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Bank Math

মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
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Bank Math

PrepBank · পাতা ৪৪ / ১৬১ · ৪,৩০১–৪,৪০০ / ১৬,১২৪

৪,৩০১.
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
  1. ক
    15 years
  2. খ
    20 years
  3. গ
    25 years
  4. ঘ
    18 years
  5. ঙ
    22 years
ব্যাখ্যা
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

Solution:
Let the present ages of the son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 6x = 84
⇒ x = 14
∴ Son's age after 6 years = (x + 6) = 20 years.
৪,৩০২.
The original cost of a machine is Tk. 10,000. If the annual depreciation is 10%, after how many years will it be valued at Tk. 6,561?
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 5
  4. ঘ
    ঘ) 6
  5. ঙ
    ঙ) 7
ব্যাখ্যা

Cost of machine 10000/-
Depreciation 10% each year.
1st year = 10000 - 1000 = 9000/-
2nd year = 9000 - 900 = 8100/-
3rs year = 8100 - 810 = 7290/-
4th year = 7290 - 729 = 6561/-
Depreciation will be deducted from the amount left after subtracting previous depreciation value.

৪,৩০৩.
A man spent 1/2 of his money and then lost 1/4 of the remainder. He was left with Tk. 3,600. How much did he start with?
  1. ক
    ক) 7200
  2. খ
    খ) 8800
  3. গ
    গ) 9600
  4. ঘ
    ঘ) 10400
ব্যাখ্যা

Let,
He has TK. x
ATQ, x - x/2 - x/2×1/4 = 3600
or, x/2 - x/8 = 3600
or, (4x - x)/8 = 3600
∴ x = (3600×8)/3 = 9600

৪,৩০৪.
An open circular tank is dug 20 m deep. The earth is taken out and has been spread all round it, to form a circular embankment. The width of an Embankment is 2 m,& diameter of circular tank is 18m. Find the height of circular embankment.
  1. ক
    36.5 m
  2. খ
    38.5 m
  3. গ
    40.5 m
  4. ঘ
    43.5 m
ব্যাখ্যা
Question: An open circular tank is dug 20 m deep. The earth is taken out and has been spread all round it, to form a circular embankment. The width of an Embankment is 2 m,& diameter of circular tank is 18m. Find the height of circular embankment.

Solution:
Volume of the Open Circular Tank = πr2h
= π × [(18)/2]2 × 20
= π × 9 × 9 × 20 m3

Area of the earth dug out = π(9 + 2)2 - π(9)2
= π[(11 + 9)(11 - 9)]
= π(20)(2)
= 40πm2
∴ Height of circular embankment = (= π × 9 × 9 × 20 )/( 40π )
= 40.5 m
৪,৩০৫.
If A : B : C = 1/2 : 1/3 : 1/5, then what is the ratio of A/B : B/C : C/A ?
  1. ক
    ক) 11 : 41 : 91
  2. খ
    খ) 19 : 18 : 13
  3. গ
    গ) 37 : 45 : 15
  4. ঘ
    ঘ) 45 : 50 : 12
ব্যাখ্যা
A : B : C = 1/2 : 1/3 : 1/5

A : B : C = 1/2 : 1/3 : 1/5
⇒ A : B : C = 30/2 : 30/3 : 30/5
⇒ A : B : C = 15 : 10 : 6

Let A = 15, B = 10 and C = 6, then

∴ A/B : B/C : C/A = 15/10 : 10/6 : 6/15 = (3/2) : (5/3) : (2/5) = 90/2 : 150/3 : 60/5 = 45 : 50 : 12

৪,৩০৬.
The length, breadth, and height of a rectangular box are in the ratio 3 : 2 : 1. If its total surface area is 352 cm2, what is its volume in cm3?
  1. ক
    324
  2. খ
    384
  3. গ
    432
  4. ঘ
    480
ব্যাখ্যা

Question: The length, breadth, and height of a rectangular box are in the ratio 3 : 2 : 1. If its total surface area is 352 cm2, what is its volume in cm3?

Solution:
দেওয়া আছে,
আয়তাকার বাক্সের দৈর্ঘ্য, প্রস্থ ও উচ্চতার অনুপাত 3 : 2 : 1।
সমগ্রতলের ক্ষেত্রফল 352 বর্গ সে. মি.

মনে করি,
আয়তাকার বাক্সের দৈর্ঘ্য, a = 3x সে. মি.
আয়তাকার বাক্সের প্রস্থ, b = 2x সে. মি.
আয়তাকার বাক্সের উচ্চতা, c = x সে. মি.

আমরা জানি,
আয়তাকার বাক্সের সমগ্রতলের ক্ষেত্রফল = 2(ab + bc + ca) বর্গ একক
= 2(3x × 2x + 2x × x + x × 3x) বর্গ একক
= 2(6x2+ 2x2+ 3x2) বর্গ একক
= 2 × 11x2 
= 22x2 বর্গ একক

প্রশ্নমতে,
22x2= 352
⇒x2= 352/22
⇒x2= 16
⇒x = √16
∴ x = 4

আয়তাকার বাক্সের আয়তন = abc ঘন একক
= 3x × 2x × x ঘন একক
= 6x3 ঘন একক
= 6 × 43 ঘন সে. মি.
= 384 ঘন সে. মি.

∴ আয়তাকার বাক্সের আয়তন 384 ঘন সে. মি. ।

৪,৩০৭.
A 240 metre long train crosses a platform twice its length in 40 seconds. What is the speed of the train in km/hr?  
  1. ক
    ক) 64.8km/hr
  2. খ
    খ) 62.8km/hr
  3. গ
    গ) 60.8km/hr
  4. ঘ
    ঘ) 57.8km/hr
ব্যাখ্যা
Length of train = 240 m
Length of platform = (2 × 240) m = 480m

∴Speed of train (240 + 480)/40 m/sec
                          = 720/40 m/sec
                          = 18 × (18/5) km/hr
                           = 64.8km/hr
৪,৩০৮.
A is thrice efficient as B and C is twice as efficient as B. What is the ratio of number of days taken by A,B and C, when they work individually?
  1. ক
    ক) 2:6:3
  2. খ
    খ) 2:3:6
  3. গ
    গ) 1:2:3
  4. ঘ
    ঘ) 3:1:2
  5. ঙ
    ঙ) None of these
ব্যাখ্যা

A : B : C
Ratio of efficiency - 3 : 1 : 2
Ratio of No. of days - 1/3 : 1/1 : 1/2
or 2 : 6 : 3

৪,৩০৯.
The average daily wage of 10 workers is Tk. 400. if the lowest wage is Tk. 300, then what is the possible maximum wage?
  1. ক
    ক) 800
  2. খ
    খ) 1000
  3. গ
    গ) 1200
  4. ঘ
    ঘ) 1300
ব্যাখ্যা
Question: The average daily wage of 10 workers is Tk. 400. if the lowest wage is Tk. 300, then what is the possible maximum wage?

Solution:
10 জন লোকের মোট মজুরি = (10 ×400) টাকা = 4000 টাকা
300 টাকা করে 9 জনের মজুরি = (300 ×9) = 2700 টাকা
সম্ভাব্য সর্বোচ্চ মজুরি =  ( 4000 - 2700) টাকা = 1300 টাকা।
৪,৩১০.
A cone’s slant height is 21 cm, and the curved surface area is 264 cm2. Determine the diameter of the cone’s base.
  1. ক
    4 cm
  2. খ
    6 cm
  3. গ
    8 cm
  4. ঘ
    9 cm
ব্যাখ্যা

Question: A cone’s slant height is 21 cm, and the curved surface area is 264 cm2. Determine the diameter of the cone’s base.

Solution:
দেওয়া আছে,
তির্যক উচ্চতা, l = 21 সে.মি
বক্রপৃষ্ঠের ক্ষেত্রফল = 264 cm2

মনে করি,
কোণকটির ভূমির ব্যাসার্ধ = r 

∴ কোণকটির বক্রপৃষ্ঠের ক্ষেত্রফল = πrl

প্রশ্নমতে,
πrl = 264
⇒ r × (22/7) × 21 = 264
⇒ 66r = 264
⇒ r = 264/66
⇒ r = 4

∴ কোণকটির ভূমির ব্যাস = 2r = 2 × 4 = 8 সে.মি

৪,৩১১.
A rectangular park is 500 meters long and 300 meters wide. There is a 10-meter wide road around the park. What is the area of the park excluding the road?
  1. ক
    137,600 square meters
  2. খ
    126,300 square meters
  3. গ
    134,400 square meters
  4. ঘ
    141,500 square meters
  5. ঙ
    128,200 square meters
ব্যাখ্যা
Question: A rectangular park is 500 meters long and 300 meters wide. There is a 10-meter wide road around the park. What is the area of the park excluding the road?

