্যাখ্যা

Question: A pizza is divided into 36 slices. If Rahim takes 1/4 of the pizza and Karim takes 1/3 of the remaining slices, how many slices are still left?

সমাধান:
• মোট স্লাইসের সংখ্যা ছিল 36 টি।
• রহিম নেয় মোট স্লাইসের 1/4 অংশ।
⇒ রহিমের নেওয়া স্লাইস = 36 × (1/4) = 9টি।

∴ অবশিষ্ট স্লাইসের সংখ্যা = 36 - 9 = 27 টি।

• করিম অবশিষ্ট স্লাইসের 1/3 অংশ নেয়।
⇒ করিমের নেওয়া স্লাইস = 27 × (1/3) = 9 টি।

∴ সবশেষে অবশিষ্ট স্লাইসের সংখ্যা = 27 - 9 = 18 টি।

৪৮৩.

What is the value of x in the following equation,

ক
45
খ
27
গ
21
ঘ
43

ব্যাখ্যা

Question: What is the value of x in the following equation,

Solution:

৪৮৪.

In a certain office, 1/3 of the workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of workers are without children?

ক
7/18
খ
5/18
গ
1/11
ঘ
7/11
ঙ
11/18

ব্যাখ্যা

Question: In a certain office, 1/3 of the workers are women, 1/2 of the women are married and 1/3 of the married women have children. If 3/4 of the men are married and 2/3 of the married men have children, what part of workers are without children?

Solution:
Given that,
Total women = 1/3
Married women = 1/2 of 1/3 = 1/6
Women who have a child = 1/3 of married women

∴ Women who has child = 1/3 of 1/6 = 1/18

And,
Total men = 2/3 (∵ 1/3 are women)
Married man = 3/4 of the total man
Married man = 3/4 of 2/3 = 1/2
Man who has a child = 2/3 of a married man

∴ Men who has child = 2/3 of 1/2 = 1/3

Now,
Men + Women (having child) = (1/18) + (1/3) = 7/18

∴ Part that don't have child = 1 - (7/18) = 11/18

∴ 11/18 workers don't have children.

৪৮৫.

The average weight of 3 friends is 33 kg. None of the friends weights less than 31 kg. What can be the maximum weight of any three friends?

ক
ক) 37
খ
খ) 35
গ
গ) 33
ঘ
ঘ) 32

ব্যাখ্যা

Question: The average weight of 3 friends is 33 kg. None of the friends weights less than 31 kg. What can be the maximum weight of any three friends?

Solution:
তিনজনের গড় ওজন ৩৩ কেজি
মোট ওজন ৩৩ × ৩ কেজি
= ৯৯ কেজি

প্রতিজনের ওজন সর্বনিম্ন ৩১ কেজি
দুজনের সর্বনিম্ন ওজন ৩১ × ২ কেজি
= ৬২ কেজি

একজনের সর্বোচ্চ ওজন হতে পারে = ৯৯ - ৬২ কেজি
= ৩৭ কেজি

৪৮৬.

A group consists of two male, two female and three children. The average age of the male is 67 years, that of the female is 35 years, and that of the children is six years. What is the average age of the group?

ক
30.71
খ
31.71
গ
28.71
ঘ
35.45

ব্যাখ্যা

Question: A group consists of two male, two female and three children. The average age of the male is 67 years, that of the female is 35 years, and that of the children is six years. What is the average age of the group?

Solution:
Total age of two male = 67 × 2 = 134
Total age of two female = 35 × 2 = 70
Total age of three children = 6 × 3 = 18

∴ Average age of the group = (134 + 70 + 18)/(2 + 2 + 3)
= 222/7
= 31.71

৪৮৭.

The average of the reciprocals of x and y is:

ক
ক) 2xy/(x + y)
খ
খ) (x + y)/2xy
গ
গ) xy/2(x + y)
ঘ
ঘ) 2(x + y)/xy

ব্যাখ্যা

Question: The average of the reciprocals of x and y is:

Solution:
The reciprocals of x and y are = 1/x and 1/y
Required average
= {(1/x) + (1/y)}/2
= {(y + x)/xy}/2
= {(y + x)/xy} × (1/2)
=(x + y)/2xy

৪৮৮.

The average of fourteen numbers is 20 and the average of the first eight is 16. What is the average for the rest?

