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Bank Math

মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math

PrepBank · পাতা ২৩ / ১৬১ · ২,২০১–২,৩০০ / ১৬,১২৪

২,২০১.
Find the number of ways the letters of the word ‘RUBBER can be arranged?
  1. ক
    ক) 450
  2. খ
    খ) 362
  3. গ
    গ) 250
  4. ঘ
    ঘ) 180
ব্যাখ্যা
Question: Find the number of ways the letters of the word ‘RUBBER can be arranged?

Solution: 
The word ‘RUBBER’ contains 6 letters: 2R, 2B, 1 U, 1 E
Therefore,
The required Number of ways: 
6!/{(2!) × (2!)}
= 180
২,২০২.
The ratio between the speeds of two trains is 5 : 6. If the second train runs 270 km in 3 hours, then the speed of the first train is:
  1. ক
    ক) 75 km/hr.
  2. খ
    খ) 65.5 km/hr.
  3. গ
    গ) 75.8 km/hr.
  4. ঘ
    ঘ) 75.5 km/hr.
ব্যাখ্যা
Question: The ratio between the speeds of two trains is 5 : 6. If the second train runs 270 km in 3 hours, then the speed of the first train is:

Solution: 
Let,
the speed of first train be 5x
the speed of second train be 6x

ATQ, 
6x = 270/3 
Or, 6x = 90
Or, x = 90/6 
Or, x = 15

∴  Speed of first train =  5x = 5 × 15 = 75 km/hr. 
২,২০৩.
200 kg of sugar solution has 30% sugar in it. How much sugar should be added to make it 50% in the solution?
  1. ক
    40 kg
  2. খ
    60 kg
  3. গ
    80 kg
  4. ঘ
    120 kg
ব্যাখ্যা
Question: 200 kg of sugar solution has 30% sugar in it. How much sugar should be added to make it 50% in the solution?

Solution: 
30% suger = 30% of 200 = 60
let, X kg of sugar should be added,

ATQ,
60 + X/200 + X = 1/2
or, 200 + X = 120 + 2X
or, X = 80 kg
২,২০৪.
If a 20-meter tall pole creates a shadow of length 20√3 meters, what is the angle of elevation of the sun?
  1. ক
    60°
  2. খ
    45°
  3. গ
    30°
  4. ঘ
    70°
ব্যাখ্যা
Question: If a 20-meter tall pole creates a shadow of length 20√3 meters, what is the angle of elevation of the sun?

Solution:

খুঁটির উচ্চতা AB = 20 m
খুঁটির ছায়ার দৈর্ঘ্য BC =20√3 m

ΔABC হতে পাই,
tanθ = লম্ব/ভূমি
বা, tanθ = AB/BC
বা, tanθ = 20/(20√3)
বা, tanθ = 1/√3
বা, tanθ = tan30°
∴ θ = 30°
২,২০৫.
What will be the difference between simple and compound interest at 10% on a sum of Tk. 5000 after 3 years?
  1. ক
    Tk. 50
  2. খ
    Tk. 120
  3. গ
    Tk. 155
  4. ঘ
    Tk. 180
  5. ঙ
    Tk. 32
ব্যাখ্যা

Question: What will be the difference between simple and compound interest at 10% on a sum of Tk. 5000 after 3 years?

Solution:
Given that,
Principal, P = Tk. 5000
Rate of interest, r = 10%
Time, n = 3 years

Simple Interest (SI):
SI = (P × r × n) / 100
⇒ SI = (5000 × 10 × 3) / 100
⇒ SI = 150000 / 100
⇒ SI = Tk. 1500

Compound Interest (CI):
CI = P × (1 + r/100)n 
= 5000 × (1 + 10/100)3
= 5000 × (1.10)3
= 5000 × 1.331 
= 6655

CI = A - P
= 6655 - 5000 = Tk. 1655

∴ Difference between CI and SI:
= CI - SI
= 1655 - 1500
= Tk. 155

২,২০৬.
In school, three rows are formed of the students. First row has 50% more students than the second row and the third row has 50% less students than the second row. If the total number of students in all the rows is 900, then find the number of students in the third row. 
  1. ক
    100
  2. খ
    150
  3. গ
    300
  4. ঘ
    450
ব্যাখ্যা
Question: In school, three rows are formed of the students. First row has 50% more students than the second row and the third row has 50% less students than the second row. If the total number of students in all the rows is 900, then find the number of students in the third row.

Solution:
Let the number of students in the second row is 100. 
Then number of students in first row is 150 and number of students in third row is 50. 
Total students = 150 + 100 + 50 = 300 
Given = 900 
Then 900/300 = 3 
Third row has 50 × 3 =150 students.
২,২০৭.
Look at letter pattern and choose the correct option.
JAK, KBL, LCM, MDN, _____
  1. ক
    MEN
  2. খ
    PFQ
  3. গ
    OEP
  4. ঘ
    NEO
ব্যাখ্যা
Question: Look at letter pattern and choose the correct option.
JAK, KBL, LCM, MDN, _____

Solution: 
শব্দাংশগুলির ১ম বর্ণগুলো J, K, L, M
শব্দাংশগুলির ২য় বর্ণগুলো A, B, C, D
শব্দাংশগুলির ৩য় বর্ণগুলো হল K, L, M, N

অর্থাৎ, বর্ণগুলো ক্রমানুসারে রয়েছে।

শুন্যস্থানে বসবে, NEO.
২,২০৮.
A pipe can fill a cistern in 8 hours. Due to an accident, the water flow became half after pouring half of the cistern. How much time will it take to fill the whole cistern?
  1. ক
    10 hours.
  2. খ
    16 hours.
  3. গ
    12 hours
  4. ঘ
    14 hours.
ব্যাখ্যা
Question: A pipe can fill a cistern in 8 hours. Due to an accident, the water flow became half after pouring half of the cistern. How much time will it take to fill the whole cistern?

Solution:
pouring alf of the cistern will take 4 hours.
after that, the flow became half, which means it will take double the time to fill the rest half.
so the next half will be filled in 8 hours.

total time = 4 + 8 = 12 hours.
২,২০৯.
Find compound interest on Tk. 8000 at 15% per annum for 2 year 4 months, compounded annually
  1. ক
    ক) 2109
  2. খ
    খ) 3109
  3. গ
    গ) 4109
  4. ঘ
    ঘ) 5109
ব্যাখ্যা

Time = 2 year 4 months = 2(4/12) year = 2(1/3) year.
Amount = Tk'. [8000 X (1+(15/100))2 X (1+((1/3)×15)/100)]
=Tk. [8000 ×(23/20) × (23/20) ×(21/20)]
= Tk. 11109.
:. C.I. = Tk. (11109 - 8000)
= Tk. 3109.

২,২১০.
A license plate begins with three letters. If the possible letters are A, B, C, D , how many different permutations of these letters can be made if no letter is used more than once?
  1. ক
    ক) 12
  2. খ
    খ) 18
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
ব্যাখ্যা
Question: A license plate begins with three letters. If the possible letters are A, B, C, D , how many different permutations of these letters can be made if no letter is used more than once?

Solution: 
For the first letter, there are 5 possible choices. After that letter is chosen, there are 4 possible choices. Finally, there are 3 possible choices.
4 × 3 × 2
= 24
২,২১১.
A wheel rotates 10 times per minutes and moves 25m during each rotation. How many meters does the wheel moves in 45 minutes?
  1. ক
    8756m
  2. খ
    11050m
  3. গ
    11250m
  4. ঘ
    None of these
ব্যাখ্যা
Question: A wheel rotates 10 times per minutes and moves 25m during each rotation. How many meters does the wheel moves in 45 minutes?

Solution:
1 মিনিটে চাকাটি অতিক্রম করে = 10 × 25 = 250 মিটার
45 মিনিটে চাকাটি অতিক্রম করে = (250 × 45) = 11250 মিটার

∴ চাকাটি 45 মিনিটে 11250 মিটার পথ অতিক্রম করবে ।


২,২১২.
A deceitful dairy seller claims to sell his milk at a cost price but he mixes water with it and thereby gains 20%. The percentage of water in the mixture is:
  1. ক
    16.67%
  2. খ
    10.67%
  3. গ
    19%
  4. ঘ
    None of the above
ব্যাখ্যা
Question: A deceitful dairy seller claims to sell his milk at a cost price but he mixes water with it and thereby gains 20%. The percentage of water in the mixture is:

Solution:
Let,
The cost price = 100
The selling price = 120

∴ The amount of milk = 100/120
= 5/6

∴ The amount of water is = (1 - 5/6) × 100%
= 16.67%
২,২১৩.
If a person walks at 18 km/hr instead of 12 km/hr, he would have walked 25 km more. The actual distance travelled by him is:
  1. ক
    ক) 50 km. 
  2. খ
    খ) 48 km. 
  3. গ
    গ) 60 km. 
  4. ঘ
    ঘ) 55 km. 
ব্যাখ্যা
Question: If a person walks at 18 km/hr instead of 12 km/hr, he would have walked 25 km more. The actual distance travelled by him is:

Solution: 
Let the actual distance travelled be x km.

