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Fraction and Simplification, Average and Mean

মোট প্রশ্ন৯৪৮এই পাতা৪৫প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Fraction and Simplification, Average and Mean

PrepBank · পাতা ১০ / ১০ · ৯০১–৯৪৫ / ৯৪৮

৯০১.
A pupils marks were wrongly entered as 84 instead of 64. Due to that the average marks for the class got increased by one fourth. What is the number of pupils in the class? 
  1. ক
    ক) 50
  2. খ
    খ) 65
  3. গ
    গ) 73
  4. ঘ
    ঘ) 80
ব্যাখ্যা
Question: A pupils marks were wrongly entered as 84 instead of 64. Due to that the average marks for the class got increased by one fourth. What is the number of pupils in the class? 

Solution: 
Let there be x pupils in the class 
∴ Total increase in marks = {x × (1/4)} = x/4

ATQ,
x/4 = (84 - 64)
⇒ x/4 = 20 
⇒ x = 20 × 4
∴ x = 80   

∴ The number of pupils in the class is 80 
৯০২.
The average of 10 integers is 16. If the sum of 6 of them is 100. What is the average of other 4?
  1. ক
    ক) 21
  2. খ
    খ) 44
  3. গ
    গ) 66
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
10 টি সংখ্যার গড় 16
10টি সংখ্যার সমষ্টি =16 × 10 = 160

6টি সংখ্যার সমষ্টি = 100

4টি সংখ্যার সমষ্টি = 160 - 100
                            = 60 
10 টি সংখ্যার গড় = 60/4 = 15
৯০৩.
The average of four numbers is 72. The sum of the second and third numbers is twice the sum of the first and fourth. What is the value of the sum of the first and fourth numbers?
  1. ক
    132
  2. খ
    116
  3. গ
    96
  4. ঘ
    88
ব্যাখ্যা
Question: The average of four numbers is 72. The sum of the second and third numbers is twice the sum of the first and fourth. What is the value of the sum of the first and fourth numbers?

Solution:
Given,
Average of four numbers is 72
∴ The sum of four numbers is = (4 × 72) = 288

Let
the sum of the first and fourth numbers be x
Then the sum of the second and third numbers = 2x

ATQ,
x + 2x = 288
⇒ 3x = 288
∴ x = 96

∴ the value of the sum of the first and fourth numbers = 96
৯০৪.
A sum of Tk. 4200 is divided among P, Q, and R such that P gets 3/5 of what Q gets and Q gets 1/4 of what R gets. Q’s share is:
  1. ক
    950 Tk
  2. খ
    750 Tk
  3. গ
    650 Tk
  4. ঘ
    550 Tk
ব্যাখ্যা

Question: A sum of Tk. 4200 is divided among P, Q, and R such that P gets 3/5 of what Q gets and Q gets 1/4 of what R gets. Q’s share is:

Solution:
Let,
R’s share = Tk. x
Then,
Q’s share = Tk. x/4
P’s share = Tk. (3/5) × (x/4) = Tk. 3x/20

∴ P + Q + R = 4200
⇒ 3x/20 + x/4 + x = 4200
⇒ (3x + 5x + 20x)/20 = 4200
⇒ 28x/20 = 4200
⇒ 28x = 4200 × 20
⇒ 28x = 84000
⇒ x = 84000/28
⇒ x = 3000

∴ Q’s share = x/4 = 3000/4 = 750 Tk.

৯০৫.
The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number?
  1. ক
    ক) 47
  2. খ
    খ) 49
  3. গ
    গ) 56
  4. ঘ
    ঘ) 10
ব্যাখ্যা
Question: The average of 13 numbers is 68. If the average of the first 7 numbers is 63 and that of the last 7 numbers is 70, find the 7th number?

