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Bank Math

মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math

PrepBank · পাতা ৩৫ / ১৬১ · ৩,৪০১–৩,৫০০ / ১৬,১২৪

৩,৪০১.
Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 16 years. What is the present age of X?
  1. ক
    ক) 48 years
  2. খ
    খ) 50 years
  3. গ
    গ) 52 years
  4. ঘ
    ঘ) 54 years
সঠিক উত্তর: ক
ক) 48 years
উত্তর
সঠিক উত্তর: ক
ক) 48 years
ক
ব্যাখ্যা
2 times the age of X = 3 times the age of Y
2X = 3Y
⇒ X : Y = 3 : 2

Let present age of X and Y be 3a and 2a respectively
3a - 8 - (2a - 8) = 16
⇒ 3a - 2a = 16
⇒ a = 16

∴ The present age of X is 16 × 3 years = 48 years
৩,৪০২.
Mr. Nur was hired for a job for 7 days. Each day, he was paid Tk. 10 more than what he was paid for their previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?
  1. ক
    Tk. 160
  2. খ
    Tk. 148
  3. গ
    Tk. 90
  4. ঘ
    Tk. 80
  5. ঙ
    None
সঠিক উত্তর: গ
Tk. 90
উত্তর
সঠিক উত্তর: গ
Tk. 90
গ
ব্যাখ্যা
Question: Mr. Nur was hired for a job for 7 days. Each day, he was paid Tk. 10 more than what he was paid for their previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

Solution:
Let,
The pays of seven days respectively: x, x + 10 x + 20 x + 30, x + 40, x + 50, x + 60

According to the question,
x + x + 10 + x + 20 + x + 30 = x + 40 + x + 50 + x + 60
⇒ 4x + 60 = 3x + 150
∴ x = 90

∴ His starting pay is Tk. 90
৩,৪০৩.
Three fair coins are tossed simultaneously. What is the probability of getting at least one head and one tail?
  1. ক
    ক) 1/4
  2. খ
    খ) 3/4
  3. গ
    গ) 3/8
  4. ঘ
    ঘ) 5/8
সঠিক উত্তর: খ
খ) 3/4
উত্তর
সঠিক উত্তর: খ
খ) 3/4
খ
ব্যাখ্যা
When three coins are tossed, total possible outcomes = 8
S = {HHH, HHT, HTT, THH, TTH, THT, HTH,TTT}
Favorable cases = {HHT,HTT,THH,TTH,THT,HTH} 

P(getting at least one head, one tail) = 6/8
                                                           = 3/4
∴ The probability is 3/4
৩,৪০৪.
A machine making cost is Tk 2000, sold with two successive discounts of 20% and 10%. An additional discount of 5% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?
  1. ক
    632 Tk
  2. খ
    540 Tk
  3. গ
    426 Tk
  4. ঘ
    None of the above
সঠিক উত্তর: ক
632 Tk
উত্তর
সঠিক উত্তর: ক
632 Tk
ক
ব্যাখ্যা
Question: A machine making cost is Tk 2000, sold with two successive discounts of 20% and 10%. An additional discount of 5% is offered for cash payment. What is the total loss in the selling price of the machine at cash payment?
 
Solution:
Making price = 2000 Tk
Selling Price after first Discount of 20% = 2000 - 20% of 2000
= 2000 - {(20/100) × 2000}
= 1600 Tk

The selling price after the second Discount of 10% = 1600 - 10% of 1600
= 1600 - {(10/100) × 1600
= 1440 Tk

∴ The final selling price at cash = 1440 - 5% of 1440
= 1440 - {(5/100) × 1440}
= 1368 Tk

Total loss = 2000 - 1368 = 632 Tk
৩,৪০৫.
1.14 expressed as a per cent of 1.9 is:
  1. ক
    45%
  2. খ
    60%
  3. গ
    72%
  4. ঘ
    65%
সঠিক উত্তর: খ
60%
উত্তর
সঠিক উত্তর: খ
60%
খ
ব্যাখ্যা
Required Percentage = 1.14 × 100/1.9 = 60%
৩,৪০৬.
Sumon sells a mobile phone to Tania at a profit of 20%. Tania then sells that phone to Rafi for Tk. 1800, making a profit of 25%. At what price did Sumon purchase the mobile phone?
  1. ক
    Tk. 1200
  2. খ
    Tk. 1000
  3. গ
    Tk. 1600
  4. ঘ
    Tk. 1400
সঠিক উত্তর: ক
Tk. 1200
উত্তর
সঠিক উত্তর: ক
Tk. 1200
ক
ব্যাখ্যা

প্রশ্ন: Sumon sells a mobile phone to Tania at a profit of 20%. Tania then sells that phone to Rafi for Tk. 1800, making a profit of 25%. At what price did Sumon purchase the mobile phone?

সমাধান:
২৫% লাভে,
তানিয়ার বিক্রয়মূল্য ১২৫ টাকা হলে ক্রয়মূল্য ১০০ টাকা
∴ তানিয়ার বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য ১০০/১২৫ টাকা
∴ তানিয়ার বিক্রয়মূল্য ১৮০০ টাকা হলে ক্রয়মূল্য (১০০ × ১৮০০)/১২৫ টাকা
= ১৪৪০ টাকা

এখানে,
তানিয়ার ক্রয়মূল্য = সুমনের বিক্রয়মূল্য

২০% লাভে,
সুমনের বিক্রয়মূল্য ১২০ টাকা হলে ক্রয়মূল্য = ১০০ টাকা
∴ সুমনের বিক্রয়মূল্য ১ টাকা হলে ক্রয়মূল্য = ১০০/১২০ টাকা
∴ সুমনের বিক্রয়মূল্য ১৪৪০ টাকা হলে ক্রয়মূল্য = (১০০ × ১৪৪০)/১২০ = ১২০০ টাকা

 ∴ সুমনের-এর ক্রয়মূল্য = ১২০০ টাকা

৩,৪০৭.
Asif obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Asif?
  1. ক
    Tk. 17550
  2. খ
    Tk. 16450
  3. গ
    Tk. 17450
  4. ঘ
    Tk. 17455
সঠিক উত্তর: গ
Tk. 17450
উত্তর
সঠিক উত্তর: গ
Tk. 17450
গ
ব্যাখ্যা
Question: Asif obtained an amount of Tk. 8376 as simple interest on a certain amount at 8 p.c.p.a. after 6 years. What is the amount invested by Asif?

Solution:
Simple interest, I = Tk. 8376
Rate of interest, r = 8%
Time, n = 6 years

We know,
I = Pnr
Or, P = I/nr
= (8376 × 100)/(6 × 8)
∴ P = 17450 Tk.
৩,৪০৮.
If logn2 = p and logn5 = q, then logn250 = ?
  1. ক
    p + q2
  2. খ
    pq2
  3. গ
    p + 2q
  4. ঘ
    p + 3q 
সঠিক উত্তর: ঘ
p + 3q 
উত্তর
সঠিক উত্তর: ঘ
p + 3q 
ঘ
ব্যাখ্যা
Question: If logn2 = p and logn5 = q, then logn250 = ?

Solution:
Given, 
logn2 = p and logn5 = q

∴ logn250 = logn(2 ×125)
= logn(2 × 53)
= logn2 + logn53
= logn2 + 3 logn5
= p + 3q
৩,৪০৯.
Q (33-56): Read the following questions carefully and choose the right answer.
৩৩) Which one of the following numbers can be removed from the set S = (0, 2, 4, 5, 9) without changing the average of set S?
  1. ক
    ক) 0
  2. খ
    খ) 2
  3. গ
    গ) 4
  4. ঘ
    ঘ) 5
সঠিক উত্তর: গ
গ) 4
উত্তর
সঠিক উত্তর: গ
গ) 4
গ
ব্যাখ্যা
The average of the elements in the original set S is:( 0+2+4+5+9)/5
                                                                                 =20/5
                                                                                 =4
If we remove an element that equals the average, then the average of the new set will remain unchanged.
The new set after removing 4 is {0, 2, 5, 9}.
The average of the elements is, (0+2+5+9)/4
                                                 =16/4
                                                 =4
৩,৪১০.
If a : b = 3 : 2, find ratio (4a + 5b) : (4a - 5b).
  1. ক
    5 : 1
  2. খ
    11 : 13
  3. গ
    11 : 1
  4. ঘ
    8 : 1
সঠিক উত্তর: গ
11 : 1
উত্তর
সঠিক উত্তর: গ
11 : 1
গ
ব্যাখ্যা
Question: If a : b = 3 : 2, find ratio (4a + 5b) : (4a - 5b).