Solution:
Total park area = (500 × 300) = 150,000 square meters
Park length after removing road = 500 - (2 × 10) = 480 meters
Park width after removing road = 300 - (2 × 10) = 280 meters
Park area excluding road = (480 × 280) square meters
= 134,400 square meters
৪,৩১২.
The hour hand of an analog clock moves (1/60)th of a degree every minute. Then how many degrees will the hour hand move in one hour?
  1. ক
    ক) 1 degree
  2. খ
    খ) 2 degree
  3. গ
    গ) 3 degree
  4. ঘ
    ঘ) 4 degree
  5. ঙ
    ঙ) 5 degree
ব্যাখ্যা
Question: The hour hand of an analog clock moves (1/60)th of a degree every minute. Then how many degrees will the hour hand move in one hour?

Solution: 
We know that,
1 hour = 60 minutes

The hour hand moves in 1 min = 1°/60
∴ The hour hand moves in 60 min = (1 × 60)°/60
= 1°
৪,৩১৩.
What is the average of the sum of the first 20 natural numbers?
  1. ক
    ক) 10
  2. খ
    খ) 10.5
  3. গ
    গ) 20
  4. ঘ
    ঘ) 21
ব্যাখ্যা
Question: What is the average of the sum of the first 20 natural numbers?

Solution:
The average is = {20(20 + 1)} / (2 × 20)
= 420/40
= 10.5
৪,৩১৪.
Out of 60 books in a school library, 18 belong to the science fiction genre. If a student chooses one book randomly, find the probability it isn’t a science fiction book.
  1. ক
    7/10
  2. খ
    3/13
  3. গ
    10/13
  4. ঘ
    3/10
ব্যাখ্যা

Question: Out of 60 books in a school library, 18 belong to the science fiction genre. If a student chooses one book randomly, find the probability it isn’t a science fiction book.

Solution:
Probability of picking a book that is a science fiction book = 18/60
= 3/10

Probability of picking a book that is not a science fiction book = (1 - 3/10)
= (10 - 3)/10
= 7/10

৪,৩১৫.
  1. ক
    15
  2. খ
    23/15
  3. গ
    6/17
  4. ঘ
    17/6
ব্যাখ্যা
Question:


Solution:
 
৪,৩১৬.
How many interior reflex angles are there in a pentagon?
  1. ক
    1
  2. খ
    2
  3. গ
    5
  4. ঘ
    None of these
ব্যাখ্যা
There is no interior reflex angle in a polygon( বহুভুজে কোন অন্তঃস্থ প্রবৃদ্ধ কোণ নেই)।
So, there is no interior reflex angle in a pentagon( তাই পঞ্চভুজে কোন অন্তঃস্থ প্রবৃদ্ধ কোণ নেই).
৪,৩১৭.
Anisha and Sara started a business by investing Tk. 85000 and Tk. 15000 each. What be will the ratio of profit earned after 2 years between Anisha and Sara respectively?
  1. ক
    11 : 5
  2. খ
    12 : 7
  3. গ
    15 : 2
  4. ঘ
    17 : 3
ব্যাখ্যা
Question: Anisha and Sara started a business by investing Tk. 85000 and Tk. 15000 each. What be will the ratio of profit earned after 2 years between Anisha and Sara respectively?

Solution: 
Given,
Anisha's investment = Tk. 85,000
Sara's investment = Tk. 15,000
Time = 2 years for both

The ratio of profit earned after 2 years between Anisha and Sara respectively = (85000 × 2) : (15000 × 2)
= 170000 : 30000
= 17 : 3
৪,৩১৮.
A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2 cm, then the area of the triangle is-
  1. ক
    36√3 cm2
  2. খ
    49√2 cm2
  3. গ
    60√2 cm2
  4. ঘ
    64√3 cm2
ব্যাখ্যা
Question: A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 12√2 cm, then the area of the triangle is-

Solution:
Let, the side of the square be a cm
Then, its diagonal √2a
√2a = 12√2
⇒ a = 12

∴ Perimeter of the square = 4a
= 4 × 12
= 48 cm

and also perimeter of the equilateral triangle = 48 cm

∴ Each side of the triangle = 48/3
= 16 cm

Area of the triangle = (√3/4) × (16)2 cm2
= (√3/4) × 256 cm2
= 64√3 cm2
৪,৩১৯.
The difference of two numbers is 1365. On dividing the larger number by smaller number, we got 6 as quotient and 15 as a reminder. What is the smaller number?
  1. ক
    240
  2. খ
    270
  3. গ
    295
  4. ঘ
    360
  5. ঙ
    400
ব্যাখ্যা

Let the smaller number be x
Then larger number = (x + 1365)
∴ x + 1365 = 6x + 15
⇒ 5x = 1350
⇒ x = 270
∴ Smaller number = 270

৪,৩২০.
What is the lowest value of sinθ?
  1. ক
    1
  2. খ
    0.5
  3. গ
    - 1
  4. ঘ
    1/3
ব্যাখ্যা
Question: What is the lowest value of sinθ?

Solution: 
θ কোণ নির্দেশ করলে
sinθ এর বৃহত্তম মান = 1
sinθ এর ক্ষুদ্রতম মান = -1
৪,৩২১.
A person travels 20 km at 10 km/h and then 30 km at 15 km/h. What is the average speed of the entire journey?
  1. ক
    12.5 km/h
  2. খ
    13.5 km/h
  3. গ
    14 km/h
  4. ঘ
    15 km/h
ব্যাখ্যা
Question: A person travels 20 km at 10 km/h and then 30 km at 15 km/h. What is the average speed of the entire journey?

Solution:
The total distance traveled is: 20 km + 30 km = 50 km
For the first part of the journey (20 km at 10 km/h), the time taken is: 20/10 = 2 hours
For the second part of the journey (30 km at 15 km/h), the time taken is: 30/15 = 2 hours
Total Time = 2hours + 2hours = 4 hours

∴ Average Speed = Total Distance/Total Time = 50/4 km/h = 12.5 km/h
৪,৩২২.
A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water.
  1. ক
    3 km/hr 
  2. খ
    11 km/hr 
  3. গ
    15 km/hr 
  4. ঘ
    17 km/hr 
ব্যাখ্যা
Question: A boatman can row a boat upstream at 14 km/hr and downstream at 20 km/hr. Find the speed of the boat in still water.

Solution:
We are given that speed downstream, D = 20 km/hr
and speed upstream, U = 14 km/hr 
Therefore, Speed of boat in still water = 0.5 × (D + U) km / hr = 0.5 × (14 + 20) = 17 km/hr 

 
Another method:
Speed of the stream = 0.5 × (D - U) = 0.5 × 6 = 3 km/hr 
Speed of the boat in still water = Speed of the stream + Speed Upstream = 3 + 14 = 17 km/hr
৪,৩২৩.
The length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high, is-
  1. ক
    30 m
  2. খ
    15 m
  3. গ
    15√2 m
  4. ঘ
    30√2 m
  5. ঙ
    60 m
ব্যাখ্যা
Question: The length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high, is-

Solution:
Length of room = 30 m
Breadth of room = 24 m
Height of room = 18 m

Length of the longest rod = Diagonal of the room = √(302 + 242 + 182)
= √(900 + 576 + 324)
= √(1800)
= √(900 × 2)
= 30√2
৪,৩২৪.
What is the ratio of 8 inches to 6 feet?
  1. ক
    ক) 9 : 1
  2. খ
    খ) 1 : 9
  3. গ
    গ) 2 : 9
  4. ঘ
    ঘ) 9 : 2
ব্যাখ্যা
Question: What is the ratio of 8 inches to 6 feet?

Solution: 
 1 feet = 12 inches
So, 6 feet = 6 × 12 = 72 inches

Now, 
8 inches : 6 feet = 8 : 72 = 1 : 9
৪,৩২৫.
The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower is:
  1. ক
    25√3 m
  2. খ
    50√3 m
  3. গ
    75√3 m
  4. ঘ
    190 m
ব্যাখ্যা
Question: The angle of depression of a car, standing on the ground, from the top of a 75 m tower, is 30°. The distance of the car from the base of the tower is:

Solution:
AB is a tower and AB = 75 m
From A, the angle of depression of a car C
on the ground is 30°


Let distance BC = x

Now, in ΔACB,
tanθ = AB/BC
⇒ tan30° = 75/x
⇒ 1/√3 = 75/x
⇒ x = 75√3
∴ BC = 75√3 m
৪,৩২৬.
The average of runs of a cricket player of 10 innings was 35. How many runs must he make in his next innings so as to increase his average of runs by 5?
  1. ক
    ক) 90
  2. খ
    খ) 135
  3. গ
    গ) 100
  4. ঘ
    ঘ) 145
ব্যাখ্যা
প্রশ্ন: The average of runs of a cricket player of 10 innings was 35. How many runs must he make in his next innings so as to increase his average of runs by 5?

