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Bank Math

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Bank Math

PrepBank · পাতা ৯৪ / ১৬১ · ৯,৩০১–৯,৪০০ / ১৬,১২৪

৯,৩০১.
The average of ten numbers is 7. What will be the new average if each of the numbers is multiplied by 8?
  1. ক
    ক) 45
  2. খ
    খ) 52
  3. গ
    গ) 56
  4. ঘ
    ঘ) 55
ব্যাখ্যা

10 টি সংখ্যার সমষ্টি = 10 × 7 = 70
8 দ্বারা ওই দশটি সংখ্যার প্রত্যেককে গুণ করার পর সমষ্টি হবে = 70 × 8 = 560
∴ নতুন গড় = 560/10 = 56 

৯,৩০২.
A sum of money doubles itself in 10 years at simple interest. What is the annual interest rate?
  1. ক
    10%
  2. খ
    15%
  3. গ
    2.5%
  4. ঘ
    5%
ব্যাখ্যা

Question: A sum of money doubles itself in 10 years at simple interest. What is the annual interest rate?

Solution: 
Let,
Principal amount = P
Sum of amount = 2P
∴ Interest, I = 2P - P = P
Time, n = 10 years
Rate of interest = r

We know, 
I = Pnr
∴ r = I/Pn
= P/(P × 10)
= 1/10 × 100%
= 10% 

৯,৩০৩.
Find the next number in the following pattern: 320, 160, 80, 40,…
  1. ক
    ক) 35
  2. খ
    খ) 30
  3. গ
    গ) 10
  4. ঘ
    ঘ) 20
ব্যাখ্যা
320, 160, 80, 40 ..... in this series every number is half of the preceding number.
So, the next number is 20
৯,৩০৪.
The product of the present ages of Rina and Mina is 1500 years. The ratio of their present ages is 5 : 3. What is the difference of their present ages?
  1. ক
    20 years
  2. খ
    21 years
  3. গ
    22 years
  4. ঘ
    23 years
ব্যাখ্যা
Question: The product of the present ages of Rina and Mina is 1500 years. The ratio of their present ages is 5 : 3. What is the difference of their present ages?

Solution:
Let,
the present age of Rina be 5x and the present age of Mina be 3x

ATQ,
5x × 3x = 1500
⇒ 15x2 = 1500
⇒ x2 = 100
∴ x = 10

∴ the present ages of Rina = (5 × 10) = 50 years
∴ the present ages of Mina = (3 × 10) = 30 years

So, the difference of their present ages = (50 - 30) = 20 years
৯,৩০৫.
Which one is undefined?
  1. ক
    sec 0°
  2. খ
    cosec 0°
  3. গ
    cos 90°
  4. ঘ
    sin 90°
ব্যাখ্যা
প্রশ্ন: Which one is undefined? 

সমাধান:
cosec0° এর মান অসংজ্ঞায়িত।
sin90° এর মান 1
cos90° এর মান 0
sec0° এর মান 1 
৯,৩০৬.
Tk. 720 was divided among A, B, C, D, E. The sum received by them was in ascending order and in arithmetic progression. E received Tk. 40 more than A. How much did B receive? 
  1. ক
    Tk. 124
  2. খ
    Tk. 144
  3. গ
    Tk. 150
  4. ঘ
    Tk. 132
  5. ঙ
    Tk. 134
ব্যাখ্যা

Question: Tk. 720 was divided among A, B, C, D, E. The sum received by them was in ascending order and in arithmetic progression. E received Tk. 40 more than A. How much did B receive? 

Solution:
Given that,
A + B + C + D + E = Tk. 720
And E - A = 40

We know,
Arithmetic progression,
a, a + d, a + 2d, a + 3d, a + 4d
And nth term = a + (n - 1)d

Let, A receive Tk. a and the difference between each consecutive person be Tk. d.
Amount, E = a + 4d
Amount, A = a

According to the question,
⇒ a + 4d - a = 40
⇒ 4d = 40
∴ d = 10

Also,
a + (a + d) + (a + 2d) + (a + 3d) + (a + 4d) = 720
⇒ 5a + 10d = 720
⇒ 5a + 10 × 10 = 720
⇒ 5a = 720 - 100
⇒ a = 620/5
∴ a = 124

So, Amount, B = a + d = 124 + 10 = Tk. 134

৯,৩০৭.
A moving train, 66 metres long, overtakes another train of 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/hr, at what speed is the first train moving ?
  1. ক
    ক) 85 km/hr
  2. খ
    খ) 50 km/hr
  3. গ
    গ) 55 km/hr
  4. ঘ
    ঘ) 45 km/hr
ব্যাখ্যা

Let the speed of the first train be x km/hr.
Then,
Sum of lengths of trains = (66 + 88)m = 154 m.

Relative speed of two trains = (x - 30) km/hr
= {(x - 30) × (5/18)} m/s

∴ 154/(x - 30) × (5/18) = 0.168 × 60
⇒ 5(x - 30) = (154 × 18)/10.08
⇒ 5(x - 30) = 275
⇒ x - 30 = 55
⇒ x = 85 km/hr.

৯,৩০৮.
If 2x2 + 12x + 18 = 0, what is the value of x?
  1. ক
    2
  2. খ
    3
  3. গ
    - 3
  4. ঘ
    - 2
ব্যাখ্যা
Question: If 2x2 + 12x + 18 = 0, what is the value of x?

Solution: 
2x2 + 12x + 18 = 0
or, 2(x2 + 6x + 9) = 0
or, (x)2 + 2.x.3 + (3)2 = 0
or, (x + 3)2 = 0
or, x + 3 = 0
∴ x = - 3
৯,৩০৯.
A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?
  1. ক
    5 : 2
  2. খ
    2 : 5
  3. গ
    2 : 3
  4. ঘ
    3 : 2 
ব্যাখ্যা
Question: A train takes 20 seconds to cross a pole. It takes 50 seconds to cross the platform. What is the ratio of the length of the platform to that of the train?

Solution:
Let,
The speed of the train is x m/s

While cross the pole the train travels 20 × x meters = 20x meters, which is the length of the train

While cross the platform the train travels 50 × x meters = 50x meters
∴ Length of the platform 50x - 20x = 30x meters

∴ Length of the platform : Length of the train = 30x : 20x = 30 : 20 = 3 : 2
৯,৩১০.
Find the average of all the numbers between 6 and 34 which are divisible by 5 
  1. ক
    ক) 15
  2. খ
    খ) 16
  3. গ
    গ) 18
  4. ঘ
    ঘ) 20
ব্যাখ্যা
Numbers between 6 and 34 divisible by 5 are 10, 15, 20, 25, 30.
Required average =(10 + 15 + 20 + 25 + 30​)/5
                             = 100/5
                             ​= 20
৯,৩১১.
A sequence of numbers a1, a2, a3, …, an is generated by the rule an + 1 = 3an. If a5 - a4 = 48, then what is the value of a5?
  1. ক
    72
  2. খ
    96
  3. গ
    144
  4. ঘ
    135
ব্যাখ্যা

Question: A sequence of numbers a1, a2, a3, …, an is generated by the rule an + 1 = 3an. If a5 - a4 = 48, then what is the value of a5?

সমাধান:
প্রদত্ত অনুক্রমের নিয়মটি হলো: an+1 = 3an
n = 4 বসালে পাই,
a4 + 1 = 3a4
⇒ a5 = 3a4 

প্রশ্নমতে,
a5 - a4 = 48
⇒ 3a4 - a4 = 48
⇒ (3 - 1)a4 = 48
⇒ 2a4 = 48
⇒ a4 = 48/2
⇒ a4 = 24

এখন,
a5 = 3a4
⇒ a5 = 3 × 24
⇒ a5 = 72

অতএব, a5 এর মান হলো 72

৯,৩১২.
A fort has provisions for 50 days. If after 10 days they are strengthened by 500 men and the food lasts for 35 days longer, the number of men originally in the fort were -
  1. ক
    2500
  2. খ
    3000
  3. গ
    3500
  4. ঘ
    4000
ব্যাখ্যা

Let, there be x men originally.
So, x men had provisions for 40 days whereas (x + 500) men consumed it in 35 days.
More men, Less days [Indirect proportion]
∴ (x + 500) : x :: 40 : 35
⇒ 35(x+ 500) = 40x
⇒ 5x = 35 × 500
⇒ x = (35 × 500)/5
= 3500.

৯,৩১৩.
A man completes a journey in 5 hours. He completes the first half of the distance of journey at a speed of 20 km/hr and the second half at a speed of 25 km/hr. What is the total journey in km?
  1. ক
    5.4 km
  2. খ
    222.2 km
  3. গ
    110.5 km km
  4. ঘ
    111.1 km
ব্যাখ্যা
Question: A man completes a journey in 5 hours. He completes the first half of the journey at a speed of 20 km/hr and the second half at a speed of 25 km/hr. What is the total journey in km?

Solution:
Man travelled for 5 hours
Average speed = 2(20 × 25)/(20 + 25) = 22.22
So, total distance = 22.22 × 5 = 111.1 km

∴ Total distance travelled by the man is 111.1 km
৯,৩১৪.
In a right triangle, the length of one of the legs is 9 and the length of the hypotenuse is 15. What is the length of the other leg?
  1. ক
    13
  2. খ
    8
  3. গ
    24
  4. ঘ
    12
ব্যাখ্যা

Question: In a right triangle, the length of one of the legs is 9 and the length of the hypotenuse is 15. What is the length of the other leg?