Solution: 
(4a + 5b) : (4a - 5b)
= b(4a/b + 5) : b (4a/b - 5)
= (4 × 3/2 + 5) : (4 × 3/2 - 5)
= (6 + 5) : (6 - 5)
= 11 : 1
৩,৪১১.
Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?
  1. ক
    4 days
  2. খ
    40/9 days
  3. গ
    5 days
  4. ঘ
    40/7 days
সঠিক উত্তর: খ
40/9 days
উত্তর
সঠিক উত্তর: খ
40/9 days
খ
ব্যাখ্যা
Question: Worker A completes a task in 8 days, and worker B completes the same task in 10 days. If both A and B work together, in how many days they will complete the task?

Solution:
Worker A completes the task in 8 days. So, in one day, he will complete 1/8 part of the task.

So, A's one day work = 1/8
Similarly, B's one day work = 1/10

∴ (A+B)'s one day work = 1/8 + 1/10 = (5 + 4)/40 = 9/40

9/40 of the task is completed in one day so both will complete the whole task in 40/9 days
৩,৪১২.
In Δ ABC, AB = BC and AC is the hypotenuse. The value of ∠C is -
  1. ক
    ক) 35°
  2. খ
    খ) 45°
  3. গ
    গ) 60°
  4. ঘ
    ঘ) 90°
সঠিক উত্তর: খ
খ) 45°
উত্তর
সঠিক উত্তর: খ
খ) 45°
খ
ব্যাখ্যা

Δ ABC-তে AB = BC এবং AC অতিভুজ 
∴ ∠C = ∠A
এখন, ∠A + ∠B + ∠C = 180°
⇒ ∠C + 90° + ∠C = 180° [AB = BC এবং AC অতিভুজ (hypotenuse) হলে ∠B = 90°]
⇒ 2∠C = 180° - 90° = 90°
∴ ∠C = 45°

৩,৪১৩.
Two pipes working together can fill a fish tank in 12 minutes. If one pipe fills the fish tank 10 minutes faster than the second pipe, at what time the second pipe alone can fill the fish tank?
  1. ক
    20 minutes
  2. খ
    25 minutes
  3. গ
    30 minutes
  4. ঘ
    35 minutes
সঠিক উত্তর: গ
30 minutes
উত্তর
সঠিক উত্তর: গ
30 minutes
গ
ব্যাখ্যা

Let the first pipe fill the reservoir in X minutes

So, the second pipe will fill the reservoir in (X+10) minutes

As per question;
(1/X) + 1/(X + 10) = 1/12
⇒ (X + 10 + X)/X(X + 10) = 1/12
⇒ 12X + 120 + 12X = X2 + 10X
⇒ X2 + 10X - 24X -120 = 0
⇒ X2 - 14X -120 =0
⇒ X2 - 20X + 6X - 120=0
⇒ X(X - 20) + 6(X - 20) =0
⇒ (X + 6) (X - 20) = 0
⇒ X = 20

∴Second pipe will fill the reservoir in 20 + 10= 30 minutes

৩,৪১৪.
The average age of X, Y and Z was 25 years and that of Y and Z was 25 years. X’s present age is-
  1. ক
    27 years
  2. খ
    35 years
  3. গ
    25 years
  4. ঘ
    22 years
  5. ঙ
    None of the above
সঠিক উত্তর: গ
25 years
উত্তর
সঠিক উত্তর: গ
25 years
গ
ব্যাখ্যা
Question: The average age of X, Y and Z was 25 years and that of Y and Z was 25 years. X’s present age is-

Solution:
The average of X, Y and Z is 25

So, the sum of their ages = 75
Now, the sum of Y and Z will be 50 (because their average is 25)

So age of X =75 - 50 = 25 years
৩,৪১৫.
In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?
  1. ক
    18,000
  2. খ
    22,000
  3. গ
    24,000
  4. ঘ
    26,000
  5. ঙ
    32,000
সঠিক উত্তর: গ
24,000
উত্তর
সঠিক উত্তর: গ
24,000
গ
ব্যাখ্যা
Question: In a mayoral election, Candidate X received 1/3 more votes than Candidate Y, and Candidate Y received 1/4 fewer votes than Candidate Z. If Candidate Z received 24,000 votes, how many votes did Candidate X receive?

Solution:
Candidate Y received 1/4 fewer votes than Candidate Z
In other words, Candidate Y received 3/4 of the votes that Candidate Z received
3/4 of 24,000 = (3/4)(24,000) = 18,000

Candidate X received 1/3 more votes than Candidate Y
1/3 of 18,000 = 6,000
Number of votes that Candidate X received = 18,000 + 6,000 = 24,000
৩,৪১৬.
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
    28%
  2. খ
    35%
  3. গ
    25%
  4. ঘ
    22%
সঠিক উত্তর: খ
35%
উত্তর
সঠিক উত্তর: খ
35%
খ
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 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%

৩,৪১৭.
The sum of four consecutive even numbers is 140. What is the sum of next two consecutive even numbers-
  1. ক
    76
  2. খ
    66
  3. গ
    82
  4. ঘ
    90
সঠিক উত্তর: গ
82
উত্তর
সঠিক উত্তর: গ
82
গ
ব্যাখ্যা
Question: The sum of four consecutive even numbers is 140. What is the sum of next two consecutive even numbers-

Solution:
let, four consecutive even numbers is
x, x + 2, x + 4, x + 6

ATQ,
⇒ x + x + 2 + x + 4 + x + 6 = 140
⇒ 4x + 12 = 140
⇒ 4x = 140 - 12 = 128
⇒ x = 128/4
∴ x = 32

So four consecutive even numbers is- 32, 34, 36, 38

∴ next two consecutive even numbers- 40, 42
∴ sum = 40 + 42 = 82
৩,৪১৮.
Two numbers are in the ratio 5 : 8. If 3 is subtracted to the first number, the ratio becomes 1 : 2. The numbers are = ?
  1. ক
    10 and 16
  2. খ
    12 and 30
  3. গ
    11 and 27
  4. ঘ
    15 and 24
সঠিক উত্তর: ঘ
15 and 24
উত্তর
সঠিক উত্তর: ঘ
15 and 24
ঘ
ব্যাখ্যা
Question : Two numbers are in the ratio 5 : 8. If 3 is subtracted to the first number, the ratio becomes 1 : 2. The numbers are = ?

Solution :
Let,
The numbers are = 5x and 8x

∴ According to question,
⇒ (5x - 3) : 8x = 1 : 2
⇒ (5x - 3)/8x = 1/2
⇒ 2(5x - 3) = 8x
⇒ 10x - 6 = 8x
⇒ 10x - 8x = 6
⇒ 2x = 6
∴ x = 3

So,The first numbers =5x
=5×3
=15
The second number = 8x
= 8 × 3
= 24
৩,৪১৯.
3/4 part of the tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is -
  1. ক
    44 litres
  2. খ
    32 litres
  3. গ
    36 litres
  4. ঘ
    38 litres
  5. ঙ
    None of the above
সঠিক উত্তর: ঙ
None of the above
উত্তর
সঠিক উত্তর: ঙ
None of the above
ঙ
ব্যাখ্যা
Question: 3/4 part of the tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is -

Solution:
Let us consider,
The tank has 4x litres of total capacity and holds 3x litres of water.
And if 30 litres of water is taken out, then the tank becomes empty.

It means 3x litres of water is taken out.
∴ 3x = 30 litres
⇒ x = 10 litres

Capacity of tank
= 4x
= 4 × 10
= 40 liters.
৩,৪২০.
Sifat traveled 2/3 as km on foot as by water and 1/3 as km on bus as by water. If he covered a total of 48 km, how many km did km he travel on foot?
  1. ক
    ক) 8 km
  2. খ
    খ) 12 km
  3. গ
    গ) 16 km
  4. ঘ
    ঘ) 24 km
সঠিক উত্তর: গ
গ) 16 km
উত্তর
সঠিক উত্তর: গ
গ) 16 km
গ
ব্যাখ্যা
Question: Sifat traveled 2/3 as km on foot as by water and 1/3 as km on bus as by water. If he covered a total of 48 km, how many km dis he travel on foot?