ক
26.25
খ
25.33
গ
28
ঘ
22.75

ব্যাখ্যা

Question: The average of fourteen numbers is 20 and the average of the first eight is 16. What is the average for the rest?

Solution:
The average of the fourteen numbers is = 20
Sum of 14 numbers = 14 × 20 = 280

The average of the first 8 numbers is = 16
Sum of first 8 numbers = 8 × 16 = 128

Total of remaining six numbers = 280 - 128 = 152
Average of the rest = 152/6 = 25.33

৪৮৯.

A car owner buys petrol at Tk.17, TK. 19 and TK. 20 per liter for three consecutive years. Compute the average cost per liter. If he spends Tk. 6460 per year.

ক
Tk. 12
খ
Tk. 18.58
গ
Tk. 24.5
ঘ
Tk. 28.92

ব্যাখ্যা

৪৯০.

Find

ক
8
খ
0.64
গ
6
ঘ
0.8

ব্যাখ্যা

Quesiton: Find

Solution:

৪৯১.

A cricketer scores 60 runs in the 10th innings and increases his average by 2 runs. What is his average after the 10th innings?

ক
40
খ
42
গ
45
ঘ
49

ব্যাখ্যা

Question: A cricketer scores 60 runs in the 10th innings and increases his average by 2 runs. What is his average after the 10th innings?

Solution:
ধরি, প্রথম 9 ইনিংসের গড় রান = x
∴ 9 ইনিংসের মোট রান = 9x

10 তম ইনিংসে 60 রান করার পর নতুন গড় = x + 2
সুতরাং, 10 ইনিংসের মোট রান = 10 × (x + 2)

এখানে, 9 তম ইনিংসের মোট রান এবং 10 তম ইনিংসের মোট রানের পার্থক্য = 60.
অর্থাৎ,
10(x + 2) - 9x = 60
⇒ 10x + 20 - 9x = 60
⇒ x + 20 = 60
∴ x = 40

অতএব, ১০ তম ইনিংসের পর গড় = 40 + 2 = 42

৪৯২.

10, 4, 26, 14 what is the median of the numbers shown?

ক
ক) 12
খ
খ) 15
গ
গ) 13
ঘ
ঘ) 14

ব্যাখ্যা

প্রশ্ন : 10, 4, 26, 14 what is the median of the numbers shown?

সমাধান :

We arrange the numbers in ascending order:
4, 10, 14, 26
the median of the numbers = (10 + 14)/2 = 24/2 = 12

৪৯৩.

The average weight of A, B and C is 45 kg. If the average weight of A and B is 40 kg and that of B and C be 43 kg, then the weight of B is:

ক
ক) 17 kg
খ
খ) 20 kg
গ
গ) 26 kg
ঘ
ঘ) 30kg
ঙ
ঙ) 31 kg

ব্যাখ্যা

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

৪৯৪.

The average of nine numbers is 18. The average of six of these numbers is 16. What is the average of the remaining three numbers?

ক
22
খ
24
গ
26
ঘ
28

ব্যাখ্যা

Question: The average of nine numbers is 18. The average of six of these numbers is 16. What is the average of the remaining three numbers?

Solution:
৯ টি সংখ্যার গড় = ১৮
৯ টি সংখ্যার সমষ্টি = ১৮ × ৯ = ১৬২

৬ টি সংখ্যার গড় = ১৬
৬ টি সংখ্যার সমষ্টি = ১৬ × ৬ = ৯৬

∴ বাকী ৩ টি সংখ্যার সমষ্টি = ১৬২ - ৯৬ = ৬৬
∴ ৩ টি সংখ্যার গড় = ৬৬/৩ = ২২

৪৯৫.

The average salary of all the workers in a workshop is Tk. 6000. The average salary of 7 technicians is Tk. 12000 and the average salary of the rest is Tk. 5000. How many workers are there?

ক
ক) 49
খ
খ) 50
গ
গ) 51
ঘ
ঘ) 52

ব্যাখ্যা

Question: The average salary of all the workers in a workshop is Tk. 6000. The average salary of 7 technicians is Tk. 12000 and the average salary of the rest is Tk. 5000. How many workers are there?