Solution: 
ধরি, সপ্তম সংখ্যাটি x

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

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

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

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

অতএব, সপ্তম সংখ্যাটি ৪৭ 
৯০৬.
  1. ক
    0.49
  2. খ
    1.21
  3. গ
    0.77
  4. ঘ
    0.44
ব্যাখ্যা

Question:

Solution:
Given that, √{(0.85)2 - (0.36)2}
Since, a2 - b2 = (a - b)(a + b)
= √{(0.85 + 0.36)(0.85 - 0.36)}
= √{(1.21)(0.49)}
= √{(1.1)(1.1) × (0.7)(0.7)}
= 1.1 × 0.7
= 0.77

৯০৭.
The average of Jewel's marks in 6 subjects is 74. If his average in five subjects excluding science is 70, how many marks he obtained in science?
  1. ক
    94
  2. খ
    92
  3. গ
    90
  4. ঘ
    88
ব্যাখ্যা
Question: The average of Jewel's marks in 6 subjects is 74. If his average in five subjects excluding science is 70, how many marks he obtained in science?

Solution:
Total marks obtained in 6 subjects = 6 × 74 = 444

Total marks in 5 subjects excluding science = 5 × 70 = 350

Therefore, marks obtained in science would be = 444 - 350 = 94
৯০৮.
The average of 5 terms is 50. If the first 4 terms are 45, 42, 119, and 84, what will be the last term?
  1. ক
    56
  2. খ
    - 20
  3. গ
    - 40
  4. ঘ
    - 50
  5. ঙ
    None of these
ব্যাখ্যা
Question: The average of 5 terms is 50. If the first 4 terms are 45, 42, 119, and 84, what will be the last term?

Solution:
Sum of all the terms = 250
Sum of first four terms = 45 + 42 + 119 + 84 = 290
So, the 5th term should be 250 - 290 = - 40.
৯০৯.
If the average of 5, 11, 18, and 'x' is 14, what is the value of 'x'?
  1. ক
    ক) 20
  2. খ
    খ) 21
  3. গ
    গ) 22
  4. ঘ
    ঘ) 24
ব্যাখ্যা
Question: If the average of 5, 11, 18, and 'x' is 14, what is the value of 'x'?

Solution:
According to the question,
(5 + 11 + 18 + x) / 4 = 14
⇒ 34 + x  = 56
⇒ x  = 22
৯১০.
In the first 10 overs of a cricket game, the run rate was only 3.2 runs per over. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?
  1. ক
    4
  2. খ
    4.50
  3. গ
    5.75
  4. ঘ
    6.25
ব্যাখ্যা

Question: In the first 10 overs of a cricket game, the run rate was only 3.2 runs per over. What should be the run rate in the remaining 40 overs to reach the target of 282 runs?

Solution:
Given that, 
Target = 282 runs
Runs scored in first 10 overs = 10 × 3.2 = 32 runs
∴ Runs remaining = 282 - 32 = 250 runs

∴ Remaining overs = 50 - 10 = 40 overs

∴ Required run rate in the remaining 40 overs
= 250/40
= 6.25 runs per over

৯১১.
In a hotel, the tariff for every odd dates is Tk. 1000 and for even dates is Tk. 2000. If the man paid total of Tk. 30000 in all. For how many days did he stay in the hotel given that the first day is 5th date of the month?
  1. ক
    50
  2. খ
    20
  3. গ
    40
  4. ঘ
    60
  5. ঙ
    None of these
ব্যাখ্যা
Question: In a hotel, the tariff for every odd dates is Tk. 1000 and for even dates is Tk. 2000. If the man paid total of Tk. 30000 in all. For how many days did he stay in the hotel given that the first day is 5th date of the month?