Solution: 
Total runs =35 × 10 = 350
Now increase in average is 5 runs
so, 
New average =35 + 5 = 40 runs
Total runs = 40 × 11= 440
Runs made in the 11th inning =440 - 950 = 90
৪,৩২৭.
Find the average of all the numbers between 7 and 46 which are divisible by 5 -
  1. ক
    25.5
  2. খ
    32.7
  3. গ
    19.2
  4. ঘ
    27.5
ব্যাখ্যা
Question: Find the average of all the numbers between 7 and 46 which are divisible by 5 -

Solution:
First, let's list all the numbers between 7 and 46 that are divisible by 5.
So, the numbers divisible by 5 in this range are,
10, 15, 20, 25, 30, 35, 40, 45 

∴ The sum of these numbers is,
10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 = 220

∴ Average = 220/​8 = 27.5
Thus, the average of all numbers between 7 and 46 that are divisible by 5 is 27.5.
৪,৩২৮.
P scored 30% marks and failed by 15 marks. Q scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?
  1. ক
    27%
  2. খ
    33%
  3. গ
    35%
  4. ঘ
    40%
ব্যাখ্যা

Question: P scored 30% marks and failed by 15 marks. Q scored 45% marks and obtained 30 marks more than the pass marks. What is the pass percentage?

Solution:
Let the total marks be x.

Given,
P scored 30% marks and failed by 15 marks:
0.30x + 15 = Pass marks
Q scored 45% marks and obtained 30 marks more than the pass marks:
0.45x - 30 = Pass marks

Now,
0.30x + 15 = 0.45x - 30
⇒ 0.45x - 0.30x = 15 + 30
⇒ 0.15x = 45
⇒ x = 45/0.15
∴ x = 300

Pass marks = 0.30 × 300 + 15
= 90 + 15 = 105

∴ Pass percentage = (105/300) × 100% = 35%

৪,৩২৯.
A committee of 3 members is to be formed by selecting out of 5 men and 4 women. In how many different ways the committee can be formed if it should have 1 man and 2 women?
  1. ক
    30
  2. খ
    40
  3. গ
    54
  4. ঘ
    60
ব্যাখ্যা
Question: A committee of 3 members is to be formed by selecting out of 5 men and 4 women. In how many different ways the committee can be formed if it should have 1 man and 2 women?

Solution:

Here,
1 man can be selected from 5 men in
= 5C1
= 5/1
= 5 ways

2 women can be selected from 4 women in
= 4C2
= (4 × 3)/(2 × 1)
= 12/2
= 6 ways

∴ The total number of ways the committee can be formed
= 5 × 6 ways
= 30 ways
৪,৩৩০.
What is the slope of the line perpendicular to the line by y = -5x + 9?
  1. ক
    ক) 5
  2. খ
    খ) -5
  3. গ
    গ) 1/5
  4. ঘ
    ঘ) -1/5
ব্যাখ্যা

y = -5x + 9
⇒ y + 5x = 9 .....(i)
সুতরাং (i) নং রেখাটির লম্বরেখার সমীকরণ 5y - x = k
⇒ y = 1/5x + k
∴ লম্ব রেখাটির ঢাল = 1/5

৪,৩৩১.
The pair of co-prime numbers is
  1. ক
    9, 4
  2. খ
    3, 18
  3. গ
    18, 92
  4. ঘ
    7, 98
ব্যাখ্যা
If hcf of two or more numbers is 1, then two or more numbers are co-prime numbers.
The hcf of 9 and 4 is 1; 
The hcf of 3 and 18 is 3
The hcf of 18 and 92 is 2
The hcf of 7 and 98 is 7
৪,৩৩২.
In a division sum, the remainder is 0. A student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient?
  1. ক
    ক) 0
  2. খ
    খ) 12
  3. গ
    গ) 13
  4. ঘ
    ঘ) 20
ব্যাখ্যা

Number = (12 x 35)
Correct Quotient = 420 /21 = 20
Answer : 20

৪,৩৩৩.
A solution has a ratio of water to acid as 4 : 1. If 5 liters of water is added, the ratio becomes 5 : 1. What was the original quantity of the solution?
  1. ক
    30 liters
  2. খ
    25 liters
  3. গ
    24 liters
  4. ঘ
    20 liters
ব্যাখ্যা
Question: A solution has a ratio of water to acid as 4 : 1. If 5 liters of water is added, the ratio becomes 5 : 1. What was the original quantity of the solution?

Solution:
Let the original quantity of water and acid be 4x liters and x liters, respectively
The total original quantity of the solution is:
4x + x = 5x

When 5 liters of water is added, the new quantity of water becomes 4x + 5 liters, while the quantity of acid remains x liters. The new ratio of water to acid is given as 5 :1, so:
(4x + 5)/x ​= 5/1
⇒ 4x + 5 = 5x
⇒ 5 = 5x - 4x
⇒ x = 5

The original quantity of the solution is:
5x = 5 × 5 = 25 liters
৪,৩৩৪.
In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election?
  1. ক
    70000
  2. খ
    60000
  3. গ
    77000
  4. ঘ
    68000
ব্যাখ্যা
Question: In an election, 30% of the voters voted for candidate A whereas 60% of the remaining voted for candidate B. The remaining voters did not vote. If the difference between those who voted for candidate A and those who did not vote was 1200, how many individuals were eligible for casting vote in that election?

Solution:
Let, the number of persons eligible to vote be = x

Then,
votes who voted for A = 30% of x
Votes who voted for B = 60% of (70% of x)
= {(60/100) × (70/100) × 100} % of x
= 42% of x

Now,
Voters who did not vote = [100 - (30 + 42)]% of x
= 28% of x

∴ 30% of x - 28% of x = 1200
⇒ 2% of x = 1200
⇒ x = (1200 × 100)/2
⇒ x = 60000
৪,৩৩৫.
In how many ways can the letters of the word 'CANVAS' be arranged?
  1. ক
    ক) 180
  2. খ
    খ) 120
  3. গ
    গ) 360
  4. ঘ
    ঘ) 240
ব্যাখ্যা
Question: In how many ways can the letters of the word 'CANVAS' be arranged?

Solution: 
The word 'CANVAS' contains 6 letters, namely 1C, 2A, 1N, 1V and 1S


Required number of ways =6!/2! = 360
৪,৩৩৬.
If - 2x + 5 < 19, then the value of x:
  1. ক
    x > - 7
  2. খ
    x < 7
  3. গ
    x < - 5
  4. ঘ
    x > 9
ব্যাখ্যা
Question: If - 2x + 5 < 19, then the value of x:

Solution: 
Here,
- 2x + 5 < 19
⇒ - 2x + 5 - 5 < 19 - 5
⇒ - 2x < 14
⇒ 2x > - 14
⇒ x > - 14/2
∴ x > - 7
৪,৩৩৭.
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
  1. ক
    30 km/hr
  2. খ
    40 km/hr
  3. গ
    50 km/hr
  4. ঘ
    60 km/hr
ব্যাখ্যা
Question: A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Solution:
Given distance=360 km.
Let the speed of the train be x km/hr.
Speed when increased by 5 km/hr = (x + 5) km/hr

(360/x) - {360/(x + 5)} = 1
⇒ [360x + 1800 - 360x]/x(x + 5) =1
⇒ 1800/(x2 + 5x) = 1
⇒ x2 + 5x = 1800
⇒ x2 + 5x - 1800 = 0
⇒ x2 + 45x - 40x - 1800 = 0
⇒ x(x + 45) - 40(x + 45) = 0
⇒ (x- 40)(x + 45) = 0
∴ x = 40, - 45

The speed of the train is 40 km/hr.
৪,৩৩৮.
A tank is 12 m long, 8 m wide and 5 m deep. The cost of plastering its walls and bottom at 75 paisa per sq. m is-
  1. ক
    222 Tk
  2. খ
    348 Tk
  3. গ
    480 Tk
  4. ঘ
    592 Tk
ব্যাখ্যা

Question: A tank is 12 m long, 8 m wide and 5 m deep. The cost of plastering its walls and bottom at 75 paisa per sq. m is-

Solution:
Let, l = 12 m, b = 8 m and, h = 5 m

∴ Area to be plastered = [2(l + b) × h] + (l × b) 
= [2(12 + 8) × 5] + (12 × 8) sq. m
= (200 + 96) sq. m
= 296 sq. m

∴ Cost of plastering = 296 × (75/100) Tk
= 296 × (3/4) Tk
= (74 × 3) Tk
= 222 Tk

৪,৩৩৯.
15% of A's income is equal to 25% of B's income. What is the ratio of the income of B to A?
  1. ক
    ক) 5 : 3
  2. খ
    খ) 3 : 2
  3. গ
    গ) 3 : 5
  4. ঘ
    ঘ) 2 : 3
ব্যাখ্যা
Question: 15% of A's income is equal to 25% of B's income. What is the ratio of the income of B to A?