ATQ, 
Or, x/12 = (x + 25)/18
Or, 18x = 12x + 300
Or, 18x − 12x = 300
Or, 6x = 300
Or, x = 50
∴ distance = 50 km.
২,২১৪.
What is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5√2 cm?
  1. ক
    10 cm
  2. খ
    10√2 cm
  3. গ
    12√2 cm
  4. ঘ
    10√5 cm
ব্যাখ্যা
Question: What is the length of the diagonal of a square whose area is 4 times of another square with diagonal as 5√2 cm?

Solution:
Area of square = (1/2) × (length of diagonal)2

Area of square2 =(1/2) × (5√2)2  
= 25 cm2

Area of square1 = 4 × 25 = 100 cm2

∴ Length of diagonal of square1 = √(2 × area)
= √(2 × 100)
= 10√2 cm
২,২১৫.
If 25a + 25b = 135, what is the average of a and b? 
  1. ক
    ক) 2.2
  2. খ
    খ) 2.3
  3. গ
    গ) 2.7
  4. ঘ
    ঘ) 2.8
ব্যাখ্যা
25a + 25b = 135
⇒ 25 (a + b) = 135
⇒ a + b = 135/25
⇒ a + b = 27/5

∴ Average of a and b = (a + b)/2
                                  = (27/5) × (1/2)
                                   = 27/10
                                   = 2.7
২,২১৬.
A woman says, ''if you will revise my own age, the figure represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of our sum. ''What is the age of the women?
  1. ক
    ক) 23
  2. খ
    খ) 34
  3. গ
    গ) 45
  4. ঘ
    ঘ) 54
ব্যাখ্যা
Question: A woman says, ''if you will revise my own age, the figure represent my husband's age. He is,  of course, senior to me and the difference between our ages is one-eleventh of our sum.'' What is the age of the women?

Solution: 
Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.
Then,
woman's age =(10x + y) years;
husband's age =(10y + x) years.

Now
(10y + x) - (10x + y)=(1/11)(10y + x + 10x + y)
⇔(9y - 9x) = (1/11)(11y+11x)
⇔ 9y - 9x = x + y
⇔ 9y - y = 9x + x
⇔10x = 8y
⇔x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age =10x + y = 45 years.
২,২১৭.
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
  1. ক
    ক) 40 years
  2. খ
    খ) 45 years
  3. গ
    গ) 52 years
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Suppose, mother's present age is x years
Therefore, person's present age = 2x/5 years
(x + 8)/2 = 2x/5 + 8
⇒ (x + 8)/2 = (2x + 40)/5
⇒ 5x + 40 = 4x + 80
⇒ x = 40 years
২,২১৮.
X, Y and Z can do a piece of work in 6 hours. X and Y can do the work in 8 hours and Y and Z can do the same work in 12 hours. In how many time will X and Z do the work?
  1. ক
    ক) 6 hours
  2. খ
    খ) 8 hours
  3. গ
    গ) 10 hours
  4. ঘ
    ঘ) 12 hours
ব্যাখ্যা

x + y + z can do 1/6 part of the job in one hour……(i)
x + y can do 1/8 part of the job in one hour……(ii)
and, y + z can do 1/12 part of the job in one hour……(iii)
(ii) + (iii),
x + y + y + z = 1/8 + 1/12
Or, x + z + 2y = 5/24 ........ (iv)
Subtracting (i) from (iv) we get,
y = 5/24 - 1/6 = 1/24
Substituting the value of y in (iv) we get,
x + z + 2/24 = 5/24
x + z = 5/24 - 2/24 = 3/24 = 1/8
Hence x and z will do 1/8 of the job in one hour
So, x and z will do all of the work in 8 hours

২,২১৯.
A and B invested in a business. The profit earned was divided in the ratio 2 : 3. If A invested Tk. 35500, the amount invested by B is -
  1. ক
    ক) Tk. 54250
  2. খ
    খ) Tk. 53250
  3. গ
    গ) Tk. 53500
  4. ঘ
    ঘ) Tk. 53350
ব্যাখ্যা
Question: A and B invested in a business. The profit earned was divided in the ratio 2 : 3. If A invested Tk. 35500, the amount invested by B is -

Solution:
ধরি,
A বিনিয়োগ করেছিল 2x টাকা এবং B বিনিয়োগ করেছিল 3x টাকা

প্রশ্নমতে, 2x = 35500
∴ x = 17750

∴ B বিনিয়োগ করেছিল = 3x = 3 × 17750
= 53250 টাকা।
২,২২০.
Sum of present ages of A, B and C is 92 years. If 4 years ago, the ratio of their ages were 1 : 2 : 3 respectively, find A’s present age.
  1. ক
    18.5 year
  2. খ
    17.3 years
  3. গ
    14.8 years
  4. ঘ
    20.3 years
ব্যাখ্যা
Question: Sum of present ages of A, B and C is 92 years. If 4 years ago, the ratio of their ages were 1 : 2 : 3 respectively, find A’s present age.

Solution:
Sum of present ages of A, B and C is = 92 years
Therefore , Sum of their ages 4 years ago = 92 - (4 × 3) = 92 - 12 = 80 years.

4 years ago ratio of the ages of A , B and C was = 1 : 2 : 3

Therefore, A’s age four years ago = (1/6) × 80 years = 13.3 years.
∴ A’s present age = 13.3 + 4 = 17.3 years
২,২২১.
There are 10 points in a plane out of which 4 are collinear. Find the number of triangles formed by the points as vertices.
  1. ক
    ক) 116
  2. খ
    খ) 120
  3. গ
    গ) 124
  4. ঘ
    ঘ) 132
ব্যাখ্যা
The number of triangle can be formed by 10 points = 10C3
Similarly, the number of triangle can be formed by 4 points when no one is collinear = 4C3
In the question, given 4 points are collinear, Thus, required number of triangle can be formed,
= 10C3 - 4C3
= 120 - 4
= 116
২,২২২.
  1. ক
    4, 4
  2. খ
    4, - 4
  3. গ
    - 4, - 4
  4. ঘ
    4, 1/4
ব্যাখ্যা
Question:

Solution:
(x + 8)/x = (x + 2)/2
⇒ 2x + 16 = x2 + 2x
⇒ 16 = x2
⇒ x2 - 16 = 0
⇒ x2 - 42 = 0
⇒ (x + 4)(x - 4) = 0
∴ x = - 4 or  x = 4
২,২২৩.
In a mixture 60 liters, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then estimate the quantity of water in liter to be further added in the mixture.
  1. ক
    30 liters
  2. খ
    40 liters
  3. গ
    80 liters
  4. ঘ
    60 liters
ব্যাখ্যা
Question: In a mixture 60 liters, the ratio of milk and water 2 : 1. If this ratio is to be 1 : 2, then estimate the quantity of water in liter to be further added in the mixture.

Solution:
Sum of the given ratio = 2 +1=3

Quantity of milk = 60 × (2/3) = 40 liters
Hence, quantity of water will be
= 60 - 40 = 20 liters

Assume,
x liters water needs to be added.
ATQ,
40/(x + 20) = 1/2
⇒ 80 = x + 20
∴ x = 60

∴ 60 liters water needs to be added.
২,২২৪.
There were 800 students in a school in 2025. In 2026, 10% of the male students left the school, while the number of female students increased by 40%. If the total number of students remained unchanged, how many female students were there in the school in 2025?
  1. ক
    160
  2. খ
    180
  3. গ
    200
  4. ঘ
    240
  5. ঙ
    224
ব্যাখ্যা

Question: There were 800 students in a school in 2025. In 2026, 10% of the male students left the school, while the number of female students increased by 40%. If the total number of students remained unchanged, how many female students were there in the school in 2025?