Solution:
Total tariff = 30000
So, for odd dates (5th , 7th , and so on) = 1000
And for even dates (6th , 8th and so on ) = 2000
So, the average amount of money for 2 days is Tk. 1500.
So, total amount paid = 30000
So, number of days he stayed in the hotel = 30000/1500 = 20.
৯১২.
If the arithmetic mean of 70 numbers is calculated, it is 25. If each number is increased by 5, then mean of new number is- 
  1. ক
    ক) 30
  2. খ
    খ) 35
  3. গ
    গ) 40
  4. ঘ
    ঘ) 45
ব্যাখ্যা
Question: If the arithmetic mean of 70 numbers is calculated, it is 25. If each number is increased by 5, then mean of new number is- 

Solution: 
Sum of 70 numbers = (70 × 25) = 1750

∴ Total increase = (70 × 5) = 350 

∴ Increased some = (1750 + 350) = 2100 

∴ Increased average = 2100/70 = 30
৯১৩.
  1. ক
    2
  2. খ
    4
  3. গ
    295
  4. ঘ
    643
ব্যাখ্যা
Question:

Solution:
৯১৪.
The value of [(0.01)2 + (0.22)2 + (0.333)2]/ [(0.001)2 + (0.022)2 + (0.0333)2] is-
  1. ক
    1/10
  2. খ
    10
  3. গ
    100
  4. ঘ
    1000
ব্যাখ্যা
Question: The value of [(0.01)2 + (0.22)2 + (0.333)2]/ [(0.001)2 + (0.022)2 + (0.0333)2] is-

Solution:
The value of [(0.01)2 + (0.22)2 + (0.333)2]/ [(0.001)2 + (0.022)2 + (0.0333)2]
We can write the expression as [(0.01)2 + (0.22)2 + (0.333)2]/ [(0.01/10)2 + (0.22/10)2 + (0.333/10)2]
= [(0.01)2 + (0.22)2 + (0.333)2] / [{(0.01)2 + (0.22)2 + (0.333)2} × (1/100)]
= [(0.01)2 + (0.22)2 + (0.333)2] × [100/{(0.01)2 + (0.22)2 + (0.333)2}]

Hence, numerator and denominator will cancel each other, and the remaining value will be 100.
৯১৫.
The average mark obtained by Ratul in 3 papers is 52 and in the fourth paper, he scored 60 marks. Find the new average of marks scored by Ratul.
  1. ক
    53.5
  2. খ
    54
  3. গ
    52
  4. ঘ
    72
ব্যাখ্যা
Question: The average mark obtained by Ratul in 3 papers is 52 and in the fourth paper, he scored 60 marks. Find the new average of marks scored by Ratul.

Solution: 
The average mark obtained by Ratul in 3 papers is 52 
total marks = 3 × 52 = 156 

New average = (156 + 60)/4
= 216/4 
= 54
৯১৬.
The average age of a group is 28. If a 42-year-old person leaves, the average becomes 26. How many people are in the group?
  1. ক
    8
  2. খ
    10
  3. গ
    12
  4. ঘ
    14
ব্যাখ্যা

Question: The average age of a group is 28. If a 42-year-old person leaves, the average becomes 26. How many people are in the group?

Solution: 
Let
The original number of people be x.

Total age of the group:
= 28 × x
= 28x

After the 42-year-old leaves, total age:
= 28x - 42

Number of people remaining = x - 1
New average = 26

Accordingly, 
(28x - 42) / (x - 1) = 26
⇒ 28x - 42 = 26(x - 1)
⇒ 28x - 42 = 26x - 26
⇒ 28x - 26x = - 26 + 42
⇒ 2x = 16
⇒ x = 8

৯১৭.
Two-fifth of one-fourth of three seventh of a number is 15. What is the half of the number?
  1. ক
    75
  2. খ
    137
  3. গ
    157
  4. ঘ
    175
ব্যাখ্যা
Question: Two-fifth of one-fourth of three seventh of a number is 15. What is the half of the number?

Solution: 
Let the number is a

ATQ,
a × (3/7) × (1/4) × (2/5) = 15
⇒ 3a/70 = 15
a = 350 

∴ Half of the number is = 350/2 = 175
৯১৮.
Fresh grapes contain 80% water, while dried grapes contain 20% water. If the weight of the dried grapes is 400 kg, what was the total weight of the grapes when fresh? 
  1. ক
    1350 kg
  2. খ
    1475 kg
  3. গ
    1500 kg
  4. ঘ
    1600 kg
ব্যাখ্যা

Question: Fresh grapes contain 80% water, while dried grapes contain 20% water. If the weight of the dried grapes is 400 kg, what was the total weight of the grapes when fresh? 