Solution:
এখানে, সমকোণী ত্রিভুজের (right triangle) অতিভুজ (hypotenuse) = 15 একক
সমকোণ সংলগ্ন এক বাহু = 9 একক
সমকোণ সংলগ্ন অপর বাহু = a একক

প্রশ্নমতে,
a2 + 92 = 152
⇒ a2 + 81 = 225
⇒ a2 = 225 - 81
⇒ a2 = 144
⇒ a = √144
⇒ a = 12

∴ সমকোণ সংলগ্ন অপর বাহুর দৈর্ঘ্য = 12 একক

৯,৩১৫.
REASON : SFBTPO :: THINK : ?
  1. ক
    ক) SGHMJ
  2. খ
    খ) UIJOL
  3. গ
    গ) UHNKI
  4. ঘ
    ঘ) UJKPM
৯,৩১৬.
The least number by which 150 must be multiplied to make it a perfect square is: 
  1. ক
    2
  2. খ
    3
  3. গ
    6
  4. ঘ
    23
ব্যাখ্যা

Question: The least number by which 150 must be multiplied to make it a perfect square is:

Solution:
Prime factorization of 150:
150 = 2 × 3 × 5 × 5
= 21 × 31 × 52

Here, the powers of 2 and 3 are odd.
∴ To make it a perfect square, we need to multiply by 2 × 3 = 6.

৯,৩১৭.
A scored 30% marks and failed by 15 marks. B scored 40% marks and obtained 35 marks more than those required to pass. The pass percentage is-
  1. ক
    33%
  2. খ
    38%
  3. গ
    43%
  4. ঘ
    46%
ব্যাখ্যা
Question: A scored 30% marks and failed by 15 marks. B scored 40% marks and obtained 35 marks more than those required to pass. The pass percentage is-

Solution: 
Let, total mark is x 

Now
0.3x + 15 = 0.4x - 35 
⇒ 0.4x - 0.3x = 35 + 15 
⇒ 0.1x = 50 
⇒ x = 50/0.1
∴ x = 500 

Pass mark = 0.3 × 500 + 15
= 150 + 15
= 165

Pass percentage = (165/500) × 100% 
= 33%
৯,৩১৮.
Three numbers which are co-prime to each other are such that the product of the first two is 119 and that of the last two is 391. What is the sum of the three numbers?
  1. ক
    ক) 43
  2. খ
    খ) 51
  3. গ
    গ) 47
  4. ঘ
    ঘ) 53
ব্যাখ্যা

Since the numbers are co-prime, their HCF = 1

Product of first two numbers = 119
Product of last two numbers = 391

The middle number is common in both of these products. Hence,
if we take HCF of 119 and 391, we get the common middle number.

HCF of 119 and 391 = 17
⇒ Middle Number = 17
First Number = 119/17 = 7
Last Number = 391/17 = 23

Sum of the three numbers = 7 + 17 + 23 = 47.

৯,৩১৯.
In a class of 30 students, 14 have taken Physics, 9 have taken Physics but not Chemistry. What is the number of students who have taken both Physics and Chemistry?
  1. ক
    ক) 2/5
  2. খ
    খ) 3/5
  3. গ
    গ) 2/3
  4. ঘ
    ঘ) None of the above
ব্যাখ্যা
Question: In a class of 30 students, 14 have taken Physics, 9 have taken Physics but not Chemistry. What is the number of students who have taken both Physics and Chemistry?

Solution:
মনে করি,
n(P) = 14
n(P ∪ C) = 30
n(P - C) = 9

সুতরাং, পদার্থ ও রসায়ন উভয়টি নিয়েছে = n(P ∩ C)
= n(P)  - n(P - C)
= 14 - 9
= 5

[অপশনে 5 না থাকায় None of the above উত্তর হবে]

 
৯,৩২০.
Two numbers when divided by 13, leaves remainder 11 and 9 respectively. If the sum of those two numbers is divided by 13, the remainder will be?
  1. ক
    3
  2. খ
    5
  3. গ
    7
  4. ঘ
    11
ব্যাখ্যা
Question: Two numbers when divided by 13, leaves remainder 11 and 9 respectively. If the sum of those two numbers is divided by 13, the remainder will be?

Solution:
Here,
Dividend = divisor × quotient + remainder
First number = (13 × n) + 11
And, Second number = (13 × n) + 9

Let,
n = 1
∴ first number = (13 × 1) + 11 = 24
and, second number = (13 ×) + 9 = 22

Now,
after adding these two the reminder is = (24 + 22)/13

∴ reminder = 7
৯,৩২১.
In a hostel, 52 students are living. If 18 students are joined in this hostel then the average expenditure will be 3 tk. less whenever the total expenditure is 510 tk. will be increased. What is the total expenditure initially?
  1. ক
    Tk. 2080
  2. খ
    Tk. 1080
  3. গ
    Tk. 8020
  4. ঘ
    Tk. 2280
ব্যাখ্যা
Question: In a hostel, 52 students are living. If 18 students are joined in this hostel then the average expenditure will be 3 tk. less whenever the total expenditure is 510 tk. will be increased. What is the total expenditure initially?

Solution:
Let, the average expenditure of initial students be x,

ATQ,
52x + 510 = (52 + 18) × (x - 3)
⇒ 52x + 510 = 70x - 210
⇒ 70x - 52x = 510 + 210
⇒ 18x = 720
∴ x = 40

Hence, the total expenditure of 52 students = 52 × 40 = 2080 tk.
৯,৩২২.
Rahim deposits 2 coins in a clay bank. What will be the number of coins on the 100th day if the deposit of coins is increased to 3 per day?
  1. ক
    199
  2. খ
    299
  3. গ
    349
  4. ঘ
    399
ব্যাখ্যা
Question: Rahim deposits 2 coins in a clay bank. What will be the number of coins on the 100th day if the deposit of coins is increased to 3 per day?

Solution:
The sequence will be,
2, (2 + 3), (2 + 3 + 3), . . . .
or, 2, 5, 8, . . . 

Here,
a = 2, d = 3, n = 100
So, After 100th day total coin will be = 2 + (100 - 1) × 3
= 2 + (99 × 3)
= 299
৯,৩২৩.
A family has several children. Each boy in the family has as many sisters as brothers and each girl has twice as many brothers as sisters. How many total brothers and sisters are there?
  1. ক
    ক) 7
  2. খ
    খ) 6
  3. গ
    গ) 5
  4. ঘ
    ঘ) 4
ব্যাখ্যা
Question: A family has several children. Each boy in the family has as many sisters as brothers and each girl has twice as many brothers as sisters. How many total brothers and sisters are there? [একটি পরিবারে কয়েকটি শিশু আছে। ঐ পরিবারের প্রতিটি ছেলের যতজন ভাই আছে, তার সমান বোন রয়েছে এবং প্রতিটি মেয়ের যতজন বোন আছে তার দ্বিগুণ ভাই আছে। পরিবারে মোট কত জন ভাই বোন আছে?]

Solution:
Let the number of boys in the family be = x
Then, each boy has (x - 1) brothers and (x - 1) sisters. [He himself will be excluded during the counting of brothers]

As many sisters as a boy has, they are the girls of that family, so
So, the number of girls = (x - 1)

Now, each girl has x brothers and (x - 1 - 1) = (x - 2) sisters [She himself will be excluded during the counting of sisters]

According to the question,
x = 2(x - 2)
⇒ x = 2x - 4
⇒ x = 4

So, there are 4 brothers and (4 - 1) = 3 sisters.
∴  There are total brothers and sisters = (4 + 3) = 7
৯,৩২৪.
If 20% of a = b, then b% of 20 is the same as-
  1. ক
    4% of a
  2. খ
    6% of a
  3. গ
    8% of a
  4. ঘ
    10% of a
ব্যাখ্যা
Question: If 20% of a = b, then b% of 20 is the same as-

Solution:
20% of a = b 
⇒ (20/100) × a = b 
∴ b = (20a)/100

Now,
b% of 20
=(b/100) × 20
= b/5
= [{(20a)/100}/5]
= {(20a)/(100 × 5)}
= (4a)/100
= 4% of a.
৯,৩২৫.
Solve for x: log2(x + 5) = 3. 
  1. ক
    4
  2. খ
    1/2
  3. গ
    2
  4. ঘ
    3
ব্যাখ্যা

Question: Solve for x: log2(x + 5) = 3.

Solution:
Given,
log2(x + 5) = 3
⇒ x + 5 = 23 [logax = b ⇒ x = ab]
⇒ x + 5 = 8
⇒ x = 8 - 5
∴ x = 3

৯,৩২৬.
When a two-digit number is reversed and added to itself we get 143. The product of the digits of that number is 36. What is the number?
  1. ক
    ক) 49
  2. খ
    খ) 50
  3. গ
    গ) 48
  4. ঘ
    ঘ) 51
ব্যাখ্যা

Let, the number be a and b.
When it is reversed and added to itself we get (10a + b) + (10b + a)
= 11a + 11b
= 11(a + b)
We are given,
143 = 11(a + b)
a + b = 143/11
a + b = 13
so the digits are a and 13 - a.
We are given their products as a(13 - a) = 36, which is a quadratic expression.
a(13 - a) = 36
13a - a2 = 36
-a2 + 13a - 36 = 0
a2 - 13a + 36 = 0
a2 - 9a - 4a + 36 = 0
a(a - 9) -4(a - 9) = 0
a - 9)(a - 4) = 0
a = 9 or a = 4
So, the number could be 49 or 94.
Hence the option is 49 then the answer will be 49.