Solution:
ধরি, 2025 সালে ছাত্রীর সংখ্যা ছিল x জন।
এবং ছাত্রের সংখ্যা ছিল (800 - x) জন।

প্রশ্ন অনুযায়ী, 2026 সালে ছাত্রীর সংখ্যা 40% বৃদ্ধি পায় এবং ছাত্রের সংখ্যা 10% হ্রাস পায়, কিন্তু মোট ছাত্র-ছাত্রীর সংখ্যা 800-ই থাকে।
অর্থাৎ, ছাত্রীর বৃদ্ধির পরিমাণ = ছাত্রের হ্রাসের পরিমাণ।

প্রশ্নমতে,
x এর 40% = (800 - x) এর 10%
⇒ 40x/100 = 10(800 - x)/100
⇒ 40x = 8000 - 10x
⇒ 40x + 10x = 8000
⇒ 50x = 8000
⇒ x = 8000/50
⇒ x = 160

∴ 2025 সালে স্কুলে ছাত্রীর সংখ্যা ছিল 160 জন।

২,২২৫.
The total surface area of a rectangular solid cube of length 5 cm, width 3 cm and height 2 cm is - 
  1. ক
    31 cm
  2. খ
    62 cm
  3. গ
    62 cm3
  4. ঘ
    62 cm2
ব্যাখ্যা
Question: The total surface area of a rectangular solid cube of length 5 cm, width 3 cm and height 2 cm is - 

Solution : 
the formula for the total surface area A is:
A = 2(lw + lh + wh)

The total surface area of a rectangular solid cube of length 5 cm, width 3 cm and height 2 cm is = 2{(5 × 3) + (3 × 2) + (2 × 5)} cm2
= 2(15 + 6 + 10) cm2
= 62 cm2 
২,২২৬.
(42-51) Choose the correct answer.
(42) If P = (x2 - 36)/(x2 - 49) and Q = (x + 6)/(x + 7), then what is the value of P/Q ?
  1. ক
    (x - 6)/(x - 7)
  2. খ
    (x - 6)/(x + 7)
  3. গ
    (x - 6)/(x + 6)
  4. ঘ
    (x + 6)/(x - 7)
ব্যাখ্যা
Question: If P = (x2 - 36)/(x2 - 49) and Q = (x + 6)/(x + 7), then what is the value of P/Q?

Solution:
Here,
P = (x2 - 36)/(x2 - 49)
= (x2 - 62)/(x2 - 72)
= {(x + 6)(x - 6)}/{(x + 7)(x - 7)}

Q = (x + 6)/(x + 7)

২,২২৭.
If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?
  1. ক
    450
  2. খ
    350
  3. গ
    152
  4. ঘ
    652
ব্যাখ্যা
Question: If 8 men can reap 80 hectares in 24 days, how many hectares can 36 men reap in 30 days?

Solution:
৮ জন ২৪ দিনে ফসল কাটে ৮০ হেক্টর
∴ ৮ জন ১ দিনে ফসল কাটে ৮০/২৪ হেক্টর
∴ ১ জন ১ দিনে ফসল কাটে ৮০/(২৪ × ৮) হেক্টর
∴ ৩৬ জন ৩০ দিনে ফসল কাটে (৮০ × ৩৬ × ৩০)/(২৪ × ৮) হেক্টর
= ৪৫০ হেক্টর
২,২২৮.
A school has only 3 classes having 20, 30 and 50 students respectively. The percentages of students passed are 30%, 50% and 60% respectively. Find the percentage of passed students of the entire school.
  1. ক
    ক) 40%
  2. খ
    খ) 51%
  3. গ
    গ) 60%
  4. ঘ
    ঘ) None
ব্যাখ্যা
Question: A school has only 3 classes having 20, 30 and 50 students respectively. The percentages of students passed are 30%, 50% and 60% respectively. Find the percentage of passed students of the entire school.

Solution:
পাশ করা ছাত্রের সংখ্যা = 20 × 30% + 30 × 50% + 50 × 60% = 6 + 15 + 30 = 51
সুতরাং, পাশ করা ছাত্রের সংখ্যার হার = 51/100 × 100 = 51%
২,২২৯.
The angle between the minute hand and the hour hand of a clock when the time is 4:20, is -
  1. ক
    5°
  2. খ
    8°
  3. গ
    10°
  4. ঘ
    15°
ব্যাখ্যা
Question: The angle between the minute hand and the hour hand of a clock when the time is 4:20, is -

Solution:
কোণ = ।11M - 60H।/2
= ।(11 × 20) - (60 × 4)।/2
= ।220 - 240। /2
= 10°
২,২৩০.
The difference between the simple interest received from two different sources on Tk.1500 for 3 year is Tk.13.50. The difference between their rates of interest is
  1. ক
    ক) 0.1%
  2. খ
    খ) 0.2%
  3. গ
    গ) 0.3%
  4. ঘ
    ঘ) 0.4%
ব্যাখ্যা

(1500 x R1 x 3)/100 
=> 4500 (R1-R2) = 1350 
=> (R1-R2)= 1350/4500 = 0.3 %

২,২৩১.
If 2A = 3B and 4B = 6C, then A : C equal to -
  1. ক
    9 : 4
  2. খ
    3 : 2
  3. গ
    4 : 9
  4. ঘ
    2 : 3
ব্যাখ্যা
Question: If 2A = 3B and 4B = 6C, then A : C equal to -

Solution:
A : B = 3 : 2
B : C = 3 : 2

A : C = A/B × B/C
= 3/2 × 3/2
= 9 : 4
২,২৩২.
An aeroplane covers a certain distance at a speed of 250 kmph in 4 hours. To cover the same distance in  hours, it must travel at a speed of: 
  1. ক
    600 kmph
  2. খ
    800 kmph
  3. গ
    900 kmph
  4. ঘ
    755.5 kmph
ব্যাখ্যা

Question: An aeroplane covers a certain distance at a speed of 250 kmph in 4 hours. To cover the same distance in hours, it must travel at a speed of:

Solution:
বিমানটির অতিক্রান্ত  মোট দূরত্ব = গতিবেগ × সময়
= 250 কিমি/ঘন্টা × 4 ঘন্টা
= 1000 কিমি

এখন, একই দূরত্ব ঘন্টায় অতিক্রম করার জন্য প্রয়োজনীয় গতিবেগ নির্ণয় করতে হবে।

ঘন্টা = (1 + 1/4) ঘন্টা = 5/4 ঘন্টা

প্রয়োজনীয় গতিবেগ = মোট দূরত্ব/সময়
= 1000 কিমি/(5/4) ঘন্টা
= (1000 × 4/5) কিমি/ঘন্টা
= 200 × 4 কিমি/ঘন্টা
= 800 কিমি/ঘন্টা

সুতরাং, একই দূরত্ব 5/4 ঘন্টায় অতিক্রম করার জন্য বিমানটিকে 800 কিমি/ঘন্টা গতিবেগে চলতে হবে।

২,২৩৩.
Two numbers have a product of 2028 and a highest common factor (HCF) of 13. How many such pairs of numbers exist?
  1. ক
    1
  2. খ
    2
  3. গ
    3
  4. ঘ
    4
ব্যাখ্যা
Question: Two numbers have a product of 2028 and a highest common factor (HCF) of 13. How many such pairs of numbers exist?

Solution:
Let the two numbers be x and y respectively.
It is given that the product of the two numbers is 2028, therefore, xy = 2028

Also, 13 is their HCF, thus both numbers must be divisible by 13.

So, let x = 13a and y = 13b, 

ATQ,
13a × 13b = 2028
⇒ 169ab = 2028
⇒ ab = 2028
∴ ab = 12

Therefore, the required possible pair of values of x and y which are prime to each other are (1, 12) and (3, 4).
Thus, the required numbers are (12, 156) and (39, 52).
Hence, the number of possible pairs is 2.
২,২৩৪.
A sum of Tk. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is?
  1. ক
    48
  2. খ
    77
  3. গ
    84
  4. ঘ
    98
ব্যাখ্যা
Question: A sum of Tk. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is?

Solution:
Given total sum = Tk. 427
And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.
Or, 3A = 4B = 7C

But given,
A + B + C = 427

Now, expressing A and B in terms of C,
(7C/3) + (7C/4) + C = 427
∴ C = 84
২,২৩৫.
A boat running downstream covers a distance of 36 km in 3 hours while for covering the same distance upstream, it takes 4 hours. What is the speed of the boat in still water?
  1. ক
    ক) 7.5 km/hr.
  2. খ
    খ) 9.5 km/hr.
  3. গ
    গ) 10.5 km/hr.
  4. ঘ
    ঘ) 12.5 km/hr.
ব্যাখ্যা
Rate downstream = (36/3) km/hr. = 12 km/hr.
Rate upstream = (36/4) km/hr. =9 km/hr.

 The speed of the boat in still water = (1/2)(12 + 9) km/hr.
                                                          = (1/2) × 21 km/hr.
                                                           = 10.5 km/hr.
২,২৩৬.
Bus fares were recently increased from Taka 1.70 to Taka 2.00. What was the approximate percentage of increase?
  1. ক
    18%
  2. খ
    15%
  3. গ
    0.15%
  4. ঘ
    0.18%
ব্যাখ্যা
Question: Bus fares were recently increased from Taka 1.70 to Taka 2.00. What was the approximate percentage of increase?