Solution:
15% of A = 25% of B
⇒ 15A/100 = 25B/100
⇒ 15A = 25B
⇒  B/A = 15/25
⇒  B/A = 3/5
∴ B : A = 3 : 5
৪,৩৪০.
If A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, what is A \ B?
  1. ক
    {2, 4}
  2. খ
    {1, 3}
  3. গ
    {6, 8}
  4. ঘ
    {1, 2, 3, 4}
  5. ঙ
    None of these
ব্যাখ্যা
Question: If A = {2, 4, 6, 8} and B = {1, 2, 3, 4}, what is A \ B?

Solution:
A \ B = {2, 4, 6, 8}\{1, 2, 3, 4}
= {6, 8}
৪,৩৪১.
The total cost of flooring a room at Tk. 8.50 per square meter is Tk. 510. If the length of the room is 8m, what is its breadth?
  1. ক
    7.5 m
  2. খ
    8.5 m
  3. গ
    10.5 m
  4. ঘ
    12.5 m
ব্যাখ্যা
Question: The total cost of flooring a room at Tk. 8.50 per square meter is Tk. 510. If the length of the room is 8m, what is its breadth?

Solution:
ঘরের ক্ষেত্রফল = 510/8.50
= 60 বর্গমিটার

প্রশ্নমতে
8 × প্রস্থ = 60
বা, প্রস্থ = 60/8
∴ প্রস্থ =7.5

আয়তাকার ক্ষেত্রের প্রস্থ =7.5 মিটার
৪,৩৪২.
A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
  1. ক
    6 : 10 : 5
  2. খ
    3 : 5 : 2
  3. গ
    5 : 3 : 2
  4. ঘ
    7 : 8 : 5
  5. ঙ
    None of the above
ব্যাখ্যা
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after six months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?

Solution:
Let the initial investments of A and B be 3a and 5a.

A : B : C = (3a × 12) : (5a × 12) : (5a × 6)
= 36 : 60 : 30
= 6 : 10 : 5
৪,৩৪৩.
The difference between a number and its two-fifths is 510. What is the ten percent of that number?
  1. ক
    65
  2. খ
    75
  3. গ
    85
  4. ঘ
    95
ব্যাখ্যা
Question: The difference between a number and its two-fifths is 510. What is the ten percent of that number?

Solution:
Let, the number be x.

ATQ,
x - (2x/5) = 510
⇒ (5x - 2x)/5 = 510
⇒ 3x/5 = 510
⇒ 3x = 510 × 5
⇒ x = 2550/3
∴ x = 850

∴ সংখ্যাটির 10% = 850 × 10/100 = 85 
৪,৩৪৪.
If (5 - 2x) ≤ 13, then which one is correct?
  1. ক
    x ≥ - 2
  2. খ
    x ≤ - 4
  3. গ
     x ≥ - 4
  4. ঘ
    x ≤ - 2
ব্যাখ্যা

Question: If (5 - 2x) ≤ 13, then which one is correct?

Solution: 

Given, 
⇒ 5 - 2x ≤ 13
⇒ 5 - 2x - 5 ≤ 13 - 5
⇒ - 2x ≤ 8
∴ x ≥ - 4

৪,৩৪৫.
In a mixture of 80 liters of juice and water, the ratio of juice to water is 5 : 3. How much water should be added to make the ratio of juice to water 1 : 1?
  1. ক
    25 liters
  2. খ
    20 liters
  3. গ
    15 liters
  4. ঘ
    30 liters
ব্যাখ্যা
Question: In a mixture of 80 liters of juice and water, the ratio of juice to water is 5 : 3. How much water should be added to make the ratio of juice to water 1 : 1?

Solution:
The ratio 5 : 3 means there are 5 parts juice and 3 parts water, making a total of 5 + 3 = 8 parts.

Juice = (5/8) × 80 = 50 liters
Water = (3/8) × 80 = 30 liters

Let, x liters of water be added
Then new amount of water = 30 + x liters

ATQ,
⇒ 50/(30 + x) = 1/1
⇒ 30 + x = 50
⇒ x = 50 - 30
∴ x = 20

∴ 20 liters of water should be added to make the ratio 1 : 1.
৪,৩৪৬.
Two towns P & Q are 275 km apart. A motorcycle rider starts from P towards Q at 8 a.m. at the speed of 25 km/hr. Another rider starts from Q towards P at 9 a.m. at the speed of 20 km/hr. Find at what time they will cross each other?
  1. ক
    2.45 p.m.
  2. খ
    2.30 p.m.
  3. গ
    1.35 p.m.
  4. ঘ
    1.15 p.m.
ব্যাখ্যা

Assume, distance traveled by P in x hrs = 25 x km -----(1)
distance traveled by Q in (x-1) hrs = 20 (x-1) km -----(2)

Adding (1) & (2),
25 x + 20 (x -1) = 275
x = 6.5 hrs
(x -1) = (6.5 -1) = 5.5 hrs

Time at which they cross each other = 9 a.m. + 5.5hrs = 2.30 p.m.
The two motorcycle riders cross each other at 2.30 p.m.

৪,৩৪৭.
The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?
  1. ক
    ক) 12000
  2. খ
    খ) 12500
  3. গ
    গ) 13000
  4. ঘ
    ঘ) 13500
ব্যাখ্যা
Question: The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

Solution: 
Given that,
The population of a village 2 years ago = 24000
Rate of growth = 25% p.a.
Time period = 2 years

Present population = P{(1 - (r/100)}n
= 24000 × {1 - (25/100)}2
= 24000 × {1 - (1/4)}2
= 24000 × (3/4)2
= 24000 × (9/16)
= 13500
৪,৩৪৮.
Find the number of the divisors of 360
  1. ক
    22
  2. খ
    24
  3. গ
    26
  4. ঘ
    30
ব্যাখ্যা
Question:  Find the number of the divisors of 360

Solution: 
360
= 32 × 23 × 5

the number of the divisors of 360 is = (2 + 1) × (3 + 1) × (1 + 1)
= 3 × 4 × 2
= 24
৪,৩৪৯.
If x2 - 3x + 1 = 0, and x > 1, then what is the value of x - 1/x? 
  1. ক
    √7
  2. খ
    √6
  3. গ
    √5
  4. ঘ
    √11
ব্যাখ্যা

Question: If x2 - 3x + 1 = 0, and x > 1, then what is the value of x - 1/x?

Solution:
Given, x2 - 3x + 1 = 0
⇒ (x2/x) - (3x/x) + (1/x) = 0 [উভয়পক্ষকে x দ্বারা ভাগ করে]
⇒ x - 3 + 1/x = 0
⇒ x + 1/x = 3

এখন, (x - 1/x)2 = (x + 1/x)2 - 4 . x . 1/x
⇒ (x - 1/x)2 = (3)2 - 4
⇒ (x - 1/x)2 = 9 - 4
⇒ (x - 1/x)2 = 5
∴ x - 1/x = ±√5

যেহেতু x > 1 দেওয়া আছে, তাই x - 1/x > 0
সুতরাং, x - 1/x = √5

৪,৩৫০.
If the mean of numbers 28, x, 42, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?
  1. ক
    ক) 58
  2. খ
    খ) 390
  3. গ
    গ) 78
  4. ঘ
    ঘ) 310
ব্যাখ্যা
Question: If the mean of numbers 28, x, 42, 78 and 104 is 62, what is the mean of 48, 62, 98, 124 and x?

Solution: 
এখানে,
(28 + x + 42 + 78 + 104)/5 = 62
252 + x = 62 × 5
252 + x = 310
x = 310 - 252 
x = 58

48, 62, 98, 124 এবং 58 এর গড় = (48 + 62 + 98 + 124 + 58)/5
                                                  = 390/5
                                                  = 78
৪,৩৫১.
In how many ways a team of 11 members can be formed from a group of 15 students if a students who is the owner of the ball is always considered a member of the team?
  1. ক
    ক) 14
  2. খ
    খ) 201
  3. গ
    গ) 210
  4. ঘ
    ঘ) 1001
ব্যাখ্যা

When the owner of the ball to be included always, we have to select 10 players out of 14.

The required no. of ways
14C10 = 14!/(10!4!) 
= 14.13.12.11 / 4.3.2.1
= 7.13.11
= 1001

৪,৩৫২.
Six identical machines can produce 540 articles in 12 hours. How many articles would 8 such machines produce in 15 hours?
  1. ক
    720
  2. খ
    800
  3. গ
    900
  4. ঘ
    1080
ব্যাখ্যা

Question: Six identical machines can produce 540 articles in 12 hours. How many articles would 8 such machines produce in 15 hours?