৯,৩২৭.
Find the number which when multiplied by 15 is increased by 196.
  1. ক
    14
  2. খ
    20
  3. গ
    26
  4. ঘ
    28
ব্যাখ্যা
Question: Find the number which when multiplied by 15 is increased by 196.

Solution:
Let, 
the number be x. 

Then,
15x - x = 196
⇒ 14x = 196
⇒ x = 14
৯,৩২৮.
  1. ক
    ক) 3/2
  2. খ
    খ) 2/3
  3. গ
    গ) 1
  4. ঘ
    ঘ) 230
ব্যাখ্যা
(2n + 2n-1)/( 2n+1- 2n)
= (2n + 2n × 0.5)/ ( 2n × 21 - 2n  ) 
= 2n( 1 + 0.5)/ 2n(2 - 1)
= 1 + 1/2
= 3/2
৯,৩২৯.
Tk. 6100 was partly invested in Scheme A at 10% p.a. compound interest for 2 years and partly in Scheme B at 10% p.a. simple interest for 4 years. Both the schemes pay equal interests. How much was invested in Scheme B?
  1. ক
    Tk. 4500 
  2. খ
    Tk. 2100 
  3. গ
    Tk. 5000 
  4. ঘ
    Tk. 4000
ব্যাখ্যা
Question: Tk. 6100 was partly invested in Scheme A at 10% p.a. compound interest for 2 years and partly in Scheme B at 10% p.a. simple interest for 4 years. Both the schemes pay equal interests. How much was invested in Scheme A?

Solution:
Total sum = Tk. 6100
In Scheme A, Compound interest
Principal = P
R = 10% per annum for 2 years

In Scheme B, Simple interest
Principal = 6100 - P
R = 10% per annum for 4 years

Here,
Compound interest = Simple interest
⇒ P[{1 + (R/100)}n - 1] = (PRN)/100
⇒ P[{1 + 10/100}2 - 1] = [(6100 - P) × 4 × 10]/100
⇒ P× (21/100) = [(6100 - P) × 4 × 10]/100
⇒ 21P = 6100 × 40 - 40P
⇒ 61P = 6100 × 40
∴  P = 4000

∴ The amount invested in Scheme B is Tk. (6100 - 4000) = Tk. 2100
৯,৩৩০.
A factory has 6 machines that produce 800 units per day. If three of the machines are out of order, how many units will be produced in a day?
  1. ক
    ক) 200 units
  2. খ
    খ) 300 units
  3. গ
    গ) 400 units
  4. ঘ
    ঘ) 500 units
ব্যাখ্যা
Question: A factory has 6 machines that produce 800 units per day. If three of the machines are out of order, how many units will be produced in a day?

Solution:
Let the total number of units produced by the 6 machines in one day be U.
Each machine produces U/6 units per day.

With three machines out of order, there are 6 - 3 = 3 machines working.
The number of units produced per day by the three working machines is (U/6) * 3 = U/2 units.

So, in a day, 800/2 = 400 units will be produced when three machines are out of order.
৯,৩৩১.
A started a business with tk 21,000 and is joined afterwards by B with tk 36,000. After how many months did B join if the profits at the end of the year are divided equally?
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 7
ব্যাখ্যা

Suppose B joined after x months
21000 × 12 = 36000 × (12 - x)
⇒ 36x = 180
⇒ x = 5

৯,৩৩২.
In a survey, it was found that 70% of people read Ittefaq, 60% read Sangbad, and 40% read both newspapers. If a person is chosen at random, find the probability that they read either Ittefaq or Sangbad.
  1. ক
    1/10
  2. খ
    3/10
  3. গ
    7/10
  4. ঘ
    9/10
ব্যাখ্যা

Question: In a survey, it was found that 70% of people read Ittefaq, 60% read Sangbad, and 40% read both newspapers. If a person is chosen at random, find the probability that they read either Ittefaq or Sangbad.

Solution:
ধরি, ইত্তেফাক পড়ার ঘটনা A 
এবং সংবাদ পড়ার ঘটনা B
P(A) = 70/100 = 7/10 
P(B) = 60/100 = 6/10
P(A ∩ B)= 40/100 = 4/10

নিরপেক্ষভাবে বাছাই করলে একজন লোকের ইত্তেফাক বা সংবাদ পড়ার সম্ভাব্যতা P( A ∪ B)

∴ P(A ∪ B) = P(A) + P(B) - P(A ∩ B) 
= (7/10) + (6/10) - (4/10)
= (7 + 6 - 4)/10
= 9/10

৯,৩৩৩.
A boy rides his bicycle 10 km at an average speed of 10 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is-
  1. ক
    10 km/hr
  2. খ
    11.25 km/hr
  3. গ
    10.75 km/hr
  4. ঘ
    15 km/hr
ব্যাখ্যা

Question: A boy rides his bicycle 10 km at an average speed of 10 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is-

Solution:
Given that,
Distance1 = 10 km, Speed1 = 10 km/hr
Distance2 = 12 km, Speed2 = 10 km/hr

∴ Total Distance = 10 + 12 = 22 km

And,
Time1 = 10 ÷ 10 = 1 hr
Time2 = 12 ÷ 10 = 1.2 hr

∴ Total Time = 1 + 1.2 = 2.2 hr

We know,
Average Speed = Total Distance ÷ Total Time
= 22/2.2 = 10 km/hr

∴ His average speed for the entire trip is 10 km/hr.

৯,৩৩৪.
'Buy Three get One Free' what is the percentage of discount being offered here?
  1. ক
    ক) 25%
  2. খ
    খ) 48.78%
  3. গ
    গ) 21%
  4. ঘ
    ঘ) 33.33%
ব্যাখ্যা
Question: 'Buy Three get One Free' what is the percentage of discount being offered here?
Solution: 
'Buy Three get One Free' এর অর্থ হলো - ৩টি পণ্য ক্রয় করলে ১টি পণ্য ফ্রী। 
 
ধরি, প্রতিটি পণ্যের ক্রয়মূল্য X টাকা 
⇒ ৩টি পণ্যের ক্রয়মূল্য = 3X টাকা 

সুতরাং, ডিসকাউন্ট হার = (X/3X) × 100 = 33.33%


৯,৩৩৫.
In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?
  1. ক
    d
  2. খ
    d/3
  3. গ
    d/2
  4. ঘ
    (3d)/4
  5. ঙ
    (3d)/2
ব্যাখ্যা
Question: In the first hour of a two-hour trip, a car traveled d kilometers, and in the second hour of the trip, the car traveled one-half that distance. What is the average rate at which the car traveled during the trip, in kilometers per hour?

Solution:
1st hour , distance travelled by car = d km
2nd hour , distance travelled by car = d/2 km
Total distance = d + d/2 
= (2d + d)/2
= (3d)/2

Average speed = Total distance/Time
= (3d/2)/2
= (3d)/4
৯,৩৩৬.
If 0 ≤ x ≤ 4 and y < 6, which of the following cannot be the value of xy?
  1. ক
    - 2
  2. খ
    0
  3. গ
    6
  4. ঘ
    None of these
ব্যাখ্যা

Question: If 0 ≤ x ≤ 4 and y < 6, which of the following cannot be the value of xy?

Solution:
y < 6 হলে y  এর মান 5, 4, 3, 2, 1, 0, - 1,..............
0 ≤ x ≤ 4 হলে x  এর মান 0, 1, 2, 3, 4

এখন
x = 0, y = 1 হলে xy = 0 × 1 = 0
x = 2, y = - 1 হলে xy = 2 × (- 1) = - 2
x = 3, y = 2 হলে xy = 3 × 2 = 6

সঠিক উত্তর: None of these

৯,৩৩৭.
The probability that a card drawn from a pack of 52 cards will be a diamond or a king is:
  1. ক
    3/52
  2. খ
    4/13
  3. গ
    1/26
  4. ঘ
    1/52
ব্যাখ্যা

Question: The probability that a card drawn from a pack of 52 cards will be a diamond or a king is: 

Solution: 
Here, n(S) = 52
There are 13 cards of diamonds (including one king), and there are three more kings.

Let E = the event of getting a diamond or a king
Then, n(E) = (13 + 3) = 16

∴ P(E) = n(E)/n(S)
= 16/52
= 4/13

৯,৩৩৮.
In a class, if 4 students sit in each bench, there are 3 empty benches, but 6 students have to stand if 3 students sit each bench. How many students are there in that class?
  1. ক
    50
  2. খ
    60
  3. গ
    70
  4. ঘ
    80
  5. ঙ
    None of these
ব্যাখ্যা
Question: In a class, if 4 students sit in each bench, there are 3 empty benches, but 6 students have to stand if 3 students sit each bench. How many students are there in that class?