Solution: 
বাস ভাড়া বাড়ে = (2.00 - 1.70) টাকা
= 0.30 টাকা

বাস ভাড়া শতকরা বাড়ে = (0.30/1.70) × 100%
= 17.647 %
≈ 18%
২,২৩৭.
In a 100m race, Javed defeated Naveed by 5 seconds. If the speed of Javed is 18 Kmph, then the speed of Naveed is-
  1. ক
    ক) 15.4 kmph
  2. খ
    খ) 14.4 kmph
  3. গ
    গ) 14.5 kmph
  4. ঘ
    ঘ) 15.4 kmph
  5. ঙ
    ঙ) 13.5 kmph
ব্যাখ্যা

Time taken by Javed =100/{18 × (5/18)} = 20 seconds
Time taken by Naveed = 20 + 5 = 25 seconds
Speed of Naveed = 100/25 × 18/5 = 14.4 km/h

২,২৩৮.
If one root of the equation P2 - 5P - 36 = 0 is same as P2 - 25P + Q = 0, then find the value of Q.
  1. ক
    16 or 9
  2. খ
    144 or - 116
  3. গ
    - 144 or 116
  4. ঘ
    - 16 or - 9
  5. ঙ
    None of these
ব্যাখ্যা
Question: If one root of the equation P2 - 5P - 36 = 0 is same as P2 - 25P + Q = 0, then find the value of Q.

Solution:
1st equation is P2 - 5P - 36 = 0
⇒ (P - 9)(P + 4) = 0
⇒ P = 9 or P = -4

If P = 9 then P2 - 25P + Q = 0
⇒ (9)2 - 25(9) + Q = 0
⇒ Q = 144

If P = - 4 then P2 - 25P + Q = 0
⇒ (- 4)2 - 25 (- 4) + Q = 0
⇒ Q = - 116.

∴ Hence answer is 2nd option.
২,২৩৯.
If Asinθ = 1 and Acosθ = √2, find the value of (3√2/tanθ) + 1 =?
  1. ক
    6
  2. খ
    8
  3. গ
    7
  4. ঘ
    9
ব্যাখ্যা
Question: If Asinθ = 1 and Acosθ = √2, find the value of (3√2/tanθ) + 1 =?

Solution: 
Asinθ = 1
Acosθ = √2

∴ Asinθ/Acosθ = 1/√2
tanθ = 1/√2

(3√2/tanθ) + 1
= 3√2/(1/√2) + 1
= 6 + 1
= 7
২,২৪০.
In a certain population group, 57% of the people have characteristics X and 63% have characteristics Y. If every person in the group has at lest one of the of the two characteristics, then what percent of the people have both X and Y?
  1. ক
    ক) 20%
  2. খ
    খ) 18%
  3. গ
    গ) 12%
  4. ঘ
    ঘ) 6%
ব্যাখ্যা
প্রশ্ন : In a certain population group, 57% of the people have characteristics, X and 63% have characteristics Y. If every person in the group has at lest one of the of the two characteristics, then what percent of the people have both X and Y?
সমাধান: 
 N (X) = 57%
 N (Y)= 63%
 N (X ∪ Y) = 100%
 
অতএব,
    N (X ∪ Y) = N (X) + N (Y) - N (X ∩ Y)
বা, N (X ∩ Y) = N (X) + N (Y) - N (X ∪ Y)
                     = 57% + 63% - 100%
                     = 120% - 100%
                     = 20%
২,২৪১.
If sec(x − 30°) = 2, then tan x = ?
  1. ক
    √3
  2. খ
    1/√2
  3. গ
    1/√3
  4. ঘ
    None of the above
ব্যাখ্যা
sec (x − 30°) = 2
Or, sec (x - 30°) = sec 60°
Or, x - 30° = 60°
Or, x = 90°
∴ tan 90° = not defined
২,২৪২.
24 men can complete a piece of work in 24 days. In how many days can 36 men complete the same piece of work ?
  1. ক
    18 days
  2. খ
    16 days
  3. গ
    14 days
  4. ঘ
    21 days
ব্যাখ্যা
Question: 24 men can complete a piece of work in 24 days. In how many days can 36 men complete the same piece of work ?

Solution: 
24 men can do in 24 days
1 man can do in = (24 × 24) days
36 men can do in = (24 × 24)/36 days
= 16 days
২,২৪৩.
In a business, the ratio of the capitals of Arun and Babul is 2 : 1, that of Babul and Chandan is 4 : 3, and that of Dipu and Chandan is 6 : 5. What is the ratio of the capitals of Arun and Dipu? 
  1. ক
    9 : 18
  2. খ
    22 : 9
  3. গ
    10 : 9
  4. ঘ
    20 : 9
ব্যাখ্যা

Question: In a business, the ratio of the capitals of Arun and Babul is 2 : 1, that of Babul and Chandan is 4 : 3, and that of Dipu and Chandan is 6 : 5. What is the ratio of the capitals of Arun and Dipu?

Solution:
Given,
Arun : Babul = 2 : 1
⇒ Arun/Babul = 2/1

Babul : Chandan = 4 : 3
⇒ Babul/Chandan = 4/3

Dipu : Chandan = 6 : 5
⇒ Chandan/Dipu = 5/6

Now,
Arun/Dipu = (Arun/Babul) × (Babul/Chandan) × (Chandan/D)
= (2/1) × (4/3) × (5/6)
= 20/9

∴ Arun/Dipu = 20 : 9

২,২৪৪.
What is the slope of a line perpendicular to the line whose equation is 3x + 4y = 12?
  1. ক
    4/3
  2. খ
    - 3/4
  3. গ
    5/2
  4. ঘ
    3/5
ব্যাখ্যা

Question: What is the slope of a line perpendicular to the line whose equation is 3x + 4y = 12?

Solution:
প্রদত্ত সরল রেখার সমীকরণ: 3x + 4y = 12
y = mx + c আকারে লিখি, যেখানে m হলো রেখার ঢাল।

4y = - 3x + 12
⇒ y = (- 3/4)x + 3

অতএব, মূল রেখার ঢাল (m) = - 3/4

আমরা জানি, কোনো রেখার উপর লম্ব রেখার ঢাল m1 = - 1/m
= - 1/(- 3/4)
= 4/3

∴ লম্ব রেখার ঢাল = 4/3

২,২৪৫.
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
  1. ক
    35 hours
  2. খ
    38 hours
  3. গ
    42 hours
  4. ঘ
    45 hours
ব্যাখ্যা
Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
∴ 1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
⇒ x = 35 hours
২,২৪৬.
A swimmer swims in a river against the current and takes 30 minutes to swim 2 km. With the current, he takes 20 minutes to swim the same distance. What is his speed in still water?
  1. ক
    3 km/h
  2. খ
    4 km/h
  3. গ
    5 km/h
  4. ঘ
    6 km/h
ব্যাখ্যা
Question: A swimmer swims in a river against the current and takes 30 minutes to swim 2 km. With the current, he takes 20 minutes to swim the same distance. What is his speed in still water?

Solution:
Given that,
distance covered= 2 km 
time consumed = 30 min = 30/60 hr = 1/2 hr
∴ speed of the swimmer against current (upstream) = 2/(1/2) = 4 km/hr

Again,
With the current,
distance covered = 2 km
time consumed= 20 min = 20/60 hr = 1/3 hr
∴ speed of the swimmer with current (downstream)= 2/(1/3) = 6 km/hr

∴ speed in still water = (speed in downstream + speed in upstream)/2
 = (6 + 4)/2
=10/2
= 5
So, the swimmer’s speed in still water is 5 km/h
২,২৪৭.
Subarna express normally reaches its destination at 60 km/h in 8 hours. Find the speed at which it travels to reduce the time by 3 hours?
  1. ক
    96 km/h
  2. খ
    106 km/h
  3. গ
    90 km/h
  4. ঘ
    85 km/h
ব্যাখ্যা
Question: Subarna express normally reaches its destination at 60 km/h in 8 hours. Find the speed at which it travels to reduce the time by 3 hours?

Solution:
Distance to be covered = Speed × Time
= 60 × 8
= 480 km

Time = (8 - 3) hours
= 5 hours

∴ Required Speed = 480/5
= 96 km/h
২,২৪৮.
A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6850, Tk. 7226 and Tk. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?
  1. ক
    ক) 4000 Taka
  2. খ
    খ) 4500 Taka
  3. গ
    গ) 5000 Taka
  4. ঘ
    ঘ) 6000 Taka
ব্যাখ্যা
Question: A grocer has a sale of Tk. 6435, Tk. 6927, Tk. 6850, Tk. 7226 and Tk. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Tk. 6500?

Solution: 
Total sale after 5 months (6435 + 6927 + 6850 + 7226 + 6562)  Taka 
= 34000 Taka

The average sale after 6 months is 6500 Taka 
∴ Total sale after 6 months (6500 × 6) Taka
= 39000 Taka

Sale must he have in the sixth month is (39000 - 34000) Taka 
= 5000 Taka
২,২৪৯.
If logx(1/9) = - 2, then x = ?
  1. ক
    ক) - 1/3
  2. খ
    খ) 1/3
  3. গ
    গ) - 3
  4. ঘ
    ঘ) 3
ব্যাখ্যা

দেওয়া আছে,
logx(1/9) = - 2
বা, 1/9 = x - 2
বা,  1/32  = 1/x2
বা,  1/x = 1/3
বা,  x = 3

২,২৫০.
If 5 ≥ x ≥ - 1 and y ≥ - 1, which of the following cannot be a value of x - y?
  1. ক
    0
  2. খ
    1
  3. গ
    5
  4. ঘ
    6
  5. ঙ
    7
ব্যাখ্যা

Question: If 5 ≥ x ≥ - 1 and y ≥ - 1, which of the following cannot be a value of x - y?