Solution:
Given that,
Dried grapes contain 20% water
∴ They contain 80% solid matter. 
Fresh grapes contain 80% water
∴ They contain 20% solid matter.

The amount of solid matter never changes during drying.

Let the weight of fresh grapes = x kg
Solid matter in fresh grapes = 20% of x = 0.20x kg
Solid matter in dried grapes = 80% of 400 kg
= (80/100) × 400
= 320 kg

Since the solid matter remains the same,
0.20x = 320
⇒ x = 320 / 0.20
⇒ x = (320 × 100)/20
∴ x = 1600 kg

The total weight of the grapes when fresh was 1600 kg.

৯১৯.
The average age of a group of 15 employees is 28 years. When 5 more employees join the group, the average age increases by 2 years. The average age of the new employees is?
  1. ক
    36 years
  2. খ
    38 years
  3. গ
    32 years
  4. ঘ
    34 years
ব্যাখ্যা

Question: The average age of a group of 15 employees is 28 years. When 5 more employees join the group, the average age increases by 2 years. The average age of the new employees is?

Solution: Average age of 15 employees = 28 years
Total age of 15 employees = 15 × 28 = 420 years

After 5 more employees join:
Total number of employees = 15 + 5 = 20 employees
New average age = 28 + 2 = 30 years
Total age of 20 employees = 20 × 30 = 600 years

Total age of 5 new employees = 600 - 420 = 180 years

Average age of 5 new employees = 180 ÷ 5 = 36 years

৯২০.
When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?
  1. ক
    ক) 55
  2. খ
    খ) 56
  3. গ
    গ) 57
  4. ঘ
    ঘ) 58
ব্যাখ্যা

Let the average weight of the 59 students be A.
So the total weight of 59 of them will be = 59 × A = 59A

The questions state that when the weight of this student who left is added,
the total weight of the class=59A + 45
When this student is also included, the average weight decreases by 0.2 kgs

(59A + 45)/60 = (A - 0.2)
⇒ 59A + 45 = 60A - 12
⇒ 45 + 12 = 60A - 59A
⇒ A = 57.

৯২১.
5 - [4 - {3 - (3 - 3 - 6)}] is equal to-
  1. ক
    9
  2. খ
    18
  3. গ
    10
  4. ঘ
    13
ব্যাখ্যা

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

Solution:
Given,
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

৯২২.
The average of 4 terms is 20 and the last term is 1/3 of the remaining terms. What will be the last number?
  1. ক
    15
  2. খ
    20
  3. গ
    25
  4. ঘ
    30
ব্যাখ্যা
Question: The average of 4 terms is 20 and the last term is 1/3 of the remaining terms. What will be the last number?

Solution:
The average of 4 terms is 20 
total sum = (4 × 20) = 80

let, last term is x 
remaining terms is 3x

3x + x = 80
⇒ 4x = 80
∴ x = 20
The last number is 20
৯২৩.
The total marks obtained by a student in Bangla, English, and Mathematics together are 150 more than the marks obtained by him in Bangla. What is the average mark obtained by him in English and Mathematics together?
  1. ক
    60
  2. খ
    75
  3. গ
    80
  4. ঘ
    95
ব্যাখ্যা

Question: The total marks obtained by a student in Bangla, English, and Mathematics together are 150 more than the marks obtained by him in Bangla. What is the average mark obtained by him in English and Mathematics together?

Solution:
Bangla + English + Mathematics = Bangla + 150
⇒ English + Mathematics = Bangla + 150 - Bangla
⇒ English + Mathematics = 150

∴ Required average = 150/2
= 75

৯২৪.
A cricketer has a certain average for 9 innings. In the 10th innings he scores 100 runs, thus increasing his average by 8 runs. What is new average?
  1. ক
    38
  2. খ
    28
  3. গ
    34
  4. ঘ
    42
ব্যাখ্যা
Question: A cricketer has a certain average for 9 innings. In the 10th innings he scores 100 runs, thus increasing his average by 8 runs. What is new average?