Solution:
ধরি,
বেঞ্চ সংখ্যা = ক টি
একটি শ্রেণির প্রতি বেঞ্চে ৪ জন করে ছাত্র বসলে ৩ টি বেঞ্চ খালি থাকে।
∴ ছাত্রসংখ্যা = (ক - ৩) × ৪ জন

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

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

ছাত্রসংখ্যা = (ক - ৩) × ৪ জন
= (১৮ - ৩) × ৪ জন
= ১৫ × ৪ জন
= ৬০ জন
৯,৩৩৯.
The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. How much time the ship will take to travel the same distance in upstream?
  1. ক
    40 hours
  2. খ
    60 hours
  3. গ
    80 hours
  4. ঘ
    120 hours
ব্যাখ্যা
Question: The time taken by a ship to travel 1000 km upstream is 40 hours more than the time taken by it to travel the same distance in downstream. The speed of the ship in still water is 200% more than that of the speed of stream. How much time the ship will take to travel the same distance in upstream?

Solution:
Given that,
Distance travelled = 1000 km
Time taken to travel upstream = 40 hours + time taken to travel downstream

Let,
The speed of the stream = X km per hour

∴ The speed of the ship in still water = X + 200% of X
= X + 2X
= 3X km per hour

ATQ,
{1000/(3X - X)} - {1000/(3X + X)} = 40
⇒ (1000/2X) - (1000/4X) = 40
⇒ (2000 - 1000)/4X = 40
⇒ 4X × 40 = 1000
⇒ X = 1000/(4 × 40)
∴ X = 6.25 km/hr

The required time in upstream = 1000/(3X - X)
= 1000/2X
= 1000/(2 × 6.25)
= 80 hours
৯,৩৪০.
Two trains A and B are moving in the same direction. A has speed of 8 km/h and B has speed of 13 km/h. What is relative speed of B with respect to A?
  1. ক
    21 km/h
  2. খ
    3 km/h
  3. গ
    5 km/h
  4. ঘ
    8 km/h
ব্যাখ্যা

Question: Two trains A and B are moving in the same direction. A has speed of 8 km/h and B has speed of 13 km/h. What is relative speed of B with respect to A?

Solution: 
Given that,
Speed of train A = 8 km/h
Speed of train B = 13 km/h

Since both are moving in the same direction, and B is faster.
∴ Relative speed of B with respect to A = Speed of B - Speed of A
= 13 km/h - 8 km/h
= 5 km/h

So the relative speed of B with respect to A is 5 km/h.

৯,৩৪১.
X, Y, and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work?
  1. ক
    ক) 12
  2. খ
    খ) 16
  3. গ
    গ) 24
  4. ঘ
    ঘ) 36
ব্যাখ্যা

(X + y)'s 1 day's work = (1/16) + (1/16)
= 2/16
= 1/8
Z's 1 day's work = (X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
= 1/6 - 1/8
= 1/24.
∴ Z alone can finish the work in 24 days.

৯,৩৪২.
Pipe A can fill a cistern in 6 hours and B in 4 hours. After filling the half cistern by A, B starting pouring water. Total time to fill the cistern is- 
  1. ক
    3.2 hours
  2. খ
    4.8 hours
  3. গ
    4.5 hours
  4. ঘ
    4.2 hours
ব্যাখ্যা
Question: Pipe A can fill a cistern in 6 hours and B in 4 hours. After filling the half cistern by A, B starting pouring water. Total time to fill the cistern is- 

Solution: 
half of the cistern filled by A in 3 hours.
After that,
bothe the pipes are open.
so in one hour they will pour = 1/6 + 1/4
= 5/12 hours
∴ half of the cisterns will be filled in = 12/(5 × 2) hours
= 12/10 = 1.2 hours

∴ total time = 3 + 1.2 hours
= 4.2 hours
৯,৩৪৩.
Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?
  1. ক
    30.8 m
  2. খ
    60 m
  3. গ
    76.8 m
  4. ঘ
    40.5 m
ব্যাখ্যা
Question: Two buildings are 40 m apart. The angle of depression of the top of one building of height 100 m with the top of second building of unknown height is 60°. Find the height of second building?

Question:

Let the height of the second building AD be h.
EC = 100 - h
DC = AB = 40

here,
EC/DC = tan60°
⇒ (100 - h)/40 = √3
⇒ 100 - h = 40√3
⇒ h = 100 - 69.2
∴ h = 30.8
৯,৩৪৪.
An article has a marked price of Tk. 500. If two successive discounts of x% and 5% reduce the selling price to Tk. 427.50, determine the value of x.
  1. ক
    7%
  2. খ
    10%
  3. গ
    14%
  4. ঘ
    19%
ব্যাখ্যা

Question: An article has a marked price of Tk. 500. If two successive discounts of x% and 5% reduce the selling price to Tk. 427.50, determine the value of x.

Solution:
Marked Price = Tk. 500
Final Selling Price after two successive discounts = Tk. 427.50
Let the first discount = x%
Second discount = 5%

First discount be:
500 × (1 - x/100​) × (1 - 0.05) = 427.50
⇒ 500 × (1 - x/100​) × 0.95 = 427.50
⇒ 475 × (1 - x/100​) = 427.50 
⇒ (1 - x/100​) = 427.50 / 475
⇒ 1 - x/100 = 0.9
⇒ - x/100 = 0.9 - 1
⇒ - x/100 = - 0.1
⇒ x = 0.1 × 100
⇒ x = 10%

∴ First discount = 10%

৯,৩৪৫.
Solve |5x + 5| - 8 ≤ 17.
  1. ক
    - 5 ≤ x ≤ 5
  2. খ
    - 5 ≤ x ≤ 4
  3. গ
    0 ≤ x ≤ 4
  4. ঘ
    - 6 ≤ x ≤ 4
ব্যাখ্যা
Question: Solve |5x + 5| - 8 ≤ 17.

Solution:
|5x + 5| - 8 ≤ 17
⇒ |5x + 5| ≤ 25
⇒ - 25 < 5x + 5 ≤ 25
⇒ - 30 < 5x ≤ 20
⇒ - 6 ≤ x ≤ 4
৯,৩৪৬.
How many spokes are there in a wheel of a bicycle, if any two spokes form an angel of 15°.
  1. ক
    ক) 12
  2. খ
    খ) 15
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
ব্যাখ্যা
প্রশ্ন: How many spokes are there in a wheel of a bicycle, if any two spokes form an angel of 15°.

সমাধান: 
বাইসাইকেলের চাকা বৃত্তাকার। 
বৃত্ত কেন্দ্রে ৩৬০° উৎপন্ন করে। 

দুটি স্পাইকের মধ্যবর্তী কোণ ১৫° 

∴ স্পাইক প্রয়োজন = ৩৬০°/১৫° 
= ২৪ টি 
৯,৩৪৭.
A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?
  1. ক
    5 months
  2. খ
    7 months
  3. গ
    10 months
  4. ঘ
    1 year
ব্যাখ্যা
Question: A started a business with Tk. 2100 and is joined afterwards by B with Tk. 3600. After how many months did B join if the profits at the end of the year are divided equally?

Solution:
Suppose,
B joined after x months.

Then,
2100 × 12 = 3600 × (12 - x)
⇒ 252 = 432 - 36x
⇒ 36x = 180
∴ x = 5

∴ B joined after 5 months
৯,৩৪৮.
A vessel contains a mixture of P and Q in the ratio of 5 : 3. 16 liters of this mixture is taken out and 5 liters of P is poured in. The new mixture has a ratio of P to Q as 11 : 6. Find the total original quantity of mixture.
  1. ক
    98 liters
  2. খ
    96 liters
  3. গ
    94 liters
  4. ঘ
    92 liters
ব্যাখ্যা
Question: A vessel contains a mixture of P and Q in the ratio of 5 : 3. 16 liters of this mixture is taken out and 5 liters of P is poured in. The new mixture has a ratio of P to Q as 11 : 6. Find the total original quantity of mixture.

Solution:
Let, 
Original Quantity of P = 5x
Original Quantity of Q = 3x

The quantity of P and Q in 16 liters of the mixture:
Quantity of P = (16 × 5x)/8x = 10 liters
Quantity of Q = (16 × 3x)/8x = 6 liters

Now,
5 liters of P poured in so the Quantity of P will be = 5x - 10 + 5 liters
= 5x - 5 liters

ATQ,
(5x - 5)/(3x - 6) = 11/6
⇒ 6(5x - 5) = 11(3x - 6)
⇒ 30x - 30 = 33x - 66
⇒ 3x = 36
∴ x = 12

So total mixture originally = 8x = 8 × 12 = 96 liters
৯,৩৪৯.
Jasim's weight is 140% of Masum's weight. Bashir's weight is 90% of Limon's Weight. Limon weights twice as much as Masum. What percentage of Jasim's weight is Bashir's weight?
  1. ক
    ক) 452/7%
  2. খ
    খ) 695/9%
  3. গ
    গ) 900/7%
  4. ঘ
    ঘ) 410/9%
ব্যাখ্যা
Masum : Jasim = 100 : 140 = 5 : 7
Limon : Bashir = 100 : 90 = 10 : 9
Limon: Masum = 2 : 1 = 10 : 5 [5 দ্বারা গুণ করে পাই]

Masum : Jasim : Limon : Bashir = 5 : 7 : 10 : 9

ধরি 
Jasim এর ওজন = 7x কেজি 
 Bashir এর ওজন = 9x কেজি 

নির্ণেয় শতাংশ = (9x/7x) × 100%
                        = 900/7%
৯,৩৫০.
If the probability that Mokhles will miss at least one of the ten jobs assigned to him is 0.55, then what is the probability that he will do all ten jobs?
  1. ক
    ক) 1
  2. খ
    খ) 0.1
  3. গ
    গ) 0.45
  4. ঘ
    ঘ) 0.85
ব্যাখ্যা
Question: If the probability that Mokhles will miss at least one of the ten jobs assigned to him is 0.55, then what is the probability that he will do all ten jobs?