Solution: 
Total articles produced by 6 machines in 12 hours = 540.
Articles produced by 1 machine in 12 hours = 540/6
Articles produced by 1 machine in 1 hour = 540/(6×12) = 7.5 articles

So, Articles produced by 8 machines in 15 hours = 7.5 × 8 × 15 
= 900 articles

৪,৩৫৩.
If 1/2 is a root of the quadratic equation x2 - mx - 3/4 = 0, then value of m is:
  1. ক
    ক) 3
  2. খ
    খ) -2
  3. গ
    গ) -1
  4. ঘ
    ঘ) -3
ব্যাখ্যা
Given,
x = 1/2 as the root of equation x2 - mx - 3/4 = 0.
(1/2)2 – m(1/2) – 3/4 = 0
=> 1/4 - m/2 - 3/4 = 0
=>  -2/4 = m/2
=> 4m = -4
=> m = -1
৪,৩৫৪.
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
  1. ক
    120960
  2. খ
    4989600
  3. গ
    10080
  4. ঘ
    1663200
  5. ঙ
    None of these
ব্যাখ্যা
Question: In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

Solution:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.

Number of ways of arranging these letters = 8!/(2! × 2!) = 10080.

Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters = 4!/2! = 12

∴ Required number of words = (10080 × 12) = 120960
৪,৩৫৫.
A man has Tk. 1050 in the denominations of five-taka notes, ten-taka notes and twenty-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has?
  1. ক
    60
  2. খ
    75
  3. গ
    90
  4. ঘ
    120
ব্যাখ্যা

Question: A man has Tk. 1050 in the denominations of five-taka notes, ten-taka notes and twenty-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has?

Solution:
ধরি, 5 টাকা, 10 টাকা ও 20 টাকার নোটের সংখ্যা প্রত্যেকটি = x

∴ মোট টাকা = 5x + 10x + 20x
= 35x

প্রশ্নমতে,
35x = 1050
∴ x = 1050/35
= 30

অতএব,
5 টাকার নোট = 30
10 টাকার নোট = 30
20 টাকার নোট = 30

∴ মোট নোটের সংখ্যা = 30 + 30 + 30
= 90

৪,৩৫৬.
log2√6 + log2√(2/3) = ?
  1. ক
    0
  2. খ
    1
  3. গ
    2
  4. ঘ
    3
ব্যাখ্যা
Question: log2√6 + log2√(2/3) = ?

Solution:
log2√6 + log2(√2/3)
= log2[√{6 · (2/3)}]
= log2√(2 · 2)
= log2√(22)
= log22
= 1
৪,৩৫৭.
The price of a mobile set is Tk 8,000 and that of a tab is 50% more than the price of a mobile set. If a total of 18 mobiles and tabs were sold for a total of Tk 188,000, how many tabs were sold?
  1. ক
    9
  2. খ
    11
  3. গ
    13
  4. ঘ
    14
  5. ঙ
    None
ব্যাখ্যা

Question: The price of a mobile set is Tk 8,000 and that of a tab is 50% more than the price of a mobile set. If a total of 18 mobiles and tabs were sold for a total of Tk 188,000, how many tabs were sold?

Solution:
Given that,
Price of mobile = Tk. 8,000
Price of tab = 50% more than mobile
= 8,000 + (50/100) × 8,000
= 8,000 + 4000 = Tk. 12,000
Total items sold = 18 (mobiles + tabs)
Total sales = Tk 188,000

Now, Let, Number of mobiles = m,Number of tabs = t 
Then we get,
m + t = 18
∴ m = 18 - t .......(1)

And, 
8000m + 12000t = 188,000
⇒ 2m + 3t = 47   ; [Dividing by 4,000]
⇒ 2(18 - t) + 3t = 47   ; [From (1)]
⇒ 36 - 2t + 3t = 47
⇒ t = 47 - 36
∴ t = 11

∴ The number of tabs sold is 11.

৪,৩৫৮.
The largest 3 digit number exactly divisible by 8 is:
  1. ক
    ক) 999
  2. খ
    খ) 990
  3. গ
    গ) 992
  4. ঘ
    ঘ) 984
ব্যাখ্যা
Question: The largest 3 digit number exactly divisible by 8 is:

Solution: 
The largest 3 digit number is 999

So, the number is (999 - 7) = 992
৪,৩৫৯.
What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?
  1. ক
    10%
  2. খ
    15%
  3. গ
    20%
  4. ঘ
    25%
ব্যাখ্যা
Question: What percentage of numbers from 1 to 70 have 1 or 9 in the unit's digit?

Solution: 
একক এর ঘরে ১ আছে এমন সংখ্যা =  ৭ টি 
একক এর ঘরে ৯ আছে এমন সংখ্যা =  ৭ টি 

মোট = ১৪ টি 

শতকরা পরিমাণ = (১৪/৭০) × ১০০% 
= ২০% 
৪,৩৬০.
Which of the following fractions lies between 2/3 and 3/5 ?
  1. ক
    2/25
  2. খ
    1/3
  3. গ
    1/15
  4. ঘ
    31/50
ব্যাখ্যা
2/3=0.666
3/5=0.6
2/5=0.4
1/3=0.333
1/15=0.066
31/50=0.62
Clearly, 0.62 lies between 0.6 and 0.666
So, 31/50 lies between 2/3 and 3/5.
৪,৩৬১.
A coin is tossed twice. What is the probability of getting head on first toss and tail on second toss?
  1. ক
    ক) 1/2
  2. খ
    খ) 1/3
  3. গ
    গ) 1/4
  4. ঘ
    ঘ) 1
ব্যাখ্যা

টসে প্রথমবারে হেড আসার সম্ভাবনা 1/2
এবং পরেরবারে টেল আসার সম্ভাবনা 1/2
সুতরাং, প্রথম টসে হেড এবং পরের টসে টেল আসার সম্ভাবনা = 1/2 × 1/2 = 1/4

৪,৩৬২.
A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days since 9 people were absent throughout. How many people were supposed to be working originally?
  1. ক
    28
  2. খ
    32
  3. গ
    36
  4. ঘ
    38
ব্যাখ্যা
Question: A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days since 9 people were absent throughout. How many people were supposed to be working originally?

Solution:
Let,
the total number of people were working originally = x
When 9 people were absent,
Total present workers were = x - 9

x workers can complete it = 24 days.
∴ 1 workers can complete it = 24x days.
∴ (x - 9) workers can complete it = 24x/(x - 9) days.

ATQ,
24x/(x - 9) = 32
⇒ 3x/(x - 9) = 4
⇒ 4x - 36 = 3x
∴ x = 36

The total number of people were working originally 36.
৪,৩৬৩.
A pole of 66 metre long breaks into two parts without complete separation and makes an angle 30° with the ground. Find the length of the broken part of the pole.
  1. ক
    22 m
  2. খ
    30 m
  3. গ
    36 m
  4. ঘ
    44 m
ব্যাখ্যা
Question: A pole of 66 metre long breaks into two parts without complete separation and makes an angle 30° with the ground. Find the length of the broken part of the pole.

Solution: 


sin30 = x/(66 - x)
⇒ 1/2 = x/(66 - x) 
⇒ 66 - x = 2x 
⇒ 3x = 66
⇒ x = 66/3 = 22

the length of the broken part of the pole = 66 - 22 = 44 m
৪,৩৬৪.
In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is -
  1. ক
    27 meters
  2. খ
    28 meters
  3. গ
    31 meters
  4. ঘ
    29 meters
ব্যাখ্যা
Question: In a race of 200 meters, B can give a start of 10 meters to A, and C can give a start of 20 meters to B. The starts that C can give to A, in the same race is -

Solution: 
According to the question,
When B runs 200 m meters, A runs 190 meters;
Hence, when B runs 180 meters,
A runs = (190×180)/200
= 171 meters

When C runs 200m, B runs 180 meters.
Hence,
C will give a start to A by = 200 - 171
= 29 meters
৪,৩৬৫.
If 36 men can do a piece of work in 25 hours, in how many hours will15 men do it?
  1. ক
    40
  2. খ
    50
  3. গ
    60
  4. ঘ
    70
  5. ঙ
    None of the above
ব্যাখ্যা

Let the required no of hours be x. Then
Less men , More hours (Indirect Proportion)
Therefore, 15:36 :: 25:x
=> (15 × x) = (36 × 25)
=> x = 60
Hence, 15 men can do it in 60 hours.