Solution:
Let average be x for 9 innings. So, A cricketer scores 9x run in 9 innings.

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

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

New average
= x + 8
= 20 + 8
= 28
৯২৫.
The average score of a class of boys and girls in an examination is A. The ratio of boys and girls in the class is 3:1. If the average score of the boys is A + 1, the average score of the girls is -
  1. ক
    ক) A - 1
  2. খ
    খ) A - 3
  3. গ
    গ) A + 1
  4. ঘ
    ঘ) A + 3
ব্যাখ্যা

Let,
The number of boys and girls in the class are 3x and x respectively.
Let the average score of the girls be y.
Then, 3x(A + 1) + xy = (3x +x)A
⇒ 3(A + 1) + y = 4A
⇒ 3A + 3 + y = 4A
⇒ y = A - 3

৯২৬.
0.009/? = 0.01
  1. ক
    .0009
  2. খ
    .09
  3. গ
    .9
  4. ঘ
    9
ব্যাখ্যা
Question: 0.009/? = 0.01

Solution:
Let
.009/x = .01;     

Then x = .009/.01
= .9/1
= .9
৯২৭.
If u, v, w, x, y, z are six consecutive odd integers. Find the average (arithmetic mean) of these six numbers.
  1. ক
    u + 10
  2. খ
    u + 5
  3. গ
    6
  4. ঘ
    5(u + 6)
ব্যাখ্যা
Question: If u, v, w, x, y, z are six consecutive odd integers. Find the average (arithmetic mean) of these six numbers.

Solution:
৯২৮.
The average of the first five multiples of 11 is-
  1. ক
    30
  2. খ
    31
  3. গ
    32
  4. ঘ
    33
ব্যাখ্যা
Question: The average of the first five multiples of 11 is-

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

∴ average = (11 × 15)/5
= 33
৯২৯.
The average age of a group of 10 students is 15 years. When 5 more students join the group, the average age increases by 1 year. The average age of the new students is?
  1. ক
    ক) 12 years
  2. খ
    খ) 16 years
  3. গ
    গ) 18 years
  4. ঘ
    ঘ) 20 years
  5. ঙ
    ঙ) 22 years
ব্যাখ্যা

Total age of 10 students = 150 years
Total age of 15 students = 240 years
Total age of 5 new students = 240 - 150 = 90 years
Therefore,
Average age of 5 new students = 90/5 = 18 years

৯৩০.
The average of ten numbers is 8. If each number is multiplied by 10, what is the new average?
  1. ক
    ক) 10
  2. খ
    খ) 40
  3. গ
    গ) 80
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Question: The average of ten numbers is 8. If each number is multiplied by 10, what is the new average? 

Solution:
The sum of ten numbers = 10 × 8 = 80

ATQ,
The average of ten numbers is = The sum of ten numbers / 10

Now, 
If each number is multiplied by 10, the new average is
= (The sum of ten numbers × 10) / 10
= (80 × 10) / 10
= 80
৯৩১.
30 pens and 75 pencils altogether were purchased for Tk. 510. If the average price of a pencil was Tk 2, what was the average price of a pen?
  1. ক
    ক) Tk. 9
  2. খ
    খ) Tk. 10
  3. গ
    গ) Tk. 11
  4. ঘ
    ঘ) Tk. 12
ব্যাখ্যা

ATQ,
30 pens + 75 pencils = Tk. 510
Given, Average price of a pencil = Tk. 2
So, Price of 75 pencils = 2 × 75 = Tk. 150
∴ Price of 30 pens = 510 - 150 = Tk. 360
∴ Average price of pen = 360/30 = Tk. 12

৯৩২.
If √(0.0169 × x) = 1.3 than, what is the value of x?
  1. ক
    169
  2. খ
    0.00169
  3. গ
    100
  4. ঘ
    1000
ব্যাখ্যা

Question: If √(0.0169 × x) = 1.3 than, what is the value of x?