Solution:
Let, he traveled x km by water, 2x/3 km on foot and x/3 km bus

ATQ,
x + (2x/3) + (x/3) = 48
⇒ (3x + 2x + x)/3 = 48
⇒ 6x = 144
⇒ x = 24

So, traveled (2 × 24)/3 = 16 km on foot.
৩,৪২১.
An outgoing pipe is attached to a tank that can empty it in 20 hours. An ingoing pipe is connected to the tank that can fill it in 8 hours. How much time will it take to fill the half-full tank?
  1. ক
    10/3 hours
  2. খ
    20/7 hours
  3. গ
    20/3 hours
  4. ঘ
    40/7 hours
সঠিক উত্তর: গ
20/3 hours
উত্তর
সঠিক উত্তর: গ
20/3 hours
গ
ব্যাখ্যা

Question: An outgoing pipe is attached to a tank that can empty it in 20 hours. An ingoing pipe is connected to the tank that can fill it in 8 hours. How much time will it take to fill the half-full tank?

Solution: 
ingoing pipe in one hour can fill = 1/8
outgoing pipe in one hour can empty = 1/20

in one hour total fill up = 1/8 - 1/20 = 3/40

to fill half the tank it will take = 40/6 = 20/3 hours.

৩,৪২২.
It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?
  1. ক
    3 times
  2. খ
    4 times
  3. গ
    5 times
  4. ঘ
    6 times
  5. ঙ
    7 times
সঠিক উত্তর: ঘ
6 times
উত্তর
সঠিক উত্তর: ঘ
6 times
ঘ
ব্যাখ্যা
Question: It takes 6 days for 3 women and 2 men working together to complete a work. 3 men would do the same work 5 days sooner than 9 women. How many times does the output of a man exceed that of a woman?

Solution:
It takes 6 days for 3 women and 2 men working together to complete a work:
As the rate of 1 woman is 1/w  job/day,
then the rate of 3 women will be 3/w job/day.

As the rate of 1 man is 1/m job/day,
then the rate of 2 men will be 2/m job/day.

Combined rate of 3 women and 2 men in one day will be: 3/w + 2/m job/day.

As they do all the job in 6 days then in 1 day they do 1/6 of the job,
which is combined rate of 3 women and 2 men ⇒ 3/w + 2/m = 1/6 ..............(1)

3 men would do the same work 5 days sooner than 9 women:
As 1 man needs m days to do the job 3 men will need m/3 days to do the job.
As 1 woman needs w days to do the job 9 women will need w/9 days to do the job.
3 men would do the same work 5 days sooner means that 3 men will need 5 less days to do the job,
hence m/3 is 5 less than w/9 ⇒ m/3 + 5 = w/9 ...................(2)

Solving (1) and (2) we get:
m = 15 and w = 90


∴ w/m = 15/90 = 1/6
∴ m = 6w
৩,৪২৩.
Gulzar is four times as old as Hashem. 10 years ago, Gulzar was 9 times as old as Hashem. What will be the sum of their ages after 6 years?
  1. ক
    92
  2. খ
    88
  3. গ
    84
  4. ঘ
    82
  5. ঙ
    None
সঠিক উত্তর: ক
92
উত্তর
সঠিক উত্তর: ক
92
ক
ব্যাখ্যা
Question: Gulzar is four times as old as Hashem. 10 years ago, Gulzar was 9 times as old as Hashem. What will be the sum of their ages after 6 years?

Solution:
Let,
The present age of Hashem is x years
∴ The present age of Gulzar is 4x years

ATQ,
4x - 10 = 9(x - 10)
⇒ 4x - 10 = 9x - 90
⇒ 5x = 80
∴ x = 16

Hashem's age after 6 years = x + 6 = 16 + 6 = 22 years
Gulzar's age after 6 years = 4x + 6 = 4 × 16 + 6 = 64 + 6 = 70 years

∴ The sum of their ages after 6 years = 70 + 22 = 92 years
৩,৪২৪.
In an army camp there was food for 150 soldiers for 30 days. But after 10 days 50 soldiers left the army. The rest of the food will last for -
  1. ক
    ক) 25 days
  2. খ
    খ) 28 days
  3. গ
    গ) 30 days
  4. ঘ
    ঘ) 32 days
সঠিক উত্তর: গ
গ) 30 days
উত্তর
সঠিক উত্তর: গ
গ) 30 days
গ
ব্যাখ্যা
Question: In an army camp there was food for 150 soldiers for 30 days. But after 10 days 50 soldiers left the army. The rest of the food will last for -

Solution: 
১০ দিন পর, ১৫০ জনের ২০ দিনের খাবার ছিল।
৫০ জন কমে যাওয়ায় এখন সৈনিক = ১৫০ -৫০ = ১০০ জন।

তাহলে, 
১৫০ জনের খাবার আছে ২০ দিনের
১ জনের আছে (২০ × ১৫০) দিনের
১০০ জনের আছে (৩০০০/১০০) দিনের
= ৩০ দিনের

Shortcut: 
ধরি, বাকি খাবারে ১০০ জনের x দিন চলবে।
150 : 100 = x : 20
100x = 3000
x = 30 days
৩,৪২৫.
Last year Parimal saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual earnings. The amount saved this year was what percent of the amount saved last year?
  1. ক
    122%
  2. খ
    124%
  3. গ
    126%
  4. ঘ
    128%
  5. ঙ
    130%
সঠিক উত্তর: গ
126%
উত্তর
সঠিক উত্তর: গ
126%
গ
ব্যাখ্যা
Question: Last year Parimal saved 10 percent of his annual earnings. This year he earned 5 percent more than last year and he saved 12 percent of his annual earnings. The amount saved this year was what percent of the amount saved last year?

Solution:
Let,
Last Year
Earnings = 100
Amount saved = 10% of 100 = 0.1 × 100 = 10

This Year
Earnings = 100 + 5% 0f 100 = 100 + (0.05 ×100) = 100 + 5 = 105
Amount saved = 12% of 105 = 0.12 × 105 = 12.6

The amount saved this year as a percent of the amount saved last year is ⇒ (this year)/(last year) × 100 = (12.6/10)× 100% =126%.
৩,৪২৬.
A man borrowed some money for 6 months. He asked the banker for the money and the banker charged Tk. 720 as interest at 6% per annum. What was the amount he borrowed?
  1. ক
    Tk. 18000
  2. খ
    Tk. 20000
  3. গ
    Tk. 24000
  4. ঘ
    Tk. 23000
সঠিক উত্তর: গ
Tk. 24000
উত্তর
সঠিক উত্তর: গ
Tk. 24000
গ
ব্যাখ্যা
Question: A man borrowed some money for 6 months. He asked the banker for the money and the banker charged Tk. 720 as interest at 6% per annum. What was the amount he borrowed?

Solution: 
এখানে 
সময় n = 6 মাস
= 6/12 বছর 
= 1/2 বছর 

মুনাফা I = 720 টাকা 
মুনাফার হার r = 6% = 6/100 = 3/50
আসল P = ?

আমরা জানি,
I = Pnr
⇒ Pnr = I
⇒ P = I/nr
= 720/{(1/2) × (3/50)}
= 720/(3/100)
= (720 × 100)/3
= 24000 টাকা 
৩,৪২৭.
A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.
  1. ক
    ক) 24300 m
  2. খ
    খ) 81 m
  3. গ
    গ) 729 m
  4. ঘ
    ঘ) 243 m
সঠিক উত্তর: ঘ
ঘ) 243 m
উত্তর
সঠিক উত্তর: ঘ
ঘ) 243 m
ঘ
ব্যাখ্যা
Question: A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

Solution:
ব্যাসার্ধ, r = 18/2 = 9 সেমি
গোলকটির আয়তন = (4/3) × π × r3
= (4/3) × π × 93
= 972π

তারটি ব্যাসার্ধ = 4/2 = 2 মিমি = 0.2 সেমি
তারটির আয়তন = πr2l
= π × (0.2)2 × l
= 0.04πl

শর্তমতে,
0.04πl = 972π
⇒ l = 972/0.04
⇒ l = 24300 cm
⇒ l = 243 m
৩,৪২৮.
Rahim is twice as fast as Karim and Karim is three times as fast as Jamal. The distance covered by Jamal in 6 hours will be covered by Rahim in how many hours?
  1. ক
    30 minutes
  2. খ
    25 minutes
  3. গ
    60 minutes
  4. ঘ
    48 minutes
  5. ঙ
    40 minutes
সঠিক উত্তর: গ
60 minutes
উত্তর
সঠিক উত্তর: গ
60 minutes
গ
ব্যাখ্যা

Question: Rahim is twice as fast as Karim and Karim is three times as fast as Jamal. The distance covered by Jamal in 6 hours will be covered by Rahim in how many hours?

Solution:
Let speed of Jamal = x
Then Speed of Karim = 3x
Then Speed of Rahim = 6x

∴ Ratio of the speed of Rahim and Jamal = 6 : 1

So, The greater the speed, the less time is taken for the journey.