Solution: 
Here, 5 ≥ x ≥ - 1 and y ≥ - 1

Now,
i) If, x = - 1 and y = - 1 then, x - y = - 1 - (- 1) = -1 + 1 = 0 
ii) If, x = 2 and y = 1 then, x - y = 2 - 1 = 1 
iii) If, x = 5 and y = 0 then, x - y = 5 - 0 = 5 
iv) If, x = 5 and y = -1 then, x - y = 5 - (- 1) = 5 + 1 = 6

∴ Any value greater than 6 cannot be a value of x - y.  

২,২৫১.
A cylindrical tank has a radius of 6 meters and a height of 7 meters. If the metal used to make the cylinder costs Tk. 40 per cubic meter, find the total cost of the metal required.
  1. ক
    Tk. 11,680
  2. খ
    Tk. 21,680
  3. গ
    Tk. 31,680
  4. ঘ
    Tk. 41,680
  5. ঙ
    None
ব্যাখ্যা

Question: A cylindrical tank has a radius of 6 meters and a height of 7 meters. If the metal used to make the cylinder costs Tk. 40 per cubic meter, find the total cost of the metal required.

Solution:
Given,
Radius of the cylinder, r = 6 m
Height of the cylinder, h = 7 m
Cost per cubic metre = Tk. 40

The volume of the cylinder:
V = πr2h = (22/7) × (6)2 × 7 = (22/7) × 36 × 7 = 22 × 36 = 792 cubic metres

Total cost = Volume × Cost per cubic metre = 792 × 40 = 31,680

∴ The cost of the cylinder is Tk. 31,680

২,২৫২.
In how many ways the letters of the word 'DIFFERENT' can be arranged?
  1. ক
    720
  2. খ
    5040
  3. গ
    40080
  4. ঘ
    90720
ব্যাখ্যা
Question: In how many ways the letters of the word 'DIFFERENT' can be arranged?

Solution:
Total nnumber of letters in the word 'DIFFERENT' = 9
Repeating letters:
F = 2 times
E = 2 times
∴ Required no. of ways = 9!/(2! × 2!)
= 90720
২,২৫৩.
If 13 = 13w/(1 - w), then (2w)2 = 
  1. ক
    ক) 1/4
  2. খ
    খ) 1/2
  3. গ
    গ) 1
  4. ঘ
    ঘ) 2
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
Question: If 13 = 13w/(1 - w), then (2w) = 

Solution:
Here,
13w/(1 - w) = 13
⇒ w/(1 - w) = 1
⇒ w = 1 - w
∴ 2w = 1

Now, 
(2w)2 = 1 × 2 = 2
২,২৫৪.
2, 5, 9, 19, 37, ?
  1. ক
    ক) 75
  2. খ
    খ) 76
  3. গ
    গ) 78
  4. ঘ
    ঘ) 73
ব্যাখ্যা

Here, 2 × 2 + 1 = 5
5 × 2 - 1 = 9
9 × 2 + 1 = 19
19 × 2 - 1 = 37
37 × 2 + 1 = 75

২,২৫৫.
A, B, C subscribe Tk. 50000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35000. B receives -
  1. ক
    ক) Tk. 11900
  2. খ
    খ) Tk. 14700
  3. গ
    গ) Tk. 10900
  4. ঘ
    ঘ) Tk. 8400
ব্যাখ্যা
Question: A, B, C subscribe Tk. 50000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35000. B receives -

Solution:
ধরি,
C বিনিয়োগ করেছিল x টাকা,
B বিনিয়োগ করেছিল (x + 5000) টাকা
A বিনিয়োগ করেছিল (x + 5000 + 4000) = (x + 9000) টাকা

প্রশ্নমতে,
x + x + 5000 + x + 9000 = 50,000
⇒ 3x + 14000 = 50000
⇒ 3x = 50000 - 14000
⇒ 3x = 36000
∴ x = 12000 টাকা

A, B, C এর বিনিয়োগের অনুপাত
= (12000 + 9000) : (12000 + 5000) : 12000
= 21000 : 17000 : 12000
= 21 : 17 : 12

∴ B এর মুনাফা = 35000 × (17/50)
= 11900 টাকা।
২,২৫৬.
A rectangular block 8 cm by 12 cm by 16 cm is cut up in to an exact number of equal cubes. Find the least possible number of cubes.
  1. ক
    ক) 24
  2. খ
    খ) 26
  3. গ
    গ) 27
  4. ঘ
    ঘ) 28
ব্যাখ্যা
প্রশ্ন :A rectangular block 8 cm by 12 cm by 16 cm is cut up in to an exact number of equal cubes. Find the least possible number of cubes.
সমাধান : 
Sides of the rectangular block = 8 cm, 12 cm, 16 cm

The HCF of the sides of the cuboid is the side of the cube

Volume of the cuboid = Length × breadth × height
Volume of the cube = side3

Let n be the number of cubes
HCF( 8, 12, 16) = 4 cm

side of the square = 4 cm
Volume of the cuboid = n × Volume of the cube
Length × breadth × height = n × side3
8 × 12 × 16 = n ×  4 ×  4 ×  4
n = 2 ×  3 ×  4
n = 24

number of cubes is 24
২,২৫৭.
What is the probability of getting a sum of 6 if two dice are thrown?
  1. ক
    1/9
  2. খ
    5/36
  3. গ
    2/3
  4. ঘ
    None of these
ব্যাখ্যা
Question: What is the probability of getting a sum of 6 if two dice are thrown?

Solution:
In two throws a dice, n(S) = 6 × 6 = 36
Let E is the event of getting a sum of 6.
E = (1, 5), (2, 4), (3, 3), (4, 2), (5, 1)
So, n(E) = 5

∴ P(E) = n(E)/n(S)
= 5/36
২,২৫৮.
A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is- 
  1. ক
    300 m
  2. খ
    400 m
  3. গ
    500 m
  4. ঘ
    600 m
ব্যাখ্যা
Question: A train travelling at 48 kmph completely crosses another train having half its length and travelling in opposite direction at 42 kmph, in 12 seconds. It also passes a railway platform in 45 seconds. The length of the platform is- 

Solution: 
relative speed = 48 + 42 kmph
= 90 kmph
= (90 × 1000)/3600 m/s
= 25 m/s

let, length of train  travelling at 48 kmph is x m

x + x/2 = 25 × 12 = 300
⇒ 3x = 600
∴ x = 200 m

speed = 48 kmph = (48 × 1000)/3600 = 40/3 m/s

ATQ, 
(40/3) × 45 = 200 + length of platform
length of platform = 600 - 200 
= 400 m
২,২৫৯.
When A, B and C are deployed for a task , A and B together do 70% of the work and B and C together do 50% of the work. Who is most efficient?
  1. ক
    ক) A
  2. খ
    খ) B
  3. গ
    গ) C
  4. ঘ
    ঘ) A & B equally efficient
  5. ঙ
    ঙ) Can't be determined
ব্যাখ্যা

A + B = 70%
B + C = 50%
[∵ (A + B) + (B + C) − (A + B + C) = B]
=> B = 20% ; A = 50% and C = 30%
Hence A is most efficient.

২,২৬০.
A passenger travels from Dhaka to Comilla at a speed of 30 kmph and returns at a speed of 60 kmph. What is the average speed?
  1. ক
    ক) 45km/h
  2. খ
    খ) 30km/h
  3. গ
    গ) 40km/h
  4. ঘ
    ঘ) 60km/h
ব্যাখ্যা
Question: A passenger travels from Dhaka to Comilla at a speed of 30 kmph and returns at a speed of 60 kmph. What is the average speed?

Solution: 
Let the distance between Dhaka to Comilla is X km

time for travelling Dhaka to Comilla = X/30 hour
time for travelling Comilla to Dhaka = X/60 hour

average speed = (total distance)/ (total time)
= 2X/{(X/30) + (X/60)}
= (2 × 30 × 60)/ (60 + 30)
= 40km/h
২,২৬১.
A college has 8 basketball players. A 4 member's team and a captain will be selected out of these 8 players. How many different selections can be made?
  1. ক
    280
  2. খ
    520
  3. গ
    480
  4. ঘ
    120
ব্যাখ্যা

Question: A college has 8 basketball players. A 4 member's team and a captain will be selected out of these 8 players. How many different selections can be made?

Solution: 
We can select the 4 member team out of the 8 in =  8C4 ways
= 8!/4!(8 - 4)! = 8!/(4! × 4!)
= 70 ways

The captain can be selected from amongst the remaining 4 players in 4 ways.

∴ The total ways the selection of 4 players and a captain can be made = 70 × 4 ways
= 280 ways

So the total number of different selections that can be made is 280.