৪,৩৬৬.
The price of a flower is 25% more than the price of a book. The price of a flower-vase is 75% more than the price of the book. How much is the price of the flower-vase more than the price of the flower?
  1. ক
    ক) 20%
  2. খ
    খ) 25%
  3. গ
    গ) 30%
  4. ঘ
    ঘ) 40%
ব্যাখ্যা
Let the price of book
= Tk. 100

Price of flower
= Tk. (100 + 100 × 25%)
= Tk. 125

Price of flower-vase
= Tk. (100 + 100 × 75%)
= Tk. 175

Difference of flower-vase and flower's price
= Tk. (175 -125)
= Tk. 50

∴ Price of the flower-vase more than the price of the flower (in percentage)
= {(50×100)/125}%
= 40%
৪,৩৬৭.
A swimming pool maintenance service charges a fixed fee of Tk. 200 plus Tk. 150 per hour for cleaning. If a customer's total budget is Tk. 1,400, what is the maximum number of full hours the technician can work?
  1. ক
    6 hours
  2. খ
    5 hours
  3. গ
    8 hours
  4. ঘ
    10 hours
ব্যাখ্যা

Question: A swimming pool maintenance service charges a fixed fee of Tk. 200 plus Tk. 150 per hour for cleaning. If a customer's total budget is Tk. 1,400, what is the maximum number of full hours the technician can work?

Solution:
Given,
Fixed service fee = 200 Tk
Charge per hour = 150 Tk
Total budget = 1,400 Tk

Let h = number of full hours the technician works.

According to the condition,
200 + 150h ≤ 1,400
⇒ 150h ≤ 1,400 - 200
⇒ 150h ≤ 1,200
⇒ h ≤ 1,200/150
∴ h ≤ 8

Therefore, the technician can work a maximum of 8 full hours.

৪,৩৬৮.
A dog sees a cat 80 m away. The cat runs at a speed of 5 m/s while the dog chases it at a speed 2 m/s more than that of the cat. Before the dog is able to catch the cat, how much distance has it already run?
  1. ক
    50 m
  2. খ
    100 m
  3. গ
    130 m
  4. ঘ
    200 m
ব্যাখ্যা

We know,
Distance(D) = Speed(S) × Time(T)
∴ S = D/T ; T = D/S

Let distance traveled by cat before dog catches it be D
We know, time for which Dog and Cat ran is the same
∴ T = T
∴ D/5 = (D + 80)/7
⇒ 7D = 5D + 400
⇒ 7D - 5D = 400
⇒ 2D = 400
⇒ D = 200 m.

৪,৩৬৯.
What is the value of the expression?
(√3 + √12)2 = ?
  1. ক
    24
  2. খ
    27
  3. গ
    30
  4. ঘ
    21
ব্যাখ্যা

Question: What is the value of the expression?
(√3 + √12)2 = ?

Solution:
(√3 + √12)2
= {√3 + √(3 × 4)}2
= (√3 + 2√3)2
= (3√3)2
= 32 × (√3)2
= 9 × 3
= 27

৪,৩৭০.
Having incurred a 16% loss on a saree sold for Tk. 3360, a shopkeeper now wishes to set a marked price that allows for a 15% profit, even after applying an 8% discount. What is that price?
  1. ক
    Tk. 3000
  2. খ
    Tk. 4500
  3. গ
    Tk. 3500
  4. ঘ
    Tk. 5000
ব্যাখ্যা
Question: Having incurred a 16% loss on a saree sold for Tk. 3360, a shopkeeper now wishes to set a marked price that allows for a 15% profit, even after applying an 8% discount. What is that price?

Solution:
After selling a saree for Tk. 3360 a shopkeeper suffers a loss of 16%.

Selling price Tk. 84 when Cost price = Tk. 100
∴ Selling price Tk. 3360 when Cost price = Tk. (100 × 3360)/84
= Tk. 4000

15% profit,
Cost price Tk. 100 then Selling price = Tk. 115
∴ Cost price Tk. 4000 then Selling price = Tk. (115 × 4000)/100
= Tk. 4600

discount 8%,
Selling price Tk. 92 When Marked price = Tk. 100
∴ Selling price Tk. 4600 When Marked price = Tk. (100 × 4600)/92
= Tk. 5000
৪,৩৭১.
A man buys an article for 20% more than its value and sells it for 20% less than its value. His gain or loss percentage is –
  1. ক
    33.33% loss
  2. খ
    40% loss
  3. গ
    36% gain
  4. ঘ
    28% gain
ব্যাখ্যা

Question: A man buys an article for 20% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

Solution:
Let the original value of the article = 100 টাকা
∴ Cost Price (CP) = 100 + 20% of 100 টাকা
= 100 + 20 = 120 টাকা

∴ Selling Price (SP) = 100 - 20% of 100 টাকা
= 100 - 20 = 80 টাকা

Since SP (80 টাকা) is less than CP (120 টাকা), there is a Loss.

∴ Loss = CP - SP = 120 - 80 = 40 টাকা
∴ Loss percentage = (Loss/CP) × 100%
= (40/120) × 100%
= (1/3) × 100%
= 33.33% loss

৪,৩৭২.
If n(A ∪ B) = 61, n(A) = 30, n(B) = 54 then what is the value of n(A ∩ B)?
  1. ক
    ক) 22
  2. খ
    খ) 24
  3. গ
    গ) 23
  4. ঘ
    ঘ) 25
ব্যাখ্যা
Question: If n(A ∪ B) = 61, n(A) = 30, n(B) = 54 then what is the value of n(A ∩ B)?

Solution:
দেওয়া আছে,
n(A ∪ B) = 61
n(A) = 30
n(B) = 54

আমরা জানি,
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
⇒ 61 = 30 + 54 - n(A ∩ B)
⇒ n(A ∩ B) = 84 - 61
∴ n(A ∩ B) = 23
৪,৩৭৩.
What is the sum of two consecutive even numbers the difference of whose squares is 84?
  1. ক
    ক) 48
  2. খ
    খ) 58
  3. গ
    গ) 42
  4. ঘ
    ঘ) 46
ব্যাখ্যা

Let the numbers be x and x + 2.
Then, (x + 2)2 - x2 = 84
⇒ 4x + 4 = 84
⇒ 4x = 80
⇒ x = 20.
∴ The required sum
= x + (x + 2)
= 2x + 2
= 42

৪,৩৭৪.
In a row of trees, a tree is 7th from the left and 14th from the right end. How many trees are there in the row?
  1. ক
    18
  2. খ
    19
  3. গ
    20
  4. ঘ
    21
ব্যাখ্যা
Question: In a row of trees, a tree is 7th from the left and 14th from the right end. How many trees are there in the row?

Solution: 
Total number of trees,
= 7 + 14 - 1
= 20
৪,৩৭৫.
How many prime numbers are there between 90 and 100?
  1. ক
    ক) 2
  2. খ
    খ) 1
  3. গ
    গ) 3
  4. ঘ
    ঘ) Nill
ব্যাখ্যা
Question: How many prime numbers are there between 90 and 100?

Solution: 
৯০ ও ১০০ এর মধ্যে মৌলিক সংখ্যা ১ টি - ৯৭।  
৪,৩৭৬.
If m is an odd integer, which of the following must be an even integer?
  1. ক
    m2 + m
  2. খ
    2m + 1
  3. গ
    5m - 2
  4. ঘ
    m3 + 2
ব্যাখ্যা

Question: If m is an odd integer, which of the following must be an even integer?

সমাধান:
ধরি, m = 3 (একটি বিজোড় সংখ্যা)

ক) m2 + m = 33 + 3 = 12 → জোড় 
খ) 2m + 1 = 2(3) + 1 = 6 + 1 = 7 → বিজোড়
গ) 5m - 2 = 5(3) - 2 = 15 - 2 = 13 → বিজোড় 
ঘ) m3 + 2 = 33 + 2 = 27 + 2 = 29 → বিজোড়

৪,৩৭৭.
To complete a work, X takes 25% more time than Y. If together they take 20 days to complete the work, how much time shall Y take to do it?
  1. ক
    38 days
  2. খ
    40 days
  3. গ
    30 days
  4. ঘ
    36 days
ব্যাখ্যা
Question: To complete a work, X takes 25% more time than Y. If together they take 20 days to complete the work, how much time shall Y take to do it?

Solution:
Let Y takes x days to complete the work
Then X will take 25% more i.e 125% of x days i.e 5/4x days.
So the one day work of X and Y together will be
(1/x) +{1/(5/4x)} = 1/20
⇒ (1/x) + (4/5x) = 1/20
⇒ 9/5x = 1/20
⇒ x = 36
∴ Y takes 36 days to complete the work.
৪,৩৭৮.
After filling half of a tank with an ingoing pipe that can fill the tank in 8 hours, an outgoing pipe was attached to empty the tank in 10 hours. How much time will it take to fill the whole tank?
  1. ক
    16 hours
  2. খ
    24 hours.
  3. গ
    26 hours.
  4. ঘ
    32 hours.
ব্যাখ্যা
Question: After filling half of a tank with an ingoing pipe that can fill the tank in 8 hours, an outgoing pipe was attached to empty the tank in 10 hours. How much time will it take to fill the whole tank?