Rahim’s speed is 6 times that of Jamal.
 So Rahim will take (1/6) of the total time taken by Jamal to cover the same distance.

So, Time taken by Rahim
= 6 × (1/6) hours
= 1 hour
= 60 minutes

৩,৪২৯.
A man travels 8 miles towards north, 5 miles towards east, then again 4 miles towards north. What is the direct distance of destination from the starting point?
  1. ক
    11 miles
  2. খ
    13 miles
  3. গ
    17 miles
  4. ঘ
    √105 miles
সঠিক উত্তর: খ
13 miles
উত্তর
সঠিক উত্তর: খ
13 miles
খ
ব্যাখ্যা

Question: A man travels 8 miles towards north, 5 miles towards east, then again 4 miles towards north. What is the direct distance of destination from the starting point?

Solution:

ধরি, যাত্রা শুরু করার স্থান A এবং গন্তব্যের স্থান B।
সরাসরি দূরত্ব নির্ণয় করতে, আমরা পিথাগোরাসের উপপাদ্য ব্যবহার করব।

এখানে, অতিক্রান্ত মোট উল্লম্ব (Vertical) দূরত্ব হলো (8 + 4) = 12 মাইল
এবং অতিক্রান্ত মোট অনুভূমিক (Horizontal) দূরত্ব হলো 5 মাইল।

পিথাগোরাসের সূত্রানুসারে,
AB2 = (8 + 4)2 + 52
⇒ AB2 = 122 + 52
⇒ AB2 = 144 + 25
⇒ AB2 = 169
⇒ AB = √169
∴ AB = 13 miles

∴ সরাসরি দূরত্ব 13 মাইল।

৩,৪৩০.
A tap fills a cistern in 6 hours, while another empties it in 9 hours. How much time will it take to fill the cistern if both taps are opened at once?
  1. ক
    18 hours
  2. খ
    28 hours
  3. গ
    16 hours
  4. ঘ
    10 hours
সঠিক উত্তর: ক
18 hours
উত্তর
সঠিক উত্তর: ক
18 hours
ক
ব্যাখ্যা
Question: A tap fills a cistern in 6 hours, while another empties it in 9 hours. How much time will it take to fill the cistern if both taps are opened at once?

Solution:
The cistern fill in 1 hour = (1/6) - (1/9) part
= 1/18 part

The cistern fill 1/18 part
= 1 hour

The cistern fill full = (1 × 18) /1 hour
= 18 hours
৩,৪৩১.
The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Determine how old Q is right now.
  1. ক
    25 years
  2. খ
    30 years
  3. গ
    40 years
  4. ঘ
    50 years
সঠিক উত্তর: গ
40 years
উত্তর
সঠিক উত্তর: গ
40 years
গ
ব্যাখ্যা
Question: The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Determine how old Q is right now.

Solution:
As the ratio of their present ages is 3 : 4 ,

let,
their present ages be 3X and 4X.
So, 5 years ago, as the ratio of their ages was = 5 : 7,

we can write,
(3x - 5) : (4x - 5) = 5 : 7
⇒ (3x - 5)/(4x - 5) = 5/7
⇒ 21x - 35 = 20x - 25
⇒ x = 10

∴ their present age of Q = 4X = 40
৩,৪৩২.
The volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m3. Find the breadth of the wall. 
  1. ক
    ক) 30cm
  2. খ
    খ) 40cm
  3. গ
    গ) 50cm
  4. ঘ
    ঘ) 60cm
সঠিক উত্তর: খ
খ) 40cm
উত্তর
সঠিক উত্তর: খ
খ) 40cm
খ
ব্যাখ্যা
ধরি, 
দেয়ালের প্রস্থ x মিটার 
দেয়ালের উচ্চতা  5x মিটার 
 দেয়ালের দৈর্ঘ্য হবে = (8 × 5x) মিটার
                               = 40x মিটার

 প্রশ্নমতে, 
            x × 5x × 40x =  12.8 
            x3 = 12.8/ 200 
            x3 = 0.064 
            x3  = (0.4)3
            x = 0.4
 অতএব 
        দেয়ালের প্রস্থ = 0.4 মিটার 
                              = ( 0.4 × 100)  সে.মি 
                              = 40 সে.মি
৩,৪৩৩.
What is the perimeter of a rectangular that is 24 meter wide and has the same area as another rectangle that is 64 meter long and 48 meter wide?
  1. ক
    112 meter
  2. খ
    152 meter
  3. গ
    256 meter
  4. ঘ
    304 meter
সঠিক উত্তর: ঘ
304 meter
উত্তর
সঠিক উত্তর: ঘ
304 meter
ঘ
ব্যাখ্যা
Let the length of another rectangle be y meter
According to the question,
24 × y = 64 × 48
or, y = 128
Therefore, perimeter = 2(128 + 24) meter = 304 meter
৩,৪৩৪.
A basketball team has a ratio of win to loss of 3 : 2. After winning 6 games in a row, the team's ratio of win to loss became 2 : 1. How many games had the team won before it played the last six games?
  1. ক
    10
  2. খ
    6
  3. গ
    12
  4. ঘ
    14
  5. ঙ
    18
সঠিক উত্তর: ঙ
18
উত্তর
সঠিক উত্তর: ঙ
18
ঙ
ব্যাখ্যা

Question: A basketball team has a ratio of win to loss of 3 : 2. After winning 6 games in a row, the team's ratio of win to loss became 2 : 1. How many games had the team won before it played the last six games?

Solution:
ধরি, দলটির জেতা খেলার সংখ্যা ছিল 3x
এবং হারা খেলার সংখ্যা ছিল 2x.
পরপর 6টি খেলা জেতার পর,
জেতা খেলার নতুন সংখ্যা = (3x + 6)
হারা খেলার সংখ্যা = 2x (যেহেতু কোনো খেলা হারেনি)

প্রশ্নমতে,
(3x + 6)/(2x) = 2/1
⇒ 3x + 6 = 2 × (2x)
⇒ 3x + 6 = 4x
⇒ 4x - 3x = 6
⇒ x = 6

∴ প্রথম অবস্থায় জেতা খেলার সংখ্যা ছিল 3x = 3 × 6 = 18
অতএব, শেষ 6টি খেলা খেলার আগে দলটি 18টি খেলায় জিতেছিল।

৩,৪৩৫.
The sum of three consecutive multiples of 4 is 300. What is the largest number?
  1. ক
    96
  2. খ
    100
  3. গ
    104
  4. ঘ
    108
সঠিক উত্তর: গ
104
উত্তর
সঠিক উত্তর: গ
104
গ
ব্যাখ্যা

Question: The sum of three consecutive multiples of 4 is 300. What is the largest number?

Solution: 
Let,
First multiple 4x
Second multiple 4(x + 1) = 4x + 4
Third multiple 4(x + 2) = 4x + 8

ATQ,
4x + 4x + 4 + 4x + 8 = 300
⇒ 12x + 12 = 300
⇒ 12x = 288
⇒ x = 288/12
∴ x = 24

So, largest number = 4x + 8
= (4 × 24) + 8
= 104

৩,৪৩৬.
The ratio of two numbers is 15 : 28 and their HCF is 17. Find the numbers.
  1. ক
    51, 95
  2. খ
    85, 152
  3. গ
    170, 280
  4. ঘ
    255, 476
সঠিক উত্তর: ঘ
255, 476
উত্তর
সঠিক উত্তর: ঘ
255, 476
ঘ
ব্যাখ্যা

Question: The ratio of two numbers is 15 : 28 and their HCF is 17. Find the numbers.

Solution:
Let the numbers be a and b.
Since the HCF is given as 17, we can write the numbers as:
a = 17 × 15 = 255,
b = 17 × 28 = 476

Check the ratio:
a : b = 255 : 476 =15 : 28 (justified)

৩,৪৩৭.
A train is passing a platform at 20m/s and a man is walking at 2m/s in the opposite direction. It took 10 sec for the train to cross the man. What is the length of the train?
  1. ক
    220m
  2. খ
    200m
  3. গ
    110m
  4. ঘ
    180m
সঠিক উত্তর: ক
220m
উত্তর
সঠিক উত্তর: ক
220m
ক
ব্যাখ্যা
Question: A train is passing a platform at 20m/s and a man is walking at 2m/s in the opposite direction. It took 10 sec for the train to cross the man. What is the length of the train?

Solution: 
as they are going opposite,
resultant speed is = (20 + 2) m/s
= 22 m/s

the length of the train is = 22 × 10 = 220m
৩,৪৩৮.
  1. ক
    45
  2. খ
    81
  3. গ
    405
  4. ঘ
    25
সঠিক উত্তর: ঘ
25
উত্তর
সঠিক উত্তর: ঘ
25
ঘ
ব্যাখ্যা
Question:


Solution:

৩,৪৩৯.