Solution: 
Given that, 
√(0.0169 × x) = 1.3
⇒ 0.0169 × x = (1.3)2   ; [Square both sides]
⇒ 0.0169 × x = 1.69
⇒ x = 1.69/0.0169
⇒ x = (169 × 10000)/(169 × 100)
∴ x = 100

৯৩৩.
A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is-
  1. ক
    ক) 250
  2. খ
    খ) 276
  3. গ
    গ) 280
  4. ঘ
    ঘ) 285
ব্যাখ্যা

Since the month begins with a Sunday, so there will be five Sunday in the month.
∴ Required average = {(510 × 5) + (240 × 25)}/30 = 8550/30 = 285
Answer: 285
Source: Quantitative Aptitude

৯৩৪.
If the Fibonacci sequence begins with zero, what is the average of the total of its first 11 terms?
  1. ক
    6
  2. খ
    10
  3. গ
    13
  4. ঘ
    8
ব্যাখ্যা
Question: If the Fibonacci sequence begins with zero, what is the average of the total of its first 11 terms?

Solution:
The first 9 logical terms of the Fibonacci series if the series starts with zero = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
So, the average = (0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55)/11
= 143/11
= 13
৯৩৫.
The average of the first 6 numbers out of 7 is 25, and the average of the last 6 numbers is 29. If the first number is 10, what is the 7th number? 
  1. ক
    30
  2. খ
    32
  3. গ
    34
  4. ঘ
    36
ব্যাখ্যা

Question: The average of the first 6 numbers out of 7 is 25, and the average of the last 6 numbers is 29. If the first number is 10, what is the 7th number? 

Solution:
Given that,
First number = 10
Average of first 6 = 25
Average of last 6 = 29

Let,
the seven numbers be A1, A2, A3, A4, A5, A6, A7
A1 = 10

Sum of first 6 numbers = 6 × 25 = 150 …(1)
Sum of last 6 numbers = 6 × 29 = 174 …(2)

Subtract equation (1) from (2):
(A2 + A3 + A4 + A5 + A6 + A7) - (A1 + A2 + A3 + A4 + A5 + A6) = 174 - 150 
⇒ A7 - A1 = 24 
⇒ A7 - 10 = 24 
⇒ A7 = 34

∴ The 7th number is 34.

৯৩৬.
In a class with a certain number of students if one new student weighing 50 kg is added, then average weight of class is increased by 1 kg. If one more student weighing 50 kg is added, then the average weight of the class increases by 1.5 kg over the original average. What is the original average weight (in kg) of the class?
  1. ক
    ক) 46
  2. খ
    খ) 42
  3. গ
    গ) 27
  4. ঘ
    ঘ) 47
ব্যাখ্যা

Let x be the number of students in the class and y be the average weight of the class
Now according to question,
(xy + 50)/(x + 1) = y + 1
x + y = 49 .......... (i) Again,
(xy + 50 + 50)/(x + 2) = y + 1.5
1.5x + 2y = 97.......... (ii) From equation (i) and (ii), we get y = 47
Answer: 47

৯৩৭.
The average of the first six multiples of 3 is-
  1. ক
    12.5
  2. খ
    9.25
  3. গ
    8
  4. ঘ
    10.5
ব্যাখ্যা
Question: The average of the first six multiples of 3 is-

Solution:
The first six multiples of 3 are,
3, 6, 9, 12, 15, 18

The sum of these multiples is,
3 + 6 + 9 + 12 + 15 + 18 = 63

∴ Average = 63/6​ = 10.5
The average of the first six multiples of 3 is 10.5
৯৩৮.
The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three numbers is 52. Then the sixth number is -
  1. ক
    ক) 30
  2. খ
    খ) 34
  3. গ
    গ) 44
  4. ঘ
    ঘ) 24
ব্যাখ্যা