Solution: 
after 4 hours, the tank will be filled in half.
in one hour,
ingoing can fill = 1/8
outgoing can pour = 1/10
total fill-up in one hour = 1/8 - 1/10
= 1/40
∴ to fill te full tank it will take 40 hours.
so, half of the tank will take 20 hours.

total time to fill the tank from the beginning is = 4 + 20 = 24 hours.
৪,৩৭৯.
If the sum of two numbers is 34 and their HCF and LCM are 2 and 120 respectively, what is the sum of the reciprocals of the numbers?
  1. ক
    ক) 15 / 160
  2. খ
    খ) 17 / 120
  3. গ
    গ) 21 / 170
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Question: If the sum of two numbers is 34 and their HCF and LCM are 2 and 120 respectively, what is the sum of the reciprocals of the numbers?

Solution: 
Let the number be a and b

Then,
a + b = 34
and
ab = 2 × 120 = 240

∴Required sum = 1/a+1/b
= (a + b) / ab
= 34 / 240
= 17 / 120
৪,৩৮০.
7 মিটার উঁচু খুঁটির ছায়ার দৈর্ঘ্য 7√3 হলে, সূর্যের উন্নতি কোণ কত?
  1. ক
    20°
  2. খ
    30°
  3. গ
    45°
  4. ঘ
    60°
  5. ঙ
    কোনোটিই নয়
ব্যাখ্যা
প্রশ্ন: 7 মিটার উঁচু খুঁটির ছায়ার দৈর্ঘ্য 7√3 হলে, সূর্যের উন্নতি কোণ কত?

সমাধান:

খুঁটির দৈর্ঘ্য AB = 7 মিটার
ছায়ার দৈর্ঘ্য BC = 7√3
সূর্যের উন্নতি কোণ ∠ACB = θ = ?

এখন,
ΔABC এ
tanθ = AB/BC
⇒ tanθ = 7/(7√3)
⇒ tanθ = 1/√3
⇒ tanθ = tan30°
⇒ θ = 30°
৪,৩৮১.
A and B invest in a business in a ratio of 3 : 2. If 5% of the total profit goes to charity. A's share is Tk. 855, the total profit is:
  1. ক
    Tk. 1425
  2. খ
    Tk. 1500
  3. গ
    Tk. 1537.50
  4. ঘ
    Tk. 1576
ব্যাখ্যা
Question: A and B invest in business in the ratio 3 : 2. If 5% of the total profit goes to charity and A's share in Tk. 855, the total profit is:

Solution:
Let the total profit be Tk. 100.
After paying to charity, A's share = (95 × 3/5) = 57

If A's share is Tk. 57, total profit = 100.
If A's share is Tk. 855, total profit = (100/57) × 855
= 1500.
৪,৩৮২.
If the radius of a circle is decreased by 20% then the area is decreased by: 
  1. ক
    ক) 20%
  2. খ
    খ) 30%
  3. গ
    গ) 36%
  4. ঘ
    ঘ) 40%
ব্যাখ্যা
ধরি,
বৃত্তের ব্যাসার্ধ = r একক,
ক্ষেত্রফল = πr2 বর্গ একক।

ব্যাসার্ধ 20% কমে = r - r এর  20% = 0.8r একক
তাহলে ক্ষেত্রফল = π (0.8r)2 = 0.64πr2 বর্গ একক

ক্ষেত্রফল কমবে = πr2 – 0.64πr2 = 0.36πr2 বর্গ একক

ক্ষেত্রফল কমার হার = (0.36πr2/πr2) x 100 = 36%

শর্টকাট পদ্ধতি:
[- 20 - 20 + (20 × 20)/100]% = - 36%

সুতরাং বৃত্তের ক্ষেত্রফল ৩৬% হ্রাস পাবে।
৪,৩৮৩.
The average age of the 20 aspirants of a class is 19.2 years. After some time two more aspirants join them and then average is increased by 0.3 years. Find the difference between the age of new aspirants.
  1. ক
    ক) 12
  2. খ
    খ) 15
  3. গ
    গ) 18
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
২০ জন ছাত্রের গড় বয়স = ১৯.২ বছর 
২০ জন ছাত্রের মোট বয়স = (১৯.২ × ২০) বছর =৩৮৪ বছর 

২২ জন ছাত্রের গড় বয়স = ১৯.৫ বছর
 ২২ জন ছাত্রের মোট বয়স = (১৯.৫× ২২) বছর =৪২৯ বছর
 
২ জন ছাত্রের মোট বয়স = (৪২৯ - ৩৮৪) বছর  
                                      = ৪৫ বছর

এখান থেকে তাদের বয়সের পার্থক্য বের করা সম্ভব নয়।
৪,৩৮৪.
A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is-
  1. ক
    4 hours
  2. খ
    4 hours 30 minutes
  3. গ
    4 hours 45 minutes
  4. ঘ
    5 hours
ব্যাখ্যা
Question: A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is-

Solution:
Time taken in walking both ways = 7 hours 45 minutes ..............(i)
Time taken in walking one way and riding back = 6 hours 15 minutes ...................(ii)

By equation (ii) × 2 - (i), we have
Time taken to man ride both ways = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes
৪,৩৮৫.
Solve the inequality: 3(2x - 5) + 1 > 4(x - 3) 
  1. ক
    x < 1
  2. খ
    x > 3
  3. গ
    x > 2
  4. ঘ
    x > 1
ব্যাখ্যা

Question: Solve the inequality: 3(2x - 5) + 1 > 4(x - 3)

Solution:
Given inequality,
3(2x - 5) + 1 > 4(x - 3)
⇒ 6x - 15 + 1 > 4x - 12
⇒ 6x - 14 > 4x - 12
⇒ 6x - 4x > −12 + 14
⇒ 2x > 2
∴ x > 1

So, the solution of the inequality is x > 1.

৪,৩৮৬.
35% of Nabila's income is equal to 25% of Sakira's income. The ratio of their income is
  1. ক
    5 : 7
  2. খ
    4 : 7
  3. গ
    7 : 3
  4. ঘ
    4 : 3
ব্যাখ্যা
35% of Nabila's income = 25% of Sakira's income
Nabila's income/Sakira's income = 25/35 = 5/7
৪,৩৮৭.
A shopkeeper marks the price of an article at TK. 80. What will be the selling price, if he allows two successive discounts of 5% each? 
  1. ক
    ক) Tk. 72
  2. খ
    খ) Tk. 85
  3. গ
    গ) Tk. 72.2
  4. ঘ
    ঘ) Tk. 7.2
ব্যাখ্যা
At 5% discount for the first time = 80 × 95/100 = Tk. 76 
At 5% discount for second time = 76 × 95/100 = Tk. 72.20
৪,৩৮৮.
A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:
  1. ক
    ক) 10 hours
  2. খ
    খ) 12 hours
  3. গ
    গ) 14 hours
  4. ঘ
    ঘ) 15 hours
ব্যাখ্যা
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water of the tank in:

Solution:
Work done by the leak in 1 hour
= 1/2 - 3/7
= 1/14

∴ The leak will empty the tank in 14 hours
৪,৩৮৯.
Each boy contributed money equal to the number of girls and each girl contributed money equal to the number of boys in a class of 60 students. If the total contribution thus collected is Tk. 1,600, how many boys are there in the class?
  1. ক
    ক) 30
  2. খ
    খ) 25
  3. গ
    গ) 50
  4. ঘ
    ঘ) 20.5
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
ছেলেদের সংখ্যা x এবং মেয়েদের সংখ্যা y হলে x + y = 60………(i)
প্রশ্নমতে, xy + xy = 2xy = 1600
xy = 800
আমরা জানি, (x-y)2 = (x + y)2 - 4xy
(x - y) = √{(x + y)2 - 4xy} = √(602 - 4×800)
∴ x - y = 20…..(ii)
(i) + (ii) => 2x= 60 + 20
⇒ x = 40
৪,৩৯০.
The ratio of the number of boys and girls in a school is 7 : 4. If the percentage increase in the number of boys and girls be 25% and 15% respectively, what will be the new ratio?
  1. ক
    160 : 92
  2. খ
    92 : 160
  3. গ
    175 : 92
  4. ঘ
    92 : 175
ব্যাখ্যা

Question: The ratio of the number of boys and girls in a school is 7 : 4. If the percentage increase in the number of boys and girls be 25% and 15% respectively, what will be the new ratio?