২,২৬২.
rsinθ = 1, rcosθ = √3 then the value of (√3tanθ - 1) = ?
  1. ক
    0
  2. খ
    - 1
  3. গ
    2
  4. ঘ
    - 2
ব্যাখ্যা
Question: rsinθ = 1, rcosθ = √3 then the value of (√3tanθ - 1) = ?

Solution:
rsinθ = 1
rcosθ = √3

Now,
rsinθ/rcosθ = 1/√3
⇒ tanθ = 1/√3
⇒ √3tanθ = 1
⇒ √3tanθ - 1 = 1 - 1
∴ √3tanθ - 1 = 0
২,২৬৩.
If loga324 = 4, what is the value of the base?
  1. ক
    4
  2. খ
    2√3
  3. গ
    1/2√3
  4. ঘ
    3√2
ব্যাখ্যা
Question: If loga324 = 4, what is the value of the base?

Solution:
loga324 = 4
⇒ a4 = 324
⇒ a4 = 4 × 81
⇒ a4 =22 × 34
⇒ a4 = ((√2)2)2 × 34
⇒ a4 = (√2)4 × 34
⇒ a4 = (3√2)4
∴ a = 3√2
২,২৬৪.
A number is 2/5 times of another number. If the sum of two numbers is 98, what is the difference of the two numbers?
  1. ক
    32
  2. খ
    42
  3. গ
    48
  4. ঘ
    98
ব্যাখ্যা
Question: A number is 2/5 times of another number. If the sum of two numbers is 98, what is the difference of the two numbers?

Solution:
Let, a number is x
another number is 2x/5

ATQ,
x + 2x/5 = 98
⇒ (5x + 2x)/5 = 98
⇒ 7x/5 = 98
⇒ 7x = 98 × 5
⇒ 7x = 490
∴ x = 70

So, a number is 70
another number is 2x/5 = (2 × 70)/5 = 28
∴ Difference = 70 - 28
= 42
২,২৬৫.
The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.
  1. ক
    38
  2. খ
    36
  3. গ
    42
  4. ঘ
    44
ব্যাখ্যা
Question: The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. Find the excluded number.

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

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

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

Hence, the excluded number is 36.
২,২৬৬.
A mixture contains sugar solution and colored water in the ratio of 4 : 3. If 10 liters of colored water is added to the mixture, the ratio becomes 4: 5. Find the initial quantity of sugar solution in the given mixture.
  1. ক
    15 liters
  2. খ
    20 liters
  3. গ
    25 liters
  4. ঘ
    30 liters
  5. ঙ
    10 liters
ব্যাখ্যা
Question: A mixture contains sugar solution and colored water in the ratio of 4 : 3. If 10 liters of colored water is added to the mixture, the ratio becomes 4: 5. Find the initial quantity of sugar solution in the given mixture.

Solution:
The initial ratio is 4 : 3.
Let ‘k’ be the common ratio.
Initial quantity of sugar solution = 4k liters
Initial quantity of colored water = 3k liters

Final quantity of sugar solution = 4k liters
Final quantity of colored water = 3k + 10 liters

Final ratio = 4k : (3k + 10) = 4 : 5
⇒ 20k = 12k + 40
⇒ 8k = 40
∴ k = 5

Therefore, the initial quantity of sugar solution in the given mixture = 4k = 4 × 5 = 20 liters
২,২৬৭.
In country A, the first 1,000 dollar of any inheritance are untaxed. After the first 1,000 dollar, inheritances are taxed at a rate of 65%. How large must an inheritance be, to the nearest dollar, in order to amount to 2,500 dollar after the inheritance tax?
  1. ক
    ক) 7,143
  2. খ
    খ) 5,286
  3. গ
    গ) 4,475
  4. ঘ
    ঘ) 3,475
ব্যাখ্যা

প্রথম 1000 ডলার এর জন্য ট্যাক্স দিতে হয় না।
বাকি টাকা = (2500 - 1000) = 1500 টাকা

এখানে, (100 - 65)% = 35%

প্রশ্নমতে, 35% = 1500
∴ 1% = 1500/35
∴ 100% = 1500×100/35
= 4285.71 ≅ 4286

∴ নির্ণেয় টাকার পরিমাণ = (4286 +1000) = 5286 টাকা

২,২৬৮.
Find the amount if Tk. 20000 is invested at 10% compound interest p.a. for 3 years.
  1. ক
    Tk. 26600
  2. খ
    Tk. 26680
  3. গ
    Tk. 26620
  4. ঘ
    Tk. 26660
ব্যাখ্যা
Question: Find the amount if Tk. 20000 is invested at 10% compound interest p.a. for 3 years.

Solution: 
Using the formula:
C = P [1 + R/100]n
C = 20000 [1 + (10/100)]3
= 20000 × 1.1 × 1.1× 1.1
= 26620
২,২৬৯.
  1. ক
    676
  2. খ
    636
  3. গ
    742
  4. ঘ
    759
  5. ঙ
    None of the above
ব্যাখ্যা
Question: 


Solution: 
২,২৭০.
What will come at the place of the question mark?
1, 16, 81, 256, 625, ?
  1. ক
    1024
  2. খ
    1296
  3. গ
    1580
  4. ঘ
    1480
ব্যাখ্যা

Question: What will come at the place of the question mark?
1, 16, 81, 256, 625, ?

Solution:
14=1
24= 16
34= 81
44 = 256
54=625
64 = 1296

২,২৭১.
Select an appropriate term that completes the series Lp F, Nq G, PrH, R s I, _____
  1. ক
    ক) m P m
  2. খ
    খ) T t J
  3. গ
    গ) t Tj
  4. ঘ
    ঘ) TTJ
ব্যাখ্যা
Select an appropriate term that completes the series Lp F, Nq G, PrH, R s I, _____

Solution: 
প্রথম অক্ষর এর ক্ষেত্রে,
L এর পর M নেই,
N এর পর O নেই,
P এর পরে Q নেই,
তাহলে অবশ্যই R এর পরে S না হয়ে T হবে,

দ্বিতীয় অক্ষরের জন্য 
p, q, r, s, তারপর অবশ্যই t হবে।

তৃতীয় অক্ষরের জন্য
F, G, H, I, এর পর অবশ্যই J হবে।

তাহলে খালি ঘরে অবশ্যই T t J
২,২৭২.
A number is doubled and 9 is added. If the resultant is trebled, it becomes 75. What is that number?
  1. ক
    ক) 6
  2. খ
    খ) 8
  3. গ
    গ) 3.5
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

ধরি, সংখ্যাটি x
প্রশ্নমতে, (2x + 9) × 3 = 75
⇒ 2x + 9 = 25
⇒ 2x = 16
⇒ x = 8

২,২৭৩.
48.95 - 32.006 = ?
  1. ক
    16.089
  2. খ
    16.35
  3. গ
    16.89
  4. ঘ
    16.944
ব্যাখ্যা
Question:  48.95 - 32.006 = ?

Solution:
48.95 - 32.006 = 16.944
২,২৭৪.
Ken left a job paying $ 75,000 per year to accept a sales job paying $ 45,000 per year plus 15 percent commission. If each of his sales is for $ 750, what is the least number of sales he must make per year if he is not to lose money because of the change?
  1. ক
    40
  2. খ
    200
  3. গ
    266
  4. ঘ
    267
ব্যাখ্যা
Question: Ken left a job paying $ 75,000 per year to accept a sales job paying $ 45,000 per year plus 15 percent commission. If each of his sales is for $ 750, what is the least number of sales he must make per year if he is not to lose money because of the change?

Solution:
In order not to lose money because of the change Ken's total commission must be at least $ 75,000 - $ 45,000 = $ 30,000,
so total sales must be at least $ 30,000/0.15 = $200,000.

Which means that he must make at least $ 200,000/750 = 800/3 = 266.6 sales ≈ 267 sales.
২,২৭৫.
The present ages of P and Q are in the ratio 2 : 7. After 8 years, the ratio of their ages will be 3 : 8. What is the difference in their present ages?
  1. ক
    24 years
  2. খ
    30 years
  3. গ
    36 years
  4. ঘ
    40 years
ব্যাখ্যা

Question: The present ages of P and Q are in the ratio 2 : 7. After 8 years, the ratio of their ages will be 3 : 8. What is the difference in their present ages?

Solution:
Let the present ages be,
P = 2x and Q = 7x

Ages after 8 years,
P = 2x + 8, Q = 7x + 8

According to the problem, the ratio becomes 3:8
(2x + 8)/(7x + 8) = 3/8
⇒ 8(2x + 8) = 3(7x + 8)
⇒ 16x + 64 = 21x + 24
⇒ 64 - 24 = 21x - 16x
⇒ 40 = 5x
⇒ x = 8

P = 2 × 8 = 16 years
Q = 7 × 8 = 56 years

∴ Difference = 56 - 16 = 40 years

২,২৭৬.
A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?
  1. ক
    Tk. 250 
  2. খ
    Tk. 200 
  3. গ
    Tk. 175
  4. ঘ
    Tk. 225
ব্যাখ্যা
Question: A machine is sold at a profit of 10%. Had it been sold for Tk. 40 less, there would have been a loss of 10%. What was the cost price?