Solution:
There are only two cases:
1) Mokhles will miss at least one of the ten jobs.
2) Mokhles will not miss any of the ten jobs.

Hence, (The probability that Mokhles will miss at least one of the ten jobs) + (The probability that he will not miss any job) = 1. Since the probability that Mokhles will miss at least one of the ten jobs is 0.55, this equation becomes
⇒ 0.55+ (The probability that he will not miss any job) = 1
⇒ (The probability that he will not miss any job) = 1 - 0.55
⇒ (The probability that he will not miss any job) = 0.45
৯,৩৫১.
A train 150 meter long and running at a speed of 60 km per hour takes 30 seconds to cross a bridge. What is the length of the bridge?
  1. ক
    350 meter
  2. খ
    450 meter
  3. গ
    500 meter
  4. ঘ
    650 meter
ব্যাখ্যা
Question: A train 150 meters long and running at a speed of 60 km per hour takes 30 seconds to cross a bridge. What is the length of the bridge?

Solution: 
সেকেন্ডে ট্রেনের গতিবেগ = (60×1000)/(60×60) মিটার/সেকেন্ড 
= 16.67 মিটার/সেকেন্ড
∴ 30 সেকেন্ডে অতিক্রান্ত দূরত্ব = (30×16.67)m = 500m
ব্রিজের দূরত্ব = 500 - 150 = 350 m
৯,৩৫২.
A, B and C can do a piece of work in 24, 36 and 72 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?
  1. ক
    15 days
  2. খ
    18 days
  3. গ
    10 days
  4. ঘ
    9 days
ব্যাখ্যা

Question: A, B and C can do a piece of work in 24, 36 and 72 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? 

Solution:
A's 2 day's work = (1/24) × 2 = 1/12
∴ (A + B + C)'s 1 day's work = 1/24 + 1/36 + 1/72

= 1/24 + 1/36 + 1/72
= (3 +2 +1)/72
= 6/72
= 1/12

Work done in 3 days = 1/12+ 1/12
= 2/12
= 1/6

Now,
1/6 work is done in 3 days.
∴ Whole work will be done in (3 × 6) = 18 days

৯,৩৫৩.
Sixty-five percent of a number is 21 less than; four-fifth of that number. What is the number?
  1. ক
    ক) 120
  2. খ
    খ) 140
  3. গ
    গ) 160
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Let the number be x
As given 65% of x = 4/5 of x -21
So, solving above equation:
65 X x/100= 4 X x/5 - 21
⇒ 65 X x /100 = ( 4x - 105)/5
⇒ (65x) X 5 = (4x- 105) X 100
⇒ 65 x = (4x -105) X 20
⇒ 65 x = 80 x - 2100
⇒ 15x = 2100
∴ x = 140
So, the number is 140.

৯,৩৫৪.
  1. ক
    ক) 10
  2. খ
    খ) 11
  3. গ
    গ) 12
  4. ঘ
    ঘ) 13
ব্যাখ্যা
প্রশ্ন:

সমাধান: 
৯,৩৫৫.
What is the sum of the squares of the digits from 1 to 11?
  1. ক
    506
  2. খ
    484
  3. গ
    286
  4. ঘ
    234
ব্যাখ্যা

Question: What is the sum of the squares of the digits from 1 to 11?

Solution: 
আমরা জানি,
n সংখ্যক ক্রমিক সংখ্যার বর্গের যোগফল, Sn = [n(n + 1)(2n + 1)]/6
= [11(11 + 1)(22 + 1)]/6
= (11 × 12 × 23)/6 
= 22 × 23 
= 506

৯,৩৫৬.
Three shirts and five ties cost Tk 23. Five shirts and one tie cost Tk 20. What is the price of one shirt?
  1. ক
    ক) Tk. 2.50
  2. খ
    খ) Tk. 3.00
  3. গ
    গ) Tk. 3.50
  4. ঘ
    ঘ) Tk. 6.00
ব্যাখ্যা

Let s=shirt and t=tie
Need to solve:
3s + 5t = 23 and 5s + 1t = 20
Look for a multiple of one (or both) formula that will match the quantity of the second. One option is to multiply the second equation by 5:
5x (5s + 1t) = 5x 20
Or, 25s + 5t = 100
Subtract the first formula :
25s + 5t - 3s - 5t = 100 - 23
Or, 22s = 77

So shirts are 77 / 22 = Tk. 3.50 each

৯,৩৫৭.
If (3/5)3 (3/5)- 6 = (3/5)2a - 1 then a is equal to?
  1. ক
    1
  2. খ
    - 1
  3. গ
    2
  4. ঘ
    - 2
ব্যাখ্যা
Question: If (3/5)3 (3/5)- 6 = (3/5)2a - 1 then a is equal to?

Solution:
(3/5)3 (3/5)- 6 = (3/5)2a - 1
⇒ (3/5)(3 - 6) = (3/5)2a - 1
⇒ (3/5)- 3 = (3/5)2a - 1
⇒ 2a - 1 = - 3
⇒ 2a = - 2
∴ a = - 1
৯,৩৫৮.
For a software development project, a given group can be divided into 8 groups of 3 coders each. How many groups can be formed if the manager decides to have 6 coders in each group?
  1. ক
    ক) 4
  2. খ
    খ) 5
  3. গ
    গ) 6
  4. ঘ
    ঘ) 8
ব্যাখ্যা

Here, Total coders = 8 × 3 = 24
∴ Numbers of groups each having 6 coders = 24/6 = 4

৯,৩৫৯.
A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is -
  1. ক
    1/12
  2. খ
    5/12
  3. গ
    7/12
  4. ঘ
    11/12
  5. ঙ
    None of these
ব্যাখ্যা

Question: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction obtained is -

Solution:
Let, the fraction is a/b

Now, (a - 1)/b = 1/3
⇒ b = 3a - 3

Again, a/(b + 8) = 1/4
⇒ b + 8 = 4a
⇒ b = 4a - 8

∴ 3a - 3 = 4a - 8
⇒ 4a - 3a = 8 - 3
⇒ a = 5

And, b = (3 × 5) - 3
= 15 - 3
= 12

∴ The fraction = a/b = 5/12 

৯,৩৬০.
The average weight of 16 boys in a class is 50.25kg and that of the remaining 8 boys is 45.15kg. Find the average weight of all the boys in the class.
  1. ক
    ক) 47.55kg
  2. খ
    খ) 48kg
  3. গ
    গ) 48.55kg
  4. ঘ
    ঘ) 49.25kg
ব্যাখ্যা
Question: The average weight of 16 boys in a class is 50.25kg and that of the remaining 8 boys is 45.15kg. Find the average weight of all the boys in the class.

Solution: 
Required average = (50.25 × 16 + 45.15 × 8​​)/(16 + 8)
                               = (804 + 361.20​​)/24
                               = 1165.2/24
                                = 48.55
৯,৩৬১.
A number, when decreased by 175 and then increased by 130, equals 297. Find the number.
  1. ক
    340
  2. খ
    334
  3. গ
    345
  4. ঘ
    342
ব্যাখ্যা
Question:  A number, when decreased by 175 and then increased by 130, equals 297. Find the number.

Solution:
Let the number be = x

According to the question,
(x - 175) + 130 = 297
⇒ x - 45 = 297
⇒ x = 297 + 45
⇒ x = 342 

So, the number is 342
৯,৩৬২.
If p/q = 5, then the value of (p + q)/(p - q) is 
  1. ক
    ক) 1
  2. খ
    খ) 2/5
  3. গ
    গ) 5/2
  4. ঘ
    ঘ) 3/2
ব্যাখ্যা
Question: If p/q = 5, then the value of (p + q)/(p - q) is-

Solution: 
Given that 
 p/q = 5/1
Now
(p + q)/(p - q) = (5 + 1)/(5 - 1)
                        = 6/4
                        = 3/2
৯,৩৬৩.
The height of a cylinder is five times the radius of the cylinder. If the volume of the cylinder is 135π cm3 , what is the height of the cylinder?
  1. ক
    11 cm
  2. খ
    19 cm
  3. গ
    12 cm
  4. ঘ
    17 cm
  5. ঙ
    15 cm
ব্যাখ্যা

​Question: The height of a cylinder is five times the radius of the cylinder. If the volume of the cylinder is 135π cm3, what is the height of the cylinder?

Solution:
Let
The radius of the cylinder is r cm
The height of the cylinder is 5r cm.

We know,
The volume of a cylinder = πr2h cubic units.

ATQ,
πr2 × 5r = 135π
⇒ 5r3 = 135
⇒ r3 = 135/5
⇒ r3 = 27
⇒ r3= 33

∴ r = 3

So the height ot the cylinder = 5 × 3 = 15 cm

৯,৩৬৪.
A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?
  1. ক
    1/4
  2. খ
    1/2
  3. গ
    3/4
  4. ঘ
    7/12
ব্যাখ্যা
Question: A problem is given to three students whose chances of solving it are 1/2, 1/3 and 1/4 respectively. What is the probability that the problem will be solved?