In the figure above, what is the value of x?
  1. ক
    50°
  2. খ
    70°
  3. গ
    80°
  4. ঘ
    90°
  5. ঙ
    100°
সঠিক উত্তর: গ
80°
উত্তর
সঠিক উত্তর: গ
80°
গ
ব্যাখ্যা
Question:

In the figure above, what is the value of x?

Solution:

Let us assume that the remaining one interior angle of the quadrilateral measures y,

Also, we know that the sum of all the interior angles of a quadrilateral = 360°

∴ 50° + 120° + 90° + y = 360°
⇒ y = 360° - 260° = 100°

Since, x and y are straight angles, So,
x + y = 180°
⇒ x + 100° = 180°
⇒ x = 80°
৩,৪৪০.
A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
  1. ক
    ক) 240 meters
  2. খ
    খ) 260 meters
  3. গ
    গ) 140 meters
  4. ঘ
    ঘ) 220 meters
সঠিক উত্তর: ক
ক) 240 meters
উত্তর
সঠিক উত্তর: ক
ক) 240 meters
ক
ব্যাখ্যা
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

Solution:
Speed = (54 × 1000)/3600 
= 15 m/sec

Length of the train = (15 × 20) m = 300 m
Let
the length of the platform be x meters.

Then,
(x + 300)/36 = 15
⇒ x + 300 = 540
∴ x = 240 meters
৩,৪৪১.
If secA + tanA = 5/2, what is the value of (secA - tanA)?
  1. ক
    5/2
  2. খ
    1/5
  3. গ
    3/5
  4. ঘ
    2/5
সঠিক উত্তর: ঘ
2/5
উত্তর
সঠিক উত্তর: ঘ
2/5
ঘ
ব্যাখ্যা
Question: If secA + tanA = 5/2, what is the value of (secA - tanA)?

Solution:
Given that
secA + tanA = 5/2
Or, 1/(secA + tanA) = 2/5
Or, (sec2A - tan2A)/(secA + tanA) = 2/5
Or, (secA + tanA)(secA - tanA)/(secA + tanA) = 2/5
∴ secA - tanA = 2/5
৩,৪৪২.
The speed of a motor-boat is that of the current of water as 36:5. The boat goes along with the current in 5 hours 10 minutes. When will it come back?
  1. ক
    5 hours 50 minutes
  2. খ
    6 hours 50 minutes
  3. গ
    12 hours 10 minutes
  4. ঘ
    6 hours 5 minutes
  5. ঙ
    10 hours 5 minutes
সঠিক উত্তর: খ
6 hours 50 minutes
উত্তর
সঠিক উত্তর: খ
6 hours 50 minutes
খ
ব্যাখ্যা
Let the speed of the motor boat = 36x kmph and
speed of current = 5x kmph.

The boat goes along with the current in 5 hours 10 minutes
= 31/6 hour.

Hence, Distance = 31/6 × (36x + 5x)
= 31/6 × 41x

Speed of boat upstream
= 36x - 5x
= 31x
Hence, time taken to come back
= 31/6 × 41x / 31x
= 41/6 hours
= 6 hours 50 minutes
৩,৪৪৩.
A car washer machine can wash 8 cars in 18 minutes. How many cars can be washed at the same rate in 3 hours?
  1. ক
    ক) 54
  2. খ
    খ) 72
  3. গ
    গ) 80
  4. ঘ
    ঘ) 87
  5. ঙ
    ঙ) 96
সঠিক উত্তর: গ
গ) 80
উত্তর
সঠিক উত্তর: গ
গ) 80
গ
ব্যাখ্যা

In 18 minutes a car washer can wash 8 cars
In 1 minutes the car washer can wash 8/18 cars
So, in 3 hrs (180 minutes) car washer can wash = (8×180)/18 = 80 cars

৩,৪৪৪.
A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 50 meters, and the speed of the train is 45 km/hr. In 4 hours, how many pillars will he count?
  1. ক
    3601
  2. খ
    3575
  3. গ
    3650
  4. ঘ
    3500
সঠিক উত্তর: ক
3601
উত্তর
সঠিক উত্তর: ক
3601
ক
ব্যাখ্যা

Question: A man sitting in a train is counting the pillars of electricity. The distance between two pillars is 50 meters, and the speed of the train is 45 km/hr. In 4 hours, how many pillars will he count?

Solution:
Distance covered by the train in 4 hours = (Speed × Time)
= (45 × 4) km
= 180 km
= 180000 m

∴ Number of pillars counted by the man = (180000/50) + 1
= (3600 + 1)
= 3601

৩,৪৪৫.
If the number of boys in a class is 8 times the number of girls, which value can never be the total number of students?
  1. ক
    42
  2. খ
    81
  3. গ
    27
  4. ঘ
    45
সঠিক উত্তর: ক
42
উত্তর
সঠিক উত্তর: ক
42
ক
ব্যাখ্যা

Let the number of girls = x
number of boys = 8x
Then, total number of students = x + 8x
= 9x
i.e., The total number of students must be a multiple of 9. In the given choices, 42 is not a multiple of 9
Hence, the total number of students cannot be 42.

৩,৪৪৬.
A barrack has enough food for 150 soldiers or 300 sailors. If 120 sailors have already taken the food, how many soldiers can be fed with the remaining food? 
  1. ক
    115
  2. খ
    100
  3. গ
    120
  4. ঘ
    90
সঠিক উত্তর: ঘ
90
উত্তর
সঠিক উত্তর: ঘ
90
ঘ
ব্যাখ্যা

Question: A barrack has enough food for 150 soldiers or 300 sailors. If 120 sailors have already taken the food, how many soldiers can be fed with the remaining food?

Solution:
এখানে,
300 জন নাবিকের খাবার = 150 জন সৈন্যের খাবার।

মোট নাবিক যাদের জন্য খাবার ছিল = 300 জন।
খাবার গ্রহণ করেছে = 120 জন।
অবশিষ্ট খাবার = (300 - 120) জন নাবিকের খাবার
= 180 জন নাবিকের খাবার।

এখন,
300 জন নাবিকের খাবার = 150 জন সৈন্যের খাবার।
∴ 1 জন নাবিকের খাবার = (150/300) জন সৈন্যের খাবার।
∴ 180 জন নাবিকের খাবার = (150 × 180)/300
= (1/2) × 180
= 90 জন সৈন্যের খাবার।

সুতরাং, অবশিষ্ট খাবার দিয়ে 90 জন সৈন্যকে দেওয়া যাবে।

৩,৪৪৭.
Jack takes 20 minutes to jog around the race course one time, and 25 minutes to jog around a second time. What is his average speed in miles per hour for the whole jog if the course is 3 miles long?
  1. ক
    6
  2. খ
    8
  3. গ
    9
  4. ঘ
    10
  5. ঙ
    None of the above
সঠিক উত্তর: খ
8
উত্তর
সঠিক উত্তর: খ
8
খ
ব্যাখ্যা

Average speed = total distance / total time
Total distance covered = 6 miles; total time = 45 minutes = 0.75 hours
Average speed = 6/ 0.75 = 8 miles/hour

৩,৪৪৮.
How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?
  1. ক
    ক) 30
  2. খ
    খ) 28
  3. গ
    গ) 20
  4. ঘ
    ঘ) 24
সঠিক উত্তর: গ
গ) 20
উত্তর
সঠিক উত্তর: গ
গ) 20
গ
ব্যাখ্যা
Question: How many litres of a 30% alcohol solution should be added to 40 litres of a 60% alcohol solution to prepare a 50% solution?

Solution:
Let,
x litres of 30% alcohol solution be added.

ATQ,
30% of x + 60% of 40 = 50% of (x + 40)
⇒ (30x/100) + (60 × 40)/100 = 50 × (x + 40)/100
⇒ (30x + 2400)/100 = (50x + 2000)/100
⇒ 30x + 2400 = 50x + 2000
⇒ 50x - 30x = 2400 - 2000
⇒ 20x = 400
∴ x = 20
৩,৪৪৯.
If A invests Tk 5,000 for 12 months and B invests Tk 6,000 for 10 months, what is the ratio of their profits?
  1. ক
    5 : 6
  2. খ
    1 : 1
  3. গ
    1 : 2
  4. ঘ
    1 : 1.2
সঠিক উত্তর: খ
1 : 1
উত্তর
সঠিক উত্তর: খ
1 : 1
খ
ব্যাখ্যা
Question: If A invests Tk 5,000 for 12 months and B invests Tk 6,000 for 10 months, what is the ratio of their profits?