Solution: 
Let, the cost price of the machine is x taka 

Selling price = 1.1x taka 

ATQ, 
1.1x - 40 = 0.9x 
⇒ 1.1x - 0.9x = 40 
⇒ 0.2x = 40
⇒ x = 40/.2
= Tk. 200 
২,২৭৭.
A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse? 
  1. ক
    12%
  2. খ
    20%
  3. গ
    16%
  4. ঘ
    21.5%
ব্যাখ্যা

Question: A bag costs 20% more than a purse. A wallet costs 30% less than the bag. If the price of the purse is 200 Tk, then by what percentage is the wallet cheaper than the purse?

Solution:
Given,
the price of the purse = 200 tk

∴ Price of the bag = 200 + (200 × 20%)
= 240 tk

Price of the wallet = 240 − (240 × 30%)
= 240 − 72
= 168 Tk

Difference is = (200 - 168) = 32 tk

∴ Percentage = (32 × 100)/200 = 16%

২,২৭৮.
  1. ক
    1
  2. খ
    4
  3. গ
    3
  4. ঘ
    1/2
ব্যাখ্যা
Question:

Solution:
২,২৭৯.
A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?
  1. ক
    ক) Tk. 16
  2. খ
    খ) Tk. 20
  3. গ
    গ) Tk. 18
  4. ঘ
    ঘ) Tk. 22
ব্যাখ্যা
Question: A man sells two chairs at Tk. 120 each and by doing so he gains 25% on one chair and loses 25% on the other. His loss on the whole in Tk. is = ?

Solution:
Cost price of first chair = (100/125) × 120
= Tk. 96

Cost price of second chair = (100/75) × 120
= Tk. 160

∴ Loss = (160 + 96) - 240
= 256 - 240
= Tk. 16
২,২৮০.
To produce an annual income of Tk. 1200 from a 12% stock at 90, the amount of stock required is-
  1. ক
    Tk. 10800
  2. খ
    Tk. 10000
  3. গ
    Tk. 14400
  4. ঘ
    Tk. 16000
ব্যাখ্যা
Question: To produce an annual income of Tk. 1200 from a 12% stock at 90, the amount of stock required is-

Solution:
12% stock at 90 mean,
Stock face value 100 and market value 90

12 Taka can be produced from Tk. 100
1 Taka can be produced from Tk. 100/12
1200 Taka can be produced from Tk. (100 × 1200)/12 = Tk. 10000
২,২৮১.
Frank scored 26 points in a basketball game. All of his points came from either a two-point basket or three-point basket. If frank scored at least one three-point basket what is the maximum number of two-point baskets that Frank could have scored?
  1. ক
    ক) 11
  2. খ
    খ) 10
  3. গ
    গ) 9
  4. ঘ
    ঘ) 8
ব্যাখ্যা

If he scored a three-point basket, then remaining points are = 26 - 3 = 23, which is not divisible by 2
∴ As, there is no one-point basket, by scoring two three-point basket, the remaining points are: 26 - 3×2 = 20
∴ He scored maximum number of = 20/2 = 10 two-point baskets

২,২৮২.
Find out the wrong number in the series:
3, 8, 15, 24, 34, 48, 63
  1. ক
    24
  2. খ
    34
  3. গ
    48
  4. ঘ
    63
ব্যাখ্যা
Question: Find out the wrong number in the series:
3, 8, 15, 24, 34, 48, 63

Solution:
8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11 [34* - 24 = 10]
48 - 35 = 13
63 - 48 = 15

The differences between consecutive terms are respectively 5, 7, 9, 11, 13 and 15.
So, 34 is the wrong number.
২,২৮৩.
A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Tk. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
  1. ক
    Tk.375
  2. খ
    Tk. 400
  3. গ
    Tk. 600
  4. ঘ
    Tk. 800
  5. ঙ
    Tk. 1000
ব্যাখ্যা

C's 1 day's work = 1/3 - (1/6 + 1/8)
= 1/3 - 7/24
= 1/24
C's share (for 3 days) = (3 × (1/24) × 3200)
= 400

২,২৮৪.
If xtan60° + cos45° = sec45°, then the value of x2 + 1 is?
  1. ক
    ক) 1/6
  2. খ
    খ) 5/6
  3. গ
    গ) 6/7
  4. ঘ
    ঘ) 7/6
ব্যাখ্যা
Question: If xtan60° + cos45° = sec45°, then the value of x2 + 1 is?

Solution:
xtan60° + cos45° = sec45°
⇒ x . √3 + (1/√2) = √2
⇒ √6x + 1 = 2
⇒ √6x = 1
⇒ x = 1/√6
⇒ x2 = (1/√6)2
⇒ x2 = 1/6
⇒ x2 + 1 = (1/6) + 1
∴ x2 + 1 = 7/6
২,২৮৫.
A sum becomes Tk 13,310 in 3 years at 10% per annum compound interest. Find the principal amount.
  1. ক
    9513 tk
  2. খ
    9831 tk
  3. গ
    10000 tk
  4. ঘ
    11234 tk
ব্যাখ্যা
Question: A sum becomes Tk 13,310 in 3 years at 10% per annum compound interest. Find the principal amount.

Solution:
Let the sum be Tk p
∴ 13310 = p{1 + (10/100)3
⇒ 13310 = p{1 + (1/10)3
⇒ 13310 = p(11/10)3
⇒ p = (13310 × 10 × 10 × 10) / (11 × 11 × 11)
⇒ p = 10000 tk
২,২৮৬.
Determine the largest number among four multiples of 5 in a row that equal 170 together.
  1. ক
    50
  2. খ
    56
  3. গ
    64
  4. ঘ
    48
ব্যাখ্যা

Question: Determine the largest number among four multiples of 5 in a row that equal 170 together.

Solution:
Let the four consecutive multiples of 5 be x, (x + 5), (x + 10) and (x + 15)

According to the question,
x + (x + 5) + (x + 10) + (x + 15) = 170
⇒ 4x + 30 = 170
⇒ 4x = 170 - 30
⇒ 4x = 140
⇒ x = 140/4
⇒ x = 35

Therefore, the largest number is = x + 15 = 35 + 15 = 50

২,২৮৭.
In a code PREMIER is written as XOILSIO, ANTAGONAISE is written as MQNMZBQMSWI, then how can PROMISE be written in the same code?
  1. ক
    XOBLSWI
  2. খ
    XOLBSWI
  3. গ
    XBOLSWI
  4. ঘ
    XOBLIWS
ব্যাখ্যা
Question: In a code PREMIER is written as XOILSIO, ANTAGONAISE is written as MQNMZBQMSWI, then how can PROMISE be written in the same code?

Solution:
PREMIER is written as XOILSIO
P ⇒ X
R ⇒ O
E ⇒ I
M ⇒ L
I ⇒ S
E ⇒ I
R ⇒ O

ANTAGONAISE is written as MQNMZBQMSWI
A ⇒ M
N ⇒ Q
T ⇒ N
A ⇒ M
G ⇒ Z
O ⇒ B
N ⇒ Q
A ⇒ M
I ⇒ S
S ⇒ W
E ⇒ I

PROMISE
P ⇒ X
R ⇒ O
O ⇒ B
M ⇒ L
I ⇒ S
S ⇒ W
E ⇒ I
∴ PROMISE is written as XOBLSWI.
২,২৮৮.
If 22x - 1 = 1/(8x - 3), then the vale of x is-
  1. ক
    ক) - 2
  2. খ
    খ) 2
  3. গ
    গ) 0
  4. ঘ
    ঘ) 5
ব্যাখ্যা
22x - 1 = 1/(8x - 3)
22x - 1 = 1/{(23)x - 3}
22x - 1 = 1/23x - 9
22x - 1 = 2 - (3x - 9)
22x - 1 =2 - 3x + 9
2x - 1 = - 3x + 9 
2x + 3x = 9 + 1
5x = 10
x = 10/5
x = 2
২,২৮৯.
The 2nd angle of a right triangle is 30 degrees. Then how many degrees is the 3rd angle?
  1. ক
    ক) 50
  2. খ
    খ) 60
  3. গ
    গ) 70
  4. ঘ
    ঘ) 80
ব্যাখ্যা
আমরা জানি 
সমকোণী ত্রিভুজের একটি কোণ 90° 
২য় কোণ 30°  হলে 
৩য় কোণ =180° - (90° + 30°) = 180° - 120° = 60°
২,২৯০.
A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?
  1. ক
    Tk. 24700
  2. খ
    Tk. 18500
  3. গ
    Tk. 30000
  4. ঘ
    Tk. 22500
ব্যাখ্যা

Question: A worker union contract specifies a 6% salary increase plus a Tk. 450 bonus for each worker. For a worker, this is equivalent to an 8% salary increase. What was this worker's salary before the new contract?