Solution: 
Let,
The number of boys and girls in a school be 7X and 4X respectively
their increased number number is (125% of 7X) and (115% of 4X)
⇒ (125/100) of 7X and (115/100) of 4X
⇒ 35X/4 and 23X/5

∴ required ratio = 35X/4 : 23X/5
= 175X : 92X        [multiply by 20]
= 175 : 92

৪,৩৯১.
The average of a group of men is increased by 6 years when a person aged of 16 years is replaced by a new person of aged 40 years. How many men are there in the group?
  1. ক
    ক) 5
  2. খ
    খ) 6
  3. গ
    গ) 3
  4. ঘ
    ঘ) 4
ব্যাখ্যা
Question: The average of a group of men is increased by 6 years when a person aged of 16 years is replaced by a new person of aged 40 years. How many men are there in the group?

Let
The no. of persons in the group be X 
Now 
Member in group × aged increased = difference of replacement
X × 6 = 40 - 16
Or, 6X = 24
Or, X = 4
৪,৩৯২.
In a set of 3 numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?
  1. ক
    3
  2. খ
    2
  3. গ
    2.5
  4. ঘ
    3.5
ব্যাখ্যা

Question: In a set of 3 numbers, the average of first two numbers is 2, the average of the last two numbers is 3, and the average of the first and the last numbers is 4. What is the average of three numbers?

Solution: 
let, the numbers are x, y, z 

x + y = 2 × 2 = 4
y + z = 2 × 3 = 6 
z + x = 2 × 4 = 8

2 (x + y + z) = 4 + 6 + 8 = 18 
⇒ (x + y + z) = 9 

∴ the average of three numbers is = 9/3 = 3 

৪,৩৯৩.
The cost of a table and a chair are in the ratio of 5 : 7. If the cost of chair and table is increased by 20% and 10% respectively, then what will be the new ratio?
  1. ক
    ক) 16 : 17
  2. খ
    খ) 55 : 84
  3. গ
    গ) 60 : 77
  4. ঘ
    ঘ) Data inadequate
ব্যাখ্যা

Let,
the cost of the table and chair be Tk. 5x and Tk. 7x respectively.
New cost of chair = 120% of Tk. 7x = Tk (6/5 × 7x)
= Tk. 42x/5.
New cost of table = 110% of Tk. 5x = Tk.(11/10 × 5x)
= Tk. 55x/10.
∴ New ratio = 55x/10 : 42x/5
= 55 : 84

এছাড়াও,
5 : 7
নতুন অনুপাতঃ
5 এর 110% : 7 এর 120%
= 5.5 : 8.4

৪,৩৯৪.
A train crosses two bridges that are 600 meters and 200 meters long in 60 seconds and 40 seconds respectively. What is the length of the train?
  1. ক
    300 meters
  2. খ
    500 meters
  3. গ
    400 meters
  4. ঘ
    600 meters
ব্যাখ্যা

Question: A train crosses two bridges that are 600 meters and 200 meters long in 60 seconds and 40 seconds respectively. What is the length of the train?

Solution:
We know,
To cross a bridge, a train must cover the length of the bridge along with its own length.

Let the length of the train = x meters

Then,
For the first bridge, the distance covered by the train = (x + 600) meters
And,
For the second bridge, the distance covered by the train = (x + 200) meters

According to the question,
(x + 600)/60 = (x + 200)/40
⇒ 40(x + 600) = 60(x + 200)

⇒ 40x + 24000 = 60x + 12000
⇒ 60x - 40x = 24000 - 12000
⇒ 20x = 12000
⇒ x = 12000/20 
⇒ x = 600

∴ The length of the train is 600 meters.

৪,৩৯৫.
In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is-
  1. ক
    1 hour
  2. খ
    2 hours
  3. গ
    3 hours
  4. ঘ
    4 hours
ব্যাখ্যা
Question: In a flight of 600 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of flight increased by 30 minutes. The duration of the flight is-

Solution:
Let the duration of the flight be x hours.
Then,
600/x - 600/(x + 1/2) = 200
⇒ 600/x - 1200/(2x + 1) = 200
⇒ 3/x - 6/(2x + 1) = 1
⇒ (6x + 3 - 6x){x(2x + 1)} = 1
⇒ x(2x + 1) = 3
⇒ 2x2 + x - 3 = 0
⇒ 2x2 + 3x - 2x - 3 = 0
⇒ x(2x + 3) - 1(2x + 3) = 0
⇒ (2x + 3)(x - 1) = 0
∴ x = 1 hr. [neglecting the (- ve) value of x]
৪,৩৯৬.
One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 24 minutes, then the slower pipe alone will be able to fill the tank in- 
  1. ক
    5 hours
  2. খ
    4 hours
  3. গ
    3 hours
  4. ঘ
    2 hours
ব্যাখ্যা

Question: One pipe can fill a tank four times as fast as another pipe. If together the two pipes can fill the tank in 24 minutes, then the slower pipe alone will be able to fill the tank in-

Solution:
Let,
the slower pipe alone fill the tank in x minutes.
Then, Faster pipe alone will fill it in x/4 minutes.

ATQ,
(1/x) + (4/x) = 1/24
⇒ 5/x = 1/24
∴ x = 120

∴ The slower pipe alone fill the tank in 120 minutes
= (120/60) hours
= 2 hours

৪,৩৯৭.
A motorcycle costs Tk. 2,500 when it is brand new. At the end of each year it is worth 4/5 of what it was at the beginning of the year. What is the motorcycle worth when it is 3 years old?
  1. ক
    ক) Tk. 1,000
  2. খ
    খ) Tk. 1,280
  3. গ
    গ) Tk. 1,340
  4. ঘ
    ঘ) Tk. 1,430
ব্যাখ্যা
Question: A motorcycle costs Tk. 2,500 when it is brand new. At the end of each year it is worth 4/5 of what it was at the beginning of the year. What is the motorcycle worth when it is 3 years old?

Solution: 
প্রথমে, মোটরসাইকেলটির দাম ২৫০০ টাকা 

১ বছর শেষে দাম = ২৫০০ × ৪/৫
= ২০০০ টাকা 

২ বছর শেষে দাম = ২০০০ × ৪/৫
= ১৬০০ টাকা 

৩ বছর শেষে দাম = ১৬০০ × ৪/৫
= ১২৮০ টাকা 
৪,৩৯৮.
A wholesaler buys a television for Tk. 18,000 and sells it to a retailer at a profit of 30%. The retailer then sells it to a customer at a profit of 25%. How much does the customer pay to the retailer?
  1. ক
    Tk. 29250
  2. খ
    Tk. 31520
  3. গ
    Tk. 33500
  4. ঘ
    Tk. 28570
ব্যাখ্যা

Question: A wholesaler buys a television for Tk. 18,000 and sells it to a retailer at a profit of 30%. The retailer then sells it to a customer at a profit of 25%. How much does the customer pay to the retailer?

সমাধান:
পাইকারের 30% লাভে বিক্রয়মূল্য = 18,000 + 18,000 এর 30%
= 18,000 + (18,000 × 30/100)
= 18,000 + 5,400 = 23,400 টাকা

পাইকারের বিক্রয়মূল্য = খুচরা বিক্রেতার ক্রয়মূল্য = 23,400 টাকা

খুচরা বিক্রেতার 25% লাভে বিক্রয়মূল্য = 23,400 + 23,400 এর 25%
= 23,400 + (23,400 × 25/100)
= 23,400 + 5,850 = 29,250 টাকা

সুতরাং, খুচরা বিক্রেতার বিক্রয়মূল্য = ক্রেতার ক্রয়মূল্য = Tk. 29,250

৪,৩৯৯.
In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates can be formed if neither the digits nor the letters are repeated?
  1. ক
    9C4  × 26P3
  2. খ
    9P4  × 26C3
  3. গ
    9P4  × 26P3
  4. ঘ
    9C4  × 26C3
ব্যাখ্যা
Question: In a certain country, the car number plate is formed by 4 digits from the digits 1, 2, 3, 4, 5, 6, 7, 8 and 9 followed by 3 letters from the alphabet. How many number plates can be formed if neither the digits nor the letters are repeated?

Solution:
Formed of number 9P4 =3024
Formed of alphabet 26P3 = 15600

∴ Number of number plates = 9P4  × 26P3 = 3024 × 15600 = 47174400
৪,৪০০.
A and B are two positive integers such that AB = 72. Which of the following cannot be the value of A + B?
  1. ক
    18
  2. খ
    27
  3. গ
    25
  4. ঘ
    38
ব্যাখ্যা

Question: A and B are two positive integers such that AB = 72. Which of the following cannot be the value of A + B?

Solution:
Factor pairs of 72:
(1, 72) → A + B = 73
(2, 36) → A + B = 38
(3, 24) → A + B = 27
(4, 18) → A + B = 22
(6, 12) → A + B = 18
(8, 9) → A + B = 17

So, possible values of A + B are: 73, 38, 27, 22, 18, 17.

Among the options, 25 cannot be the value of A + B.