Solution:
We know, profit = (investment × time)
A has a profit of 5,000 × 12 = 60,000
B has a profit of  6,000 × 10 = 60,000
∴ So ratio of A's profit to B's profit = 60,000 : 60,000 = 1 : 1
৩,৪৫০.
Half percent, written as a decimal, is -
  1. ক
    ক) 0.5
  2. খ
    খ) 0.05
  3. গ
    গ) 0.005
  4. ঘ
    ঘ) 0.0005
সঠিক উত্তর: গ
গ) 0.005
উত্তর
সঠিক উত্তর: গ
গ) 0.005
গ
ব্যাখ্যা
Question: Half percent, written as a decimal, is - 

Solution:
As we know,
1% = 1/100

Hence,
1/2% = 1/2 × 1/100 = 1/200 = 0.005
৩,৪৫১.
What is the smallest 5-digit number that can be formed using the digits 0, 1, 4, 6, and 9, where digits may repeat?
  1. ক
    01469
  2. খ
    10469
  3. গ
    90146
  4. ঘ
    10000
সঠিক উত্তর: ঘ
10000
উত্তর
সঠিক উত্তর: ঘ
10000
ঘ
ব্যাখ্যা
Question: What is the smallest 5-digit number that can be formed using the digits 0, 1, 4, 6, and 9, where digits may repeat?

Solution:
If we arrange the digits 0, 1, 4, 6, 9 in ascending order, we get the smallest number.

The smallest non-zero digit is 1.
Digits like 4, 6, 9 are larger than 1 and 0.

By using 1 once and 0 multiple times, the smallest 5-digit number that can be formed is =  10000.
৩,৪৫২.
(√1372 + √959) ÷ √292 × 19.003 = ?
  1. ক
    ক) 77
  2. খ
    খ) 97
  3. গ
    গ) 39
  4. ঘ
    ঘ) 19
সঠিক উত্তর: ক
ক) 77
উত্তর
সঠিক উত্তর: ক
ক) 77
ক
ব্যাখ্যা
(√1372 + √959) ÷ √292 × 19.003
= (37.04 + 30.96) ÷  17 × 19.003
= 68  ÷ 17 × 19.003
= 4 × 19.003 = 76.012 ≈ 77
৩,৪৫৩.
List price of a book is Tk. 100. A dealer sells three such books for Tk. 274.50 after allowing discount at a certain rate, find the rate of discount = ?
  1. ক
    ক) 8.33%
  2. খ
    খ) 8.16%
  3. গ
    গ) 8.50%
  4. ঘ
    ঘ) 8.34%
সঠিক উত্তর: গ
গ) 8.50%
উত্তর
সঠিক উত্তর: গ
গ) 8.50%
গ
ব্যাখ্যা

Given,
= MRP of book = Tk. 100
= Selling price of 3 books = Tk. 274.50
= Selling price of 1 book = Tk. 91.50
Discount on each book
= 100 - 91.50 = Tk. 8.50
Therefore discount %
=8.50/100×100%
=8.50%

৩,৪৫৪.
How many permutations of the letters of the word 'APPLE' are there?
  1. ক
    ক) 20
  2. খ
    খ) 30
  3. গ
    গ) 60
  4. ঘ
    ঘ) 120
সঠিক উত্তর: গ
গ) 60
উত্তর
সঠিক উত্তর: গ
গ) 60
গ
ব্যাখ্যা
APPLE = 5 letters.
But two letters PP is of same kind.
Thus, required permutations,
= 5!/2!
= 120/2
= 60
৩,৪৫৫.
A man works twice as much as his assistant. The man can finish the job in 9 days. Find the number of days in which the man and his assistant can finish the job if they work together? 
  1. ক
    ক) 6 days 
  2. খ
    খ) 8 days 
  3. গ
    গ) 12 days 
  4. ঘ
    ঘ) 15 days 
সঠিক উত্তর: ক
ক) 6 days 
উত্তর
সঠিক উত্তর: ক
ক) 6 days 
ক
ব্যাখ্যা
Question: A man works twice as much as his assistant. The man can finish the job in 9 days. Find the number of days in which the man and his assistant can finish the job if they work together? 

Solution: 
Since, Man works twice as much as his assistant 
Assistant can do the work in (2 × 9) days = 18 days 
A man can do in 1 day = 1/9 part
Assistant can do in 1 day = 1/18 part 
They together can do in 1 day = (1/9) + (1/18) = 3/18 = 1/6 part 
They can do the job in = 1/(1/6) days = 6 days 
৩,৪৫৬.
If x + 1/x = 7, find the value of 3x/(x2 - 6x + 1)
  1. ক
    1
  2. খ
    3
  3. গ
    0
  4. ঘ
    - 2
সঠিক উত্তর: খ
3
উত্তর
সঠিক উত্তর: খ
3
খ
ব্যাখ্যা
Question: If x + 1/x = 7, find the value of 3x/(x2 - 6x + 1)

Solution:
Given,
x + 1/x = 7
⇒ (x2 + 1)/x = 7
∴ x2 + 1 = 7x

Now,
3x/(x2 - 6x + 1)
= 3x/(x2 + 1 - 6x)
= 3x/(7x - 6x)
= 3x/x
= 3
৩,৪৫৭.
A trapezium has a total area of 25 square feet. if the height of this trapezium is 2 feet and one of the two parallel sides is one foot longer than the other. What is the length of the longer side?
  1. ক
    ক) 10 Feet
  2. খ
    খ) 12 Feet
  3. গ
    গ) 13 Feet
  4. ঘ
    ঘ) 25 Feet
  5. ঙ
    ঙ) None
সঠিক উত্তর: গ
গ) 13 Feet
উত্তর
সঠিক উত্তর: গ
গ) 13 Feet
গ
ব্যাখ্যা

We know, Area of trapezium = 1/2(a + b)h
let the length of parallel side = x and x + 1
ATQ, 1/2(x + x + 1)2 = 25
⇒ 2x = 25 - 1
⇒ x = 12
∴ length of the longer side = 12 + 1 = 13 feet

৩,৪৫৮.
A leak in the bottom of a tank can empty the whole tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened, and due to the leak, the tank is empty in 12 hours. How many liters does the tank hold? 
  1. ক
    6840 liters
  2. খ
    8290 liters
  3. গ
    8640 liters
  4. ঘ
    6890 liters
সঠিক উত্তর: গ
8640 liters
উত্তর
সঠিক উত্তর: গ
8640 liters
গ
ব্যাখ্যা
Question: A leak in the bottom of a tank can empty the whole tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened, and due to the leak, the tank is empty in 12 hours. How many liters does the tank hold? 

Solution:
Work done by the inlet pipe in 1 hour = (1/8 - 1/12) = (3 - 2)/24 = 1/24
Work done by the inlet pipe in 1 minute = (1/24 × 1/60) = 1/1440

 Volume of 1/1440 part = 6 liters
 Volume of the whole tank = (1440 × 6) = 8640 liters
৩,৪৫৯.
In a box, there are 4 red, 5 blue and 7 green balls. One ball is picked up randomly. What is the probability that it is neither red nor blue?
  1. ক
    1/8
  2. খ
    1/16
  3. গ
    7/8
  4. ঘ
    7/16
সঠিক উত্তর: ঘ
7/16
উত্তর
সঠিক উত্তর: ঘ
7/16
ঘ
ব্যাখ্যা

Question: In a box, there are 4 red, 5 blue and 7 green balls. One ball is picked up randomly. What is the probability that it is neither red nor blue?

Solution: 
 
মোট বলের সংখ্যা, n(S) = 4 + 5 + 7
= 16

ধরি, লাল বা নীল না হওয়ার সম্ভাবনা = P(E)
সবুজ হওয়ার সম্ভাবনা = n(G) = 7

∴ লাল বা নীল না হওয়ার সম্ভাবনা = P(E) 
= n(G)/n(S)
= 7/16

৩,৪৬০.
Three individuals contributed Tk. 9000 each toward the purchase of television. If they bought the television on sale for Tk. 22000 plus 8% sales tax, how much money should be refunded to each individual?
  1. ক
    Tk 1080
  2. খ
    Tk 880
  3. গ
    Tk 700
  4. ঘ
    Tk 1200
সঠিক উত্তর: ক
Tk 1080
উত্তর
সঠিক উত্তর: ক
Tk 1080
ক
ব্যাখ্যা
Question: Three individuals contributed Tk. 9000 each toward the purchase of television. If they bought the television on sale for Tk. 22000 plus 8% sales tax, how much money should be refunded to each individual?