Solution:
ধরি, কর্মীর পূর্বের বেতন = x টাকা।

6% বৃদ্ধিতে বেতন = x + x এর 6%
= x + (6x/100) = 106x/100

বোনাস হিসেবে 450 টাকা যোগ করলে মোট বেতন = (106x/100) + 450

8% বৃদ্ধিতে বেতন = x + x এর 8%
= x + (8x/100) = (108x/100)

প্রশ্নমতে,
(106x/100) + 450 = (108x/100)
⇒ 450 = (108x/100) - (106x/100)
⇒ 450 = (2x/100)
⇒ x = (450 × 100)/2
∴ x = 22500

অর্থাৎ, কর্মীর পূর্ববর্তী বেতন ছিল 22500 টাকা।

২,২৯১.
Two groups, A and B wrote an exam. The probability of A's pass is 2/7 and the probability of B's pass is 2/5. What is the probability that only one of them is passed out?
  1. ক
    ক) 5/6
  2. খ
    খ) 1/3
  3. গ
    গ) 18/35
  4. ঘ
    ঘ) 16/35
ব্যাখ্যা

Let, A be the event of the group A pass
Let, B be the event of the group B pass

Then,
A'= Event of the group A's fail and B'= event of the group B's fail.
Therefore, p(A) = 2/7 and p(B) = 2/5,
P(A') = 1 - P(A) = 1- 2/7 = 5/7 and P(B') = 1- P(B) = 1- 2/5 = 3/5

Required probability = P[( A And B') Or (B And A')]
= P[( A And B') Or (B And A')]
= P[( A And B') + (B And A')]
= P[( A And B')] + P[(B And A')]
= p(A) x P(B') + P(A') x P(B)
= (2/7 x 3/5) + (2/5 x 5/7)
= (6/35 + 10/35)
= 16/35

২,২৯২.
What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is - 13 and the 6th term is - 4?
  1. ক
    - 25
  2. খ
    30
  3. গ
    - 36
  4. ঘ
    25
  5. ঙ
    - 30
ব্যাখ্যা

Question: What is the sum of the first 12 terms of an arithmetic progression if the 3rd term is - 13 and the 6th term is - 4?

Solution:
In an arithmetic progression. We know
nth term = a + (n - 1)d
where a = first term,
d = common difference

Given that,
3rd term = a + 2d = - 13  … (1)
6th term = a + 5d = - 4   … (2)

Subtract equation (1) from equation (2) then we get,
⇒ (a + 5d) - (a + 2d) = - 4 - (- 13)
⇒ 3d = 9
⇒ d = 9/3
∴ d = 3

Equation (1) we get,
⇒ a + 2(3) = - 13
⇒ a + 6 = - 13
⇒ a = - 13 - 6
∴ a = - 19

Sum of first n terms of an arithmetic progression.
Sₙ = (n/2) × [2a + (n - 1)d]
S12 = (12/2) × [2(- 19) + (12 - 1)3]
= 6 × [- 38 + 11 × 3]
= 6 × [- 38 + 33]
= 6 × (- 5)
= - 30

২,২৯৩.
A reduction of 15% in the price of apples would enable a purchaser to get 2 kg more apples for Tk.240. The new price (per kg) of apple
  1. ক
    Tk.12
  2. খ
    Tk.15
  3. গ
    Tk.18
  4. ঘ
    Tk. 20
ব্যাখ্যা
Question: A reduction of 15% in the price of apples would enable a purchaser to get 2 kg more apples for Tk.240. The new price (per kg) of apples is-

Solution:
Let, the original rate = x per kg
New rate = 85% of x = 85x/100
= 17x/20
Original quantity for Tk. 240 = 240/x

∴ New quantity = 240 × (20/17x)
= 4800/17x

ATQ,
(4800/17x) - (240/x) = 2
⇒ (4800 - 4080)/17x = 2
⇒ (720/17x) = 2
⇒ x = 720/(2 × 17)  

∴ Original rate per kg = Tk. 720/34
So, Reduced rate = Tk. 17x/20
= Tk. (17/20) × (720/34)
= Tk.18
২,২৯৪.
An airplane flies along the four sides of a square at the speeds of 200, 400, 600 and 800 kmh. Find the average speed of the plane around the field.
  1. ক
    ক) 432 km/hr
  2. খ
    খ) 375 km/hr
  3. গ
    গ) 384 km/h
  4. ঘ
    ঘ) 221 km/hr
ব্যাখ্যা

Speed of aeroplane is 200, 400, 600 and 800 km/h respectively
Let the side of side be LCM of (200, 400, 600 and 800) = 2400
Time taken by aeroplane to travel the side at the speed of 200 km/hr 
⇒ 2400/200 = 12 hours
Time taken by aeroplane to travel the side at the speed of 400 km/hr 
⇒ 2400/400 = 6 hours
Time taken by aeroplane to travel the side at the speed of 600 km/hr 
⇒ 2400/600 = 4 hours
Time taken by aeroplane to travel the side at the speed of 800 km/hr 
⇒ 2400/800 = 3 hours

Average speed = (Total Distance travelled)/(Total time taken)
∴ Average speed = (4×2400)/25 = 384 km/hr

২,২৯৫.
If 2x - 1 + 2x + 1 = 320, then x is equal to-
  1. ক
    5
  2. খ
    6
  3. গ
    7
  4. ঘ
    8
  5. ঙ
    4
ব্যাখ্যা
Question: If 2x - 1 + 2x + 1 = 320, then x is equal to-

Solution:

∴ x - 6 = 1
⇒ x = 7
২,২৯৬.
In how many ways, a committee consisting of 5 men and 6 women can be formed from 8 men and 10 women?
  1. ক
    1760
  2. খ
    5040
  3. গ
    11760
  4. ঘ
    86400
ব্যাখ্যা

Required number of ways = (8C5 × 10C6)
= (8C3 × 10C4)
= (8 × 7 × 6)/3! × (10 × 9 × 8 × 7)/4!
= (8 × 7 × 6)/6 ×(10 × 9 × 8 × 7)/(4 × 3 × 2 × 1)
= 11760.

২,২৯৭.
45 toymakers can prepare 30 toys per day. Raj wants 360 toys. How many toymakers should he employ to get the job done in 12 days?
  1. ক
    39
  2. খ
    45
  3. গ
    42
  4. ঘ
    35
ব্যাখ্যা
Question: 45 toymakers can prepare 30 toys per day. Raj wants 360 toys. How many toymakers should he employ to get the job done in 12 days?

Solution:
Let, the required number of toymakers x
45 toymakers make 30 toys per day
So, 1 toymaker makes = 30/45 = 2/3 toys per day
Each toymaker in 12 days makes = (2/3) × 12 = 8 toys
So, x toymakers will make = 8x toys

ATQ,
8x = 360
⇒ x = 360 × (1/8)
∴ x = 45
২,২৯৮.
A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is-
  1. ক
    3 : 1
  2. খ
    2 : 1
  3. গ
    3 : 2
  4. ঘ
    3 : 4
ব্যাখ্যা
Question: A man takes twice as long to row a distance against the stream as to row the same distance in favour of the stream. The ratio of the speed of the boat (in still water) and the stream is-

Solution:
Let,
man's rate upstream be = a kmph
Then, his rate downstream = 2a kmph

Now,
(speed in still water) : (Speed of stream)
= {(2a + a)/2 : (2a - a)/2}
= (3a/2) : (a/2)
= 3 : 1
২,২৯৯.
The difference between two positive numbers is 4 and the sum of their squares is 346. Then the sum of the numbers is-
  1. ক
    ক) 34
  2. খ
    খ) 24
  3. গ
    গ) 26
  4. ঘ
    ঘ) 28
ব্যাখ্যা
Question: The difference between two positive numbers is 4 and the sum of their squares is 346. Then the sum of the numbers is-

Solution: 
Let the numbers be x and (x + 4)
Then,
x2 + (x + 4)2 = 346
⇒ x2 + x2 + 8x + 16 = 346
⇒ 2x2 + 8x - 330 = 0
⇒ x2 + 4x - 165 = 0
⇒ x2 + 15x - 11x - 165 = 0
⇒ x(x + 15) - 11(x + 15) = 0
⇒ (x + 15)(x - 11)=0
⇒ x = 11

So, the numbers are 11 and (11 + 4) = 15

∴ Required sum = (11 + 15) = 26
২,৩০০.
If q < 0 and 4p > q, which of the following could be equal to p/q?
  1. ক
    2
  2. খ
    1/2
  3. গ
    3
  4. ঘ
    0
ব্যাখ্যা
Question: If q < 0 and 4p > q, which of the following could be equal to p/q? 

Solution: 
4p > q
p > q/4
p/q < 1/4 [q < 0; q ["A negative number"]

The only number smaller than 1/4 in the options is 0.