Solution:
let, there are x number of workers
The average salary of all the workers in a workshop is Rs. 6000
∴ total salary = 6000 × x = 6000x

The average salary of 7 technicians is Tk. 12000
∴ salary of 7 technicians is = (12000 × 7) = 84000 tk

the average salary of the rest is Tk. 5000
∴ salary of the rest = 5000 × (x - 7) tk

5000 × (x - 7) + 84000 = 6000x
⇒ 5000x - 35000 + 84000 = 6000x
⇒ 1000x = 49000
∴ x = 49

so, there are 49 workers

৪৯৬.

A car owner buys petrol at Tk.17. TK. 19 and TK. 20 per liter for three consecutive years. Compute the average cost per liter. If he spends Tk. 6460 per year.

ক
ক) Tk. 18.49
খ
খ) Tk. 18.58
গ
গ) Tk. 19.20
ঘ
ঘ) Tk. 21.66

ব্যাখ্যা

Total quantity of petrol consumed in 3 years
= (6460/17 + 6460/19 + 6460/20) litres
= (380 + 340 + 323) litres
= 1043 litres
Total amount spent
= Tk. (3 × 6460)
= Tk. 19380
∴ Average cost
= Tk. (19380/1043)
= Tk. 18.58

৪৯৭.

{(2.39)² - (1.61)²}/(2.39 - 1.61) = ?

ক
2
খ
4
গ
6
ঘ
8

ব্যাখ্যা

Question: {(2.39)² - (1.61)²}/(2.39 - 1.61) = ?

Solution:
Expression = (a² - b²)/(a - b)
= {(a + b)(a - b)}/(a - b)
= (a + b)

∴ {(2.39)² - (1.61)²}/(2.39 - 1.61)
= (2.39 + 1.61)
= 4

৪৯৮.

In a school, average marks of three batches of 40, 50 and 60 students respectively is 45, 55 and 70. Find the average marks of all the students.

ক
ক) 54.78
খ
খ) 55.23
গ
গ) 50.36
ঘ
ঘ) 58.33

ব্যাখ্যা

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

Here,
Number of quantities = Number of students in each batch

As average marks of students are given, calculate total marks of each batch first. So total marks for
Batch 1 = (40 x 45) = 1800
Batch 2 = (50 x 55) = 2750
Batch 3 = (60 x 70) = 4200

Sum of marks = (1800 + 2750 + 4200) = 8750

Therefore,
Required Average = (Some of works)/(Total number of students in each batch)
= 8750/(40 + 50 + 60)
= 8750/150
= 58.33

৪৯৯.

The batting average for 27 innings of a cricket player is 47 runs. His highest score in an innings exceeds his lowest score by 157 runs. If these two innings are excluded, the average score of the remaining 25 innings is 42 runs. Find his highest score in an innings.

ক
188
খ
176
গ
190
ঘ
165

ব্যাখ্যা

Question: The batting average for 27 innings of a cricket player is 47 runs. His highest score in an innings exceeds his lowest score by 157 runs. If these two innings are excluded, the average score of the remaining 25 innings is 42 runs. Find his highest score in an innings.

Solution:
Given that,
The batting average for 27 innings of a cricket player is 47 runs.
His highest score exceeds his lowest score by 157 runs.
If these two innings are excluded, the average of the remaining 25 innings is 42 runs.

Now,
Sum of runs for 27 innings of a cricket player = 47 × 27 = 1269
Sum of runs for 25 innings of a cricket player = 42 × 25 = 1050

∴ Sum of remaining 2 innings = 1269 - 1050 = 219

Let,
The minimum score be x and the maximum score be x + 157

According to the question,
x + x + 157 = 219
⇒ 2x = 219 - 157
⇒ 2x = 62
∴ x = 31

So, highest score = 157 + 31 = 188

৫০০.

The average of 50 numbers is 36. When 4 more numbers are included, the average of 54 numbers becomes 40. Find the average of the 4 new numbers.

ক
90
খ
85
গ
80
ঘ
95
ঙ
75

ব্যাখ্যা

Question: The average of 50 numbers is 36. When 4 more numbers are included, the average of 54 numbers becomes 40. Find the average of the 4 new numbers.

Solution:
Total of 50 numbers = 50 × 36 = 1800
Now, total of 54 numbers = 54 × 40 = 2160
Hence, sum of 4 numbers = 2160 - 1800 = 360

∴ Average of four numbers = 360/4
= 90