Solution:
Three individuals contributed Tk 9000 each,
So the total contribution of=  9000 × 3 = 27000

∴ The sales tax is 8% of Tk 22000 is = 22000 × (8/100) = 1760

∴  The total cost of the television, including tax, is
= 22000 +1760
= 23760

∴  Excess Money = 27000 − 23760 = 3240
∴  Refund per individual = 3240​/3 = 1080

So Each individual should be refunded Tk 1080.
৩,৪৬১.
A boat running downstream covers a distance of 40 km in 4 hours, while covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?
  1. ক
    8 km/hr
  2. খ
    6.5 km/hr
  3. গ
    7 km/hr
  4. ঘ
    9 km/hr
সঠিক উত্তর: ঘ
9 km/hr
উত্তর
সঠিক উত্তর: ঘ
9 km/hr
ঘ
ব্যাখ্যা

Question: A boat running downstream covers a distance of 40 km in 4 hours, while covering the same distance upstream, it takes 5 hours. What is the speed of the boat in still water?

Solution:
স্রোতের অনুকূলে নৌকার গতিবেগ (Downstream Rate):
= অতিক্রান্ত দূরত্ব/সময়
= 40 কিমি/4 ঘন্টা
= 10 কিমি/ঘন্টা

স্রোতের প্রতিকূলে নৌকার গতিবেগ (Upstream Rate):
= অতিক্রান্ত দূরত্ব/সময়
= 40 কিমি/5 ঘন্টা
= 8 কিমি/ঘন্টা

স্থির পানিতে নৌকার গতিবেগ = (স্রোতের অনুকূলে গতিবেগ + স্রোতের প্রতিকূলে গতিবেগ)/2
= (10 + 8)/2 কিমি/ঘন্টা
= 18/2 কিমি/ঘন্টা
= 9 কিমি/ঘন্টা

সুতরাং, স্থির পানিতে নৌকাটির গতিবেগ হলো 9 কিমি/ঘন্টা।

৩,৪৬২.
Solve the equation x2 + 4x - 5 = 0.
  1. ক
    5, 1
  2. খ
    5, - 1
  3. গ
    - 5, 1
  4. ঘ
    - 5, - 1
সঠিক উত্তর: গ
- 5, 1
উত্তর
সঠিক উত্তর: গ
- 5, 1
গ
ব্যাখ্যা
Question: Solve the equation x2 + 4x - 5 = 0.

Solution:
x2 + 4x - 5 = 0
⇒ x2 - 1x + 5x - 5 = 0
⇒ x(x - 1) + 5(x - 1) = 0
⇒ (x - 1)(x + 5) = 0
Hence, (x - 1) = 0, and (x + 5) =0
⇒ x - 1 = 0
∴ x = 1

similarly, x + 5 = 0
∴ x = - 5.

Therefore,
x = - 5 & x = 1
৩,৪৬৩.
3/4 part of the tank is full of water. When 30 litres of water is taken out, the tank becomes empty. The capacity of the tank is -
  1. ক
    ক) 36 litres
  2. খ
    খ) 42 litres
  3. গ
    গ) 40 litres
  4. ঘ
    ঘ) 32 litres
সঠিক উত্তর: গ
গ) 40 litres
উত্তর
সঠিক উত্তর: গ
গ) 40 litres
গ
ব্যাখ্যা

If the tank has 4x liters of total capacity and holds 3x liters of water and if 30 liters of water is taken out, then the tank becomes empty.
It means 3x liters of water is taken out
3x = 30 liters
x = 10 liters
Capacity of tank
= 4x
= 4 × 10
= 40 liters.

৩,৪৬৪.
Three angles of a triangle are in proportion 3 : 4 : 5. Then what is the difference in degrees between the biggest and the smallest angles?
  1. ক
    ক) 25°
  2. খ
    খ) 15°
  3. গ
    গ) 20°
  4. ঘ
    ঘ) 30°
সঠিক উত্তর: ঘ
ঘ) 30°
উত্তর
সঠিক উত্তর: ঘ
ঘ) 30°
ঘ
ব্যাখ্যা
We know that, Sum of 3 angles of a triangle is 180°
Here, Sum of the ratios are = 3+4+5 = 12
The larger angle = 180° × 5/12 = 75°
And, the smaller angle = 180° × 3/12 = 45°

Difference between the biggest and smallest angel = 75° - 45° = 30°
৩,৪৬৫.
Find the greatest number that will divide 964, 1238 and 1400 leaving remainders 41, 31 and 51 respectively.
  1. ক
    71
  2. খ
    75
  3. গ
    79
  4. ঘ
    81
সঠিক উত্তর: ক
71
উত্তর
সঠিক উত্তর: ক
71
ক
ব্যাখ্যা

Question: Find the greatest number that will divide 964, 1238 and 1400 leaving remainders 41, 31 and 51 respectively.

Solution:
If a number divides the given numbers with the mentioned remainders, then
964 - 41 = 923
1238 - 31 = 1207
1400 - 51 = 1349

Required number:
= HCF of (964 - 41), (1238 - 31) and (1400 - 51)
HCF of 923, 1207 and 1349 = 71

৩,৪৬৬.
A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 4 cm to form a cone. What is the volume of the cone so formed?
  1. ক
    12π cm3
  2. খ
    16π cm3
  3. গ
    14π cm3
  4. ঘ
    10π cm3
সঠিক উত্তর: ক
12π cm3
উত্তর
সঠিক উত্তর: ক
12π cm3
ক
ব্যাখ্যা
Question: A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side of 4 cm to form a cone. What is the volume of the cone so formed?

Solution:

Given that, radius, r = 3 cm and height, h = 4 cm
Therefore, volume, V = (1/3) × πr2h
= (1/3) × π × 32 × 4
= 12π cm3
৩,৪৬৭.
Three pipes A, B, and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours, B fills the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank?
  1. ক
    6 hours 40 minutes to empty
  2. খ
    6 hours 40 minutes to fill
  3. গ
    6 hours 30 minutes to empty
  4. ঘ
    6 hours 30 minutes to fill
  5. ঙ
    6 hours 20 minutes to fill
সঠিক উত্তর: খ
6 hours 40 minutes to fill
উত্তর
সঠিক উত্তর: খ
6 hours 40 minutes to fill
খ
ব্যাখ্যা
Question: Three pipes A, B, and C are connected to a tank. Out of the three, A and B are the inlet pipes and C is the outlet pipe. If opened separately, A fills the tank in 10 hours, B fills the tank in 12 hours and C empties the tank in 30 hours. If all three are opened simultaneously, how much time does it take to fill / empty the tank?

Solution:
Part of tank filled by pipe A in one hour working alone = 1/10
Part of tank filled by pipe B in one hour working alone = 1/12
Part of tank emptied by pipe C in one hour working alone = 1/30

Part of tank filled by pipes A, B and C in one hour working together = (1/10) + (1/12) - (1/30) = (6 + 5 - 2)/60 = 9/60 = 3/20
Therefore, time taken to completely fill the tank if A, B and C work together = 20/3 hours = 6 hours 40 minutes
৩,৪৬৮.
The present ages of Kamal and Jamal are in the ratio 5 : 7. After 8 years, the ratio of their ages will be 3 : 4. What is the difference in their present ages?
  1. ক
    8 years
  2. খ
    12 years
  3. গ
    10 years
  4. ঘ
    16 years
সঠিক উত্তর: ঘ
16 years
উত্তর
সঠিক উত্তর: ঘ
16 years
ঘ
ব্যাখ্যা

Question: The present ages of Kamal and Jamal are in the ratio 5 : 7. After 8 years, the ratio of their ages will be 3 : 4. What is the difference in their present ages?

Solution:
Let, their present ages be 5x and 7x.
After 8 years,
Kamal's age = 5x + 8
Jamal's age = 7x + 8

According to the question,
(5x + 8)/(7x + 8) = 3/4
⇒ 4(5x + 8) = 3(7x + 8)
⇒ 20x + 32 = 21x + 24
⇒21x - 20x = 32 - 24
∴ x = 8

Kamal's Present age = 5 × 8 = 40 years
Jamal's Present age = 7 × 8 = 56 years

∴ Difference = 56 - 40 = 16 years

৩,৪৬৯.
What is the greatest prime factor of (24)2 - 1 ?
  1. ক
    ক) 3
  2. খ
    খ) 5
  3. গ
    গ) 11
  4. ঘ
    ঘ) 17
সঠিক উত্তর: ঘ
ঘ) 17
উত্তর
সঠিক উত্তর: ঘ
ঘ) 17
ঘ
ব্যাখ্যা

Question: What is the greatest prime factor of (24)2 - 1 ?