Required number = (Sum of all numbers) - [(Sum of first 5 numbers) + (Sum of last 3 numbers)]
= 50 x 9 - (54 x 5 + 3 x 52)
= 450 - (270 + 156)
= 450 - 426
= 24

৯৩৯.
The average of 15 numbers is 48. If the average of first 7 numbers is 44 and the average of last 7 numbers is 50, what is the middle number?
  1. ক
    64
  2. খ
    62
  3. গ
    60
  4. ঘ
    58
ব্যাখ্যা

Question: The average of 15 numbers is 48. If the average of first 7 numbers is 44 and the average of last 7 numbers is 50, what is the middle number?

Solution:
Let
The middle number be x

Total sum of 15 numbers,
= 15 × 48
= 720

Sum of first 7 numbers,
= 7 × 44
= 308

Sum of last 7 numbers,
= 7 × 50
= 350

∴ Sum of first 7 numbers + x + Sum of last 7 numbers = 720
⇒ 308 + x + 350 = 720 
⇒ 658 + x = 720
⇒ x = 720 - 658
∴ x = 62

So the middle number be 62.

৯৪০.
What is the value of 12 × 5 – 8 ÷ 2 = ?
  1. ক
    - 12
  2. খ
    12
  3. গ
    60
  4. ঘ
    56
ব্যাখ্যা
Question:  What is the value of 12 × 5 - 8 ÷ 2 = ?

Solution:
12 × 5 - 8 ÷ 2
= 60 - 4 [ According to the BODMAS rule ]
= 56
৯৪১.
Jamil's average score in 4 tests was 85 out of a possible 100. If his scores in 2 of the tests were 70, and 80. What is the lowest that either of his other scores could have been?
  1. ক
    94
  2. খ
    88
  3. গ
    92
  4. ঘ
    90
ব্যাখ্যা
Question: Jamil's average score in 4 tests was 85 out of a possible 100. If his scores in 2 of the tests were 70, and 80. What is the lowest that either of his other scores could have been?

Solution:
Average of 4 test was 85
Total marks = 85 × 4 = 340

Marks of other 2 subjects = (340 - 70 - 80)= 290
He can get highest 100 marks in one of the subjects.

∴ Lowest marks will be = (290 - 100) = 190
৯৪২.
The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
  1. ক
    63
  2. খ
    33
  3. গ
    27
  4. ঘ
    25
  5. ঙ
    None of these
ব্যাখ্যা
Question: The average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
 
Solution:
Given,
Average of 10 numbers = 23
⇒ Sum/Total numbers = 23
⇒ Sum/10 = 23
∴ Sum of the 10 numbers = 230

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

Therefore, the new average = 270/10 = 27
৯৪৩.
What decimal of an hour is 45 seconds?
  1. ক
    0.015
  2. খ
    0.0125
  3. গ
    0.018
  4. ঘ
    0.0225
ব্যাখ্যা

Question: What decimal of an hour is 45 seconds?

Solution:
1 hour = 60 × 60 = 3600 seconds

∴ Required decimal
= 45/3600
= 1/80
= 0.0125

৯৪৪.
The mean of the first 12 even natural number numbers is-
  1. ক
    14
  2. খ
    13
  3. গ
    12
  4. ঘ
    11
ব্যাখ্যা
Question: The mean of the first 12 even natural number numbers is-

Solution:
First 10 even natural numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24.

Mean = (2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24​)/12
= 156/12
= 13
৯৪৫.
Find the average of first 97 natural numbers.
  1. ক
    49
  2. খ
    52
  3. গ
    47
  4. ঘ
    50
  5. ঙ
    53
ব্যাখ্যা

Question: Find the average of first 97 natural numbers.

Solution:
We know,
Average = Sum of first n natural numbers​/n

And the sum of first n natural numbers = n(n + 1)/2

∴ Average = {n(n + 1)/2}/n = (n + 1)/2
= (97 + 1)/2  ; [Substitute n = 97]
= 98/2
= 49