Solution:
১ম ছাত্রের সমস্যাটি সমাধান করার সম্ভাবনা ১/২
১ম ছাত্রের সমস্যাটি সমাধান না করার সম্ভাবনা ১ - ১/২ = ১/২

২য় ছাত্রের সমস্যাটি সমাধান করার সম্ভাবনা ১/৩
২য় ছাত্রের সমস্যাটি সমাধান না করার সম্ভাবনা ১ - ১/৩ = ২/৩

৩য় ছাত্রের সমস্যাটি সমাধান করার সম্ভাবনা ১/৪
৩য় ছাত্রের সমস্যাটি সমাধান না করার সম্ভাবনা ১ - ১/৪ = ৩/৪

তিন ছাত্রেরই সমস্যা সমাধান না করার সম্ভাবনা = (১/২) × (২/৩) × (৩/৪)
= ১/৪

∴ সমস্যাটি সমাধানের সম্ভাবনা = ১ - ১/৪
= ৩/৪ 
৯,৩৬৫.
Approximately 90 percent of the volume of a certain cube that is floating in a tank of water is beneath the surface. If 6.4 cubic centimeters of the cube is above the surface of the water, what is the approximate length, in centimeters, of an edge of the cube?
  1. ক
    10
  2. খ
    8
  3. গ
    6
  4. ঘ
    4
  5. ঙ
    2
ব্যাখ্যা
Question: Approximately 90 percent of the volume of a certain cube that is floating in a tank of water is beneath the surface. If 6.4 cubic centimeters of the cube is above the surface of the water, what is the approximate length, in centimeters, of an edge of the cube?

Solution:
If 90% of a cube is below the surface, then 10% of the cube is above the surface.
So 10% of the volume of the cube is equal to 6.4 cubic centimeters.

We know that,
The volume of a cube with edge A is A3

Then:
(10/100) × A3 = 6.4
⇒ A3 = 6.4 × 10
⇒ A3 = 64
⇒ A3 = 43
∴ A = 4
৯,৩৬৬.
If a rectangular photograph that Is 10 inches wide by 15 inches long Is to be enlarged so that the width will be 22 inches and the ratio of width to length will be unchanged, then the length, in inches, of the enlarged photograph will be-
  1. ক
    33
  2. খ
    32
  3. গ
    30
  4. ঘ
    27
  5. ঙ
    25
ব্যাখ্যা
Question: If a rectangular photograph that is 10 inches wide by 15 inches long is to be enlarged so that the width will be 22 inches and the ratio of width to length will be unchanged, then the length, in inches, of the enlarged photograph will be-

Solution:
We can use the ratio width/length
Let x = the length of the enlarged photograph

ATQ,
10/15 = 22/x
⇒ 2/3 = 22/x
⇒ 2x = 66
∴ x = 33
৯,৩৬৭.
A square and a circle have the same perimeter. The length of the side of the square is 44 cm. What is the area of the circle?
  1. ক
    616 square cm
  2. খ
    1760 square cm
  3. গ
    2024 square cm
  4. ঘ
    2464 square cm
ব্যাখ্যা

Question: A square and a circle have the same perimeter. The length of the side of the square is 44 cm. What is the area of the circle?

Solution:
বর্গের পরিসীমা = 4 × বাহুর দৈর্ঘ্য
= 4 × 44 সেমি
= 176 সেমি

প্রশ্নমতে, বর্গ এবং বৃত্তের পরিসীমা সমান।
সুতরাং, বৃত্তের পরিধি = 176 সেমি

আমরা জানি,
বৃত্তের পরিধি = 2πr
⇒ 2πr = 176
⇒ 2 × (22/7) × r = 176
⇒ (44/7) × r = 176
⇒ r = 176 × (7/44)
∴ r = 28 সেমি

এখন, বৃত্তের ক্ষেত্রফল = πr2
= (22/7) × (28)2
= (22/7) × 784
= 22 × 112
= 2464 বর্গ সেমি

৯,৩৬৮.
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
    36
  2. খ
    38
  3. গ
    40
  4. ঘ
    42
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.
৯,৩৬৯.
What is the angle between the hour and minute hands of a clock when it is 3 : 15 pm? 
  1. ক
    37.5°
  2. খ
    97.5°
  3. গ
    10.5°
  4. ঘ
    7.5°
ব্যাখ্যা

Question: What is the angle between the hour and minute hands of a clock when it is 3 : 15 pm?

Solution:
3টা 15 মিনিট = 3 + (15/60) ঘন্টা = 3 + 1/4 = 13/4 ঘন্টা

আমরা জানি, ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/4 ঘণ্টায় ঘোরে = (30° × 13)/4
= 390°/4
= 97.5°

আবার, মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 15 মিনিটে ঘোরে = 15 × 6° = 90°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |97.5° - 90°|
= 7.5°

৯,৩৭০.
What percentage should be added to 40 to make it 70?
  1. ক
    10
  2. খ
    75
  3. গ
    25
  4. ঘ
    50
ব্যাখ্যা
Let, x% should be added.
Therefore, 40 + x% of 40 = 70
⇒ 40 + 40x/100 = 70
⇒ 40x/100 = 30
2x/5 = 30
2x = 150
x = 75
Therefore, 75% should be added to 40 to make it 50
৯,৩৭১.
The cost of 21 pencils and 9 clippers is Tk. 819. The cost price of 7 pencils and 3 clippers is = ?
  1. ক
    ক) Tk. 91
  2. খ
    খ) Tk. 182
  3. গ
    গ) Tk. 273
  4. ঘ
    ঘ) Tk. 364
ব্যাখ্যা
Cost of 21 pencils and 9 clippers = Tk. 819
That means, cost of 3(7 pencils and 3 clippers) = Tk. 819
Cost of (7 pencils and 3 clippers) = Tk.  819/3
 = Tk. 273
৯,৩৭২.
What is the angle between the hour and minute hands of a clock when it is 3 : 15 pm? 
  1. ক
    14.5°
  2. খ
    7.5°
  3. গ
    27.25°
  4. ঘ
    19°
ব্যাখ্যা

Question: What is the angle between the hour and minute hands of a clock when it is 3 : 15 pm?

Solution:
3টা 15 মিনিট = 3 + (15/60) ঘন্টা = 3 + 1/4 = 13/4 ঘন্টা

আমরা জানি, ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/4 ঘণ্টায় ঘোরে = (30° × 13)/4
= 390°/4
= 97.5°

আবার, মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 15 মিনিটে ঘোরে = 15 × 6° = 90°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = |97.5° - 90°|
= 7.5°

৯,৩৭৩.
A milkman purchases the milk at Tk. x per liter and sells it at Tk. 2x per liter still he mixes 2 liters of water with every 6 liters of pure milk. What is the profit percentage?
  1. ক
    ক) 116%
  2. খ
    খ) 166.66%
  3. গ
    গ) 60%
  4. ঘ
    ঘ) 100%
ব্যাখ্যা

Let,
He purchases 6 liters milk.
So, cost of 6 liters = 6x tk.
After mixing 2 liters waters, he sells , (6 + 2) = 8 liters
Now, selling price of 8 liters = 8 × 2x = 16x tk
Profit = 16x – 6x = 10x tk.
∴ Profit percentage = (10x/6x) × 100 = 166.66%

৯,৩৭৪.
Raju and Saju were carrying some money such that their money was in the ratio 3 : 8. A friend gives each of them Tk. 5 and their money is now in the ratio 2 : 5. Which is the smaller money of the two?
  1. ক
    ক) 45
  2. খ
    খ) 64
  3. গ
    গ) 105
  4. ঘ
    ঘ) 120
ব্যাখ্যা

The ratio of original money numbers = 3:8
Common factor helps in finding actual values easily
So, take 'M' as a common factor.
∴ Original numbers will be 3M and 8M
Adding 5 to them, we get (3M + 5) and (8M+5)
∴ (3M + 5)/(8M + 5) = 2/5 ............ (Ratio of new numbers is 2:5)
∴ 15M + 25 = 16M + 10
∴ M = 15
Smaller money value is 3M = 3 x 15 = 45.

৯,৩৭৫.
A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?
  1. ক
    ক) 16 : 15
  2. খ
    খ) 15 : 16
  3. গ
    গ) 15 : 11
  4. ঘ
    ঘ) 11 : 15
ব্যাখ্যা
Question: A cat leaps 5 leaps for every 4 leaps of a dog, but 3 leaps of the dog are equal to 4 leaps of the cat. What is the ratio of the speed of the cat to that of the dog?

Solution:
Given;
3dog = 4 cat
Or, dog/cat = 4/3

Let cat's 1 leap = 3 meter and dogs 1 leap = 4 meter

Then, ratio of speed of cat and dog = (3 × 5) / (4 × 4) = 15 : 16
৯,৩৭৬.
A retailer buys pens in packs of 24 for Tk.336/pack and then resells them in packs of 5 for Tk.80/pack. If the retailer sold all the pens it purchased and made a profit of Tk.960. How many packs of pens did the retailer purchase?
  1. ক
    ক) 10
  2. খ
    খ) 20
  3. গ
    গ) 25
  4. ঘ
    ঘ) None
ব্যাখ্যা
No explanation added.
৯,৩৭৭.
The ratio of income and expenditure of a person is 5 : 3 per annum. If he saves Tk 24000 per annum, his monthly income is -
  1. ক
    ক) 5000 Tk
  2. খ
    খ) 6000 Tk
  3. গ
    গ) 7200 Tk
  4. ঘ
    ঘ) 8000 Tk
ব্যাখ্যা
Question: The ratio of income and expenditure of a person is 5 : 3 per annum. If he saves Tk 24000 per annum, his monthly income is - 

Solution:
Let income be Tk 5x
and expenditure is Tk 3x

ATQ,
5x - 3x = 24000
⇒ 2x = 24000
⇒ x = 12000

His annual income = 5 × 12000 = 60000 Tk
His monthly income = 60000/12 = 5000 Tk
৯,৩৭৮.
The speed of three motorcycles are in the ratio 2 : 3 : 4. The ratio of the times taken by three motorcycles to travel the same distance is - 
  1. ক
    ক) 6 : 5 : 3
  2. খ
    খ) 2 : 4 : 3
  3. গ
    গ) 6 : 4 : 3
  4. ঘ
    ঘ) 6 : 4 : 1
ব্যাখ্যা
Question: The speed of three motorcycles are in the ratio 2 : 3 : 4. The ratio of the times taken by three motorcycles to travel the same distance is - 

Solution: 
ধরি, তাদের বেগ যথাক্রমে 2x, 3x, 4x 

y কিমি যেতে সময় লাগে (y/2x), (y/3x), (y/4x)

সময়ের অনুপাত =  (y/2x) : (y/3x) : (y/4x)
= (1/2) : (1/3) : (1/4)
= (12/2) : (12/3) : (12/4)
= 6 : 4 : 3
৯,৩৭৯.
The average age of 8 men is increased by 4 years when one of them whose age is 30 years is replaced by a new man. What is the age of a new man?
  1. ক
    65 years
  2. খ
    57 years
  3. গ
    62 years
  4. ঘ
    76 years
  5. ঙ
    72 years
ব্যাখ্যা
Let, the average age of 8 men be x
Sum of the age of 8 men = 8x
Let, age of new man be y
According to question,
8x + y - 30 = 8 (x + 4)
8x + y - 30 = 8x + 32
y = 8x + 32 + 30 - 8x
y = 62 years

So, Age of the new man is 62 years.
৯,৩৮০.
A jar contains only marbles of three colour: red, green and yellow. The red and green marbles are in the ratio of 2 : 5 and the yellow and red marbles are in ration of 5 : 6. Which of the following could be the total number of marbles?
  1. ক
    52
  2. খ
    64
  3. গ
    100
  4. ঘ
    None of these
ব্যাখ্যা
Question: A jar contains only marbles of three colour: red, green and yellow. The red and green marbles are in the ratio of 2 : 5 and the yellow and red marbles are in ration of 5 : 6. Which of the following could be the total number of marbles?

Solution:
Red : Green = 2 : 5 = 6 : 15
Yellow : Red = 5 : 6 = 5 : 6
Red : Green : Yellow = 6 : 15 : 5

অনুপাতের রাশিগুলোর সমষ্টি = 6 + 15 + 5 = 26
মার্বেল সংখ্যা হবে 26 এর গুণিতক।
মার্বেল সংখ্যা হতে পারে 26, 52, 78, 104,..............
৯,৩৮১.
Jowel got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Jowel's wife was 10 years younger to him at the time of his marriage. The age of Jowel's wife is-
  1. ক
    32 years
  2. খ
    35 years
  3. গ
    38 years
  4. ঘ
    42 years
  5. ঙ
    None
ব্যাখ্যা
Question: Jowel got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Jowel's wife was 10 years younger to him at the time of his marriage. The age of Jowel's wife is-

Solution:
Let Jowel's age 8 years ago be x years,
Then, present age = (x + 8) years

ATQ,
x + 8 = 6x/5
⇒ 6x = 5x + 40
⇒ x = 40

Jowel's wife's age 8 years ago = (40 - 10) years
= 30 years

∴ His wife's age now = (30 + 8) years
= 38 years
৯,৩৮২.
Manoj sold an article for TK.15,000. Had he offered a discount of 10% on the selling price he would have earned a profit of 8%. What is the cost price?
  1. ক
    ক) TK.12,500
  2. খ
    খ) TK.13,500
  3. গ
    গ) TK.12,250
  4. ঘ
    ঘ) TK.13,250
  5. ঙ
    ঙ) Tk. 14,250
ব্যাখ্যা

Let the cost price x.
Therefore, 90% of 15000 = 108% of x .
Or, x = 90 × 15000108
Or, x = Tk. 12500

৯,৩৮৩.
If tan 2A = cot(A - 30°) and 2A is an acute angle, then find 'A' is-
  1. ক
    40°
  2. খ
    60°
  3. গ
    120°
  4. ঘ
    45°
ব্যাখ্যা
Question: If tan 2A = cot(A - 30°) and 2A is an acute angle, then find 'A' is-

Solution:
Given that,
tan 2A = cot (A - 30°)
⇒ tan 2A = tan [90° - (A - 30°)]
⇒ 2A = 90° - A + 30°
⇒ 3A = 120°
⇒ A = 120°/3
∴ A = 40°
৯,৩৮৪.
Find the equation of the line with x-intercept = 3 and y-intercept = 4.
  1. ক
    4x + 3y - 12 = 0
  2. খ
    3x + 4y - 12 = 0
  3. গ
    4x - 3y - 12 = 0
  4. ঘ
    3x + 4y - 1 = 0
ব্যাখ্যা

Question: Find the equation of the line with x-intercept = 3 and y-intercept = 4.

Solution:
Given
x-intercept = 3 (line passes through point (3, 0)
y-intercept = 4 (line passes through point (0, 4)

We know,
The intercept form of a line is:
x/a + y/b =1 ,where a = x-intercept and b = y-intercept.
⇒ x/3 + y/4 = 1
⇒ (4x + 3y)/12 =1
⇒ 4x + 3y = 12 
⇒ 4x + 3y - 12 = 0

∴ The equation of the line is 4x + 3y - 12 = 0

৯,৩৮৫.
In each word of the following questions consists of pair of words bearing a relationship among these, from amongst the alternatives, pick up the pair that best illustrate a similar relationship.
Glove : Hand-
  1. ক
    ক) Neck : Collar
  2. খ
    খ) Tie : Shirt
  3. গ
    গ) Socks : Feet
  4. ঘ
    ঘ) Coat : Pocket
ব্যাখ্যা
As Glove is worn in Hands similarly Socks are worn on feet.
৯,৩৮৬.
Rabbi first goes 12 meters north. Then goes 12 meters west. From there he again goes 4 meters north. What is the direct distance from the starting point to that place?
  1. ক
    24 meters
  2. খ
    20 meters
  3. গ
    16 meters
  4. ঘ
    28 meters
ব্যাখ্যা
Question: Rabbi first goes 12 meters north. Then goes 12 meters west. From there he again goes 4 meters north. What is the direct distance from the starting point to that place?

Solution:

ধরি,
রাব্বি প্রথমে AB = 12 মিটার উত্তরে যায়।
পরে BC = 12 মিটার পশ্চিমে যায়।
সেখান থেকে CD = 4 মিটার উত্তরে যায়।
যাত্রা স্থান থেকে ঐ স্থানের দূরত্ব AD 

এখানে AB ও CD রেখা সমান্তরাল এবং CD = BE = 4 মিটার
∴ AE = 12 + 4 = 16 মিটার 
BC = DE = 12 মিটার

ADE একটি সমকোণী ত্রিভুজ গঠন করে যার অতিভুজ AD এবং এটিই যাত্রা স্থান থেকে নির্দিষ্ট স্থানের সরাসরি দূরত্ব

পিথাগোরাসের উপপাদ্য হতে পাই,
AD2 = AE2 + DE2
⇒ AD = √(AE2 + DE2)
= √(162 + 122)
= √(256 + 144)
=√400
∴ AD = 20 মিটার

∴ যাত্রা স্থান থেকে ঐ স্থানের সরাসরি দূরত্ব = 20 মিটার।
৯,৩৮৭.
A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?
  1. ক
    75
  2. খ
    82
  3. গ
    100
  4. ঘ
    110
  5. ঙ
    120
ব্যাখ্যা
Question: A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

Solution:
Originally let there be x men.
Less men, More days (Indirect Proportion)
Therefore, (x - 10) : x : : 100 :110
⇒ (x - 10)/x = 100/110
⇒ (x - 10) × 110 = x × 100
⇒ 11x - 110 = 10x
∴ x = 110
৯,৩৮৮.
A square park is surrounded by a path of uniform width 3 meters. If the area of the path is 75 square meters, find the side length of the park.
  1. ক
    3.25 meters
  2. খ
    5 meters
  3. গ
    4.5 meters
  4. ঘ
    6 meters
ব্যাখ্যা

Question: A square park is surrounded by a path of uniform width 3 meters. If the area of the path is 75 square meters, find the side length of the park.

Solution:
Let the side of the park = x meters.
Then, the side of the park including the path = x + (2 × 3)
= x + 6 meters.

Area of the path = Area of park with path - Area of park
⇒ 75 = (x + 6)2 - x2
⇒ 75 = x2 + 12x + 36 - x2
⇒ 75 = 12x + 36
⇒ 12x = 75 - 36 = 39
⇒ x = 39/12 = 3.25 meters

Therefore, the side length of the park is 3.25 meters.

৯,৩৮৯.
What is the total interest on Tk 800 at 12.5% per annum for 9 months (in taka)? 
  1. ক
    75
  2. খ
    110
  3. গ
    88
  4. ঘ
    22
  5. ঙ
    None of these
ব্যাখ্যা
Question: What is the total interest on Tk 800 at 12.5% per annum for 9 months (in taka)?

Solution:
আসল, P = Tk. 800
সুদের হার, r = 12.5% = 0.125
বছর, n = 9 months = 9/12 year

সুদ = Pnr
= 800 × (9/12) × 0.125
= 75 Taka
৯,৩৯০.
Aslam bought 5 apples at taka 10 and sold 4 apples at taka 10. What will be the rate of profit? 
  1. ক
    ক) 25%
  2. খ
    খ) 20%
  3. গ
    গ) 30%
  4. ঘ
    ঘ) 33.33%
ব্যাখ্যা
5টি আপেলের ক্রয়মূল্য 10 টাকা 
1টি আপেলের ক্রয়মূল্য 10/5 টাকা 
                                    = 2 টাকা 

4টি আপেলের বিক্রয়মূল্য 10 টাকা 
1টি আপেলের বিক্রয়মূল্য 10/4 টাকা 
                                       = 2.5 টাকা 
লাভ = (2.5 - 2)টাকা  = 0.5 


শতকরা লাভ = {(0.5/2) × 100}%
                      = 25%
৯,৩৯১.
Two trains of equal length are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. If the faster train passes the slower train in 36 seconds,what is the length of each train?
  1. ক
    ক) 50 metre
  2. খ
    খ) 60 metre
  3. গ
    গ) 40 metre
  4. ঘ
    ঘ) 45 metre
  5. ঙ
    ঙ) 35 metre
ব্যাখ্যা

Let length of each train = x metre
Total distance covered while passing the slower train = (x + x) = 2x metre
Relative speed = (46 − 36)
= 10 km/hr
= 10 × 5/18
= 50/18 m/s

Time = 36 seconds
⇒ 2 x/36 = 50/18
⇒ x = 50

৯,৩৯২.
If x2 - √(7). x + 1 = 0 then, x2 + 1/x2 = ?
  1. ক
    3
  2. খ
    5
  3. গ
    3√7
  4. ঘ
    7
ব্যাখ্যা

Question: If x2 - √(7). x + 1 = 0 then, x2 + 1/x2 = ?

Solution:
দেওয়া আছে,
x2 - √7x + 1 = 0
⇒ x2 + 1 = √7x  
⇒ x2/x + 1/x = √7x/x [উভয় পক্ষকে x দ্বারা ভাগ]
⇒ x + 1/x = √7

এখন,
x2 + 1/x2
= (x + 1/x)2 - 2 . x . 1/x
= (√7)2 - 2
= 7 - 2
= 5

∴ x2 + 1/x2 এর মান 5।

৯,৩৯৩.
What annual rate was paid if Tk. 50000 earned Tk. 3000 in interest in two years?
  1. ক
    12%
  2. খ
    9%
  3. গ
    6%
  4. ঘ
    3%
ব্যাখ্যা
Question: What annual rate was paid if Tk. 50000 earned Tk. 3000 in interest in two years?

Solution:
Tk. 50000 earned in 2 years Tk. 3000
∴ Tk. 100 earned in 1 year Tk. (3000 × 100)/(50000 × 2)
= 3%
৯,৩৯৪.
What is the value of tan240°
  1. ক
    - √3
  2. খ
    √2
  3. গ
    √3
  4. ঘ
    3
ব্যাখ্যা

Question: What is the value of tan240°

Solution: 
tan240°
= tan(180° + 60°)
= tan(180° + θ)
= tanθ
= tan60°
= √3


Note:
240° lies in the 3rd quadrant.
In the 3rd quadrant, tan θ is positive (because both sin θ and cos θ are negative).

৯,৩৯৫.
What is the meaning of the word 'Trepidation'?
  1. ক
    An uncomfortable feeling of nervousness.
  2. খ
    Very comfortable situation.
  3. গ
    Find a solution.
  4. ঘ
    Always being confident.
ব্যাখ্যা

Trepidation (noun)
- English Meaning: An uncomfortable feeling of nervousness or worry about something that is happening or might happen in the future.
-  Bangla Meaning: সচকিত উত্তেজিত মনোভাব।  

Synonyms:
• Anxiety - ভবিষ্যৎ বিষয়ে ভয় ও অনিশ্চয়তাবোধ; উদ্বেগ; দুশ্চিন্তা।

• Apprehension - আশঙ্কা; ভবিষ্যৎ বিষয়ে উৎকণ্ঠার অনুভূতি; উপলব্ধি; চেতনা; বোধ।

• Disquietude - মানসিক অস্থিরতা বা উদ্বেগ।

Antonyms:
• Calmness - শান্ততা, বিশ্রান্ততা।

• Equanimity - মনমেজাজের প্রশান্তি।

• Composure - শান্তি; স্থৈর্য; আত্মসংবরণ।

Other options:
খ) Very comfortable situation.
- Translations: খুবই আরামদায়ক অবস্থা। 

গ) Find a solution.
- Translations:  সমাধান বের করা। 

ঘ) Always being confident.
- Translations: সবসময় আত্মবিশ্বাসী।

Source: Live MCQ Lecture.

৯,৩৯৬.
The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Tk. 1. The sum (in Tk.) is:
  1. ক
    ক) Tk.645
  2. খ
    খ) Tk. 635
  3. গ
    গ) Tk. 625
  4. ঘ
    ঘ) Tk. 655
ব্যাখ্যা
Let the sum be Tk. x.
Then
C. I = x(1 + 4/100)2 - x
      = x(104/100)2 - x
      = x(26/25)2 - x
      = 676x/625 - x
      = (676x - 625x)/625
      = 51x/625

S.I =(x × 4 × 2)/100 = 2x/25

Now
(51x/625) - (2x/25) = 1
(51x - 50x)/625 = 1
x /625 = 1
x = 625
৯,৩৯৭.
The difference between a two-digit number and the number obtained by interchanging the digits is 36. What is the difference between the sum and the difference of the digits of the number if the ratio between the digits of the number is 1: 2?
  1. ক
    ক) 4
  2. খ
    খ) 8
  3. গ
    গ) 16
  4. ঘ
    ঘ) None of these
ব্যাখ্যা

Since the number is greater than the number obtained on reversing the digits, so the ten's digit is greater than the unit's digit.
Lets, ten's and unit's be 2x and x respectively
Then, (10 times; 2x + x) - (10x + 2x) = 36
⇒ 9x = 36
⇒ x = 4

∴ Required difference (2x + x) - (2x - x ) = 2x = 4 × 2 = 8
Answer : 8

৯,৩৯৮.
If n is an odd integer, which of the following must be an odd integer?
  1. ক
    ক) n - 1
  2. খ
    খ) n + 1
  3. গ
    গ) 4n + 1
  4. ঘ
    ঘ) 3n + 1
ব্যাখ্যা

Let, n =  3

n - 1 = 2
n + 1 = 4
4n + 1 =  13
3n + 1 =  10

৯,৩৯৯.
Sixty-five percent of a number is 42 less than four-fifth of that number. What is the number?
  1. ক
    320
  2. খ
    280
  3. গ
    260
  4. ঘ
    240
ব্যাখ্যা
Question: Sixty-five percent of a number is 42 less than four-fifth of that number. What is the number?

Solution:
Let, the number = x.

ATQ,
65% of x = (4/5) of x - 42
⇒ 65x/100 = (4x/5) - 42
⇒ 13x/20 = (4x/5) - 42
⇒ (4x/5) - (13x/20) = 42
⇒ (16x - 13x)/20 = 42
⇒ 3x/20 = 42
⇒ 3x = 840
⇒ x = 840/3
∴ x = 280

So, the number is 280
৯,৪০০.
A bike traveled twice a many kms from X to Y as it did from Y to Z. From X to Y, the bike averaged 16 Km/gallon and from Y to Z, the bike averaged 24 Km/gallon. What is the average Km/gallon that the bike achieved on its trip from X through Y to Z?
  1. ক
    ক) 28.8
  2. খ
    খ) 32
  3. গ
    গ) 36.8
  4. ঘ
    ঘ) 48
  5. ঙ
    ঙ) None
ব্যাখ্যা
Question: A bike traveled twice a many kms from X to Y as it did from Y to Z. From X to Y, the bike averaged 16 Km/gallon and from Y to Z, the bike averaged 24 Km/gallon. What is the average Km/gallon that the bike achieved on its trip from X through Y to Z?

Solution: 
X থেকে Y এর দূরত্ব = 2a কিমি
Y থেকে Z এর দূরত্ব = a কিমি
মোট দূরত্ব = 2a + a = 3a

নির্ণেয় গড় গতিবেগ = 3a/{(2a/16) + (a/24)}
= 3a/{(6a + 2a)/48}
= 3a/(8a/48)
= 3a/(a/6)
= 3a × (6/a)
= 18