Solution:
 (24)2 - 1
= (24 - 1)(24 + 1)
= (16 + 1)(16 - 1)
= 17 × 15
= 3 × 5 × 17  

বৃহত্তম মৌলিক উৎপাদক হলো = 17  

৩,৪৭০.
If the ratio of simple interest and principal is 8 : 25/2 and rate of interest is equal to the time invested then find the time of investment?
  1. ক
    ক) 12 years
  2. খ
    খ) 8 years
  3. গ
    গ) 10 years
  4. ঘ
    ঘ) 16 years
সঠিক উত্তর: খ
খ) 8 years
উত্তর
সঠিক উত্তর: খ
খ) 8 years
খ
ব্যাখ্যা
সরল সুদ  ও আসলের অনুপাত  8 : 25/2
ধরি 
 n বছরের জন্য বিনিয়োগ করা হয়েছিল  

আমরা জানি 
সরল সুদ I =  prn/100
         ⇒ (25 × n × n)/(2×100 ) = 8 
         ⇒  n2 = (8 ×2×100)/25 
         ⇒ n2 = 64 
         ⇒ n = √64 
          ∴ n = 8
৩,৪৭১.
To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?
  1. ক
    20 days
  2. খ
    25 days
  3. গ
    30 days
  4. ঘ
    33 days
  5. ঙ
    35 days
সঠিক উত্তর: গ
30 days
উত্তর
সঠিক উত্তর: গ
30 days
গ
ব্যাখ্যা
Question: To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:
Let
B takes x days to complete the work
Then A will take 50% more i.e 150% of x days i.e 3/2x days.

So the one day work of A and B together will be
(1/x) + {1/(3/2x)} = 1/18
⇒ (1/x) + (2/3x) = 1/18
⇒ 5/3x = 1/18
⇒ x = 30

∴ B takes 30 days to complete the work.
৩,৪৭২.
When a person weighing 60 kg leaves a group of 50 people, the average weight of the remaining people increases by 0.3 kg. What is the new average weight of the remaining 49 people?
  1. ক
    60 kg
  2. খ
    65 kg
  3. গ
    68 kg
  4. ঘ
    75 kg
  5. ঙ
    None
সঠিক উত্তর: ঘ
75 kg
উত্তর
সঠিক উত্তর: ঘ
75 kg
ঘ
ব্যাখ্যা
Question: When a person weighing 60 kg leaves a group of 50 people, the average weight of the remaining people increases by 0.3 kg. What is the new average weight of the remaining 49 people?

Solution:
let,
The average weight of 49 people is x kg
Total weight of 49 people = 49x
Total weight of 50 people = 49x + 60

ATQ,
50(x - 0.3) = (49x + 60)
⇒ 50x - 15 = 49x + 60
⇒ 50x - 49x = 60 + 15
∴ x = 75

∴ the new average weight of the remaining 49 people is 75 kg.
৩,৪৭৩.
If angle B of isosceles triangle ABC is a right angle, what is the tangent of angle A?
  1. ক
    ক) 0
  2. খ
    খ) 1
  3. গ
    গ) 1/2
  4. ঘ
    ঘ) 1/√3
সঠিক উত্তর: খ
খ) 1
উত্তর
সঠিক উত্তর: খ
খ) 1
খ
ব্যাখ্যা
∠B = 90°
ABC সমদ্বিবাহু ত্রিভুজ 
∠A + ∠C = 90°
∠A =45°, ∠C =45°

tanA = tan45° = 1
৩,৪৭৪.
Find the value of n, if 81{n - (1/2)} = 729
  1. ক
    0
  2. খ
    -1
  3. গ
    1
  4. ঘ
    2
  5. ঙ
    -2
সঠিক উত্তর: ঘ
2
উত্তর
সঠিক উত্তর: ঘ
2
ঘ
ব্যাখ্যা
Question: Find the value of n, if 81{n - (1/2)} = 729

Solution:
81{n - (1/2)} = 729
⇒ (34){n - (1/2)} = 36
⇒ 3(4n - 2) = 36
⇒ 4n - 2 = 6
⇒ 4n = 6 + 2
⇒ 4n = 8
∴ n = 2
৩,৪৭৫.
The area of a triangle is 216 cm2 and sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is-
  1. ক
    66 cm
  2. খ
    72 cm
  3. গ
    78 cm
  4. ঘ
    82 cm
সঠিক উত্তর: খ
72 cm
উত্তর
সঠিক উত্তর: খ
72 cm
খ
ব্যাখ্যা
Question: The area of a triangle is 216 cm2 and sides are in the ratio 3 : 4 : 5. The perimeter of the triangle is- 

Solution: 
32 + 42 = 52 
It is a right-angled triangle.
let, the sides 3x, 4x, 5x

(1/2) × 3x × 4x = 216 
⇒ 12x2 = 432 
⇒ x2 = 36 
⇒ x = 6

perimeter = (3 × 6) + (4 × 6) + (4 × 6)
= 72 cm
৩,৪৭৬.
A leak in the bottom of a tank can empty the whole tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened, and due to the leak, the tank is empty in 12 hours. How many liters does the tank hold? 
  1. ক
    8650 liters
  2. খ
    6840 liters
  3. গ
    8460 liters
  4. ঘ
    8640 liters
সঠিক উত্তর: ঘ
8640 liters
উত্তর
সঠিক উত্তর: ঘ
8640 liters
ঘ
ব্যাখ্যা
Question: A leak in the bottom of a tank can empty the whole tank in 8 hours. An inlet pipe fills water are the rate of 6 liters a minute. When the tank is full, the inlet is opened, and due to the leak, the tank is empty in 12 hours. How many liters does the tank hold? 

Solution:
Work done by the inlet pipe in 1 hour = (1/8 - 1/12) = (3 - 2)/24 = 1/24
Work done by the inlet pipe in 1 minute = (1/24 × 1/60) = 1/1440

 Volume of 1/1440 part = 6 liters
 Volume of the whole tank = (1440 × 6) = 8640 liters
৩,৪৭৭.
A circle of radius 14cm is divided into 8 equal sectors. Find the area of each sector.
  1. ক
    ক) 12cm2
  2. খ
    খ) 24cm2
  3. গ
    গ) 48cm2
  4. ঘ
    ঘ) 77cm2
সঠিক উত্তর: ঘ
ঘ) 77cm2
উত্তর
সঠিক উত্তর: ঘ
ঘ) 77cm2
ঘ
ব্যাখ্যা
দেয়া আছে 
বৃত্তের ব্যাসার্ধ r = 14 cm 
বৃত্তের ক্ষেত্রফল = πr2 = (22/7) × 142  = (22/7) × 196 = 616 cm2
যেহেতু 
বৃত্তটি ৮ টি সমান ভাগে বিভক্ত 
বৃত্তের প্রতিটি ভাগের ক্ষেত্রফল = 616/8 = 77 cm2
৩,৪৭৮.
Rahim finishes 40% of a task in 10 days. He then asks Karim to help and together they complete the remaining work in 10 days. How many days would Karim take to complete the whole task alone?
  1. ক
    24 days
  2. খ
    30 days
  3. গ
    42 days
  4. ঘ
    50 days
সঠিক উত্তর: ঘ
50 days
উত্তর
সঠিক উত্তর: ঘ
50 days
ঘ
ব্যাখ্যা

Question: Rahim finishes 40% of a task in 10 days. He then asks Karim to help and together they complete the remaining work in 10 days. How many days would Karim take to complete the whole task alone?

Solution:
রহিম 40% বা 2/5 অংশ কাজ করে 10 দিনে।
∴ রহিম 1 দিনে কাজ করে = (2/5) ÷ 10 = 1/25 অংশ
∴ রহিম শেষ 10 দিনেও কাজ করেছে = 10 × (1/25) = 2/5 অংশ

মোট কাজ বাকি ছিল = 1 - 2/5 = 3/5 অংশ
এই 3/5 অংশ কাজের মধ্যে রহিম করেছে 2/5 অংশ
বাকি কাজ টুকু করিম করেছে = 3/5 - 2/5 = 1/5 অংশ

করিম 1/5 অংশ কাজ করে = 10 দিনে
∴ করিম সম্পূর্ণ (1 অংশ) কাজ একা করতে সময় নেবে = 10 × 5 দিন
= 50 দিন

৩,৪৭৯.
The price of a motorbike is 1,50,000. How much do you need to pay if you get a 10% discount?
  1. ক
    Tk. 135000
  2. খ
    Tk. 140000
  3. গ
    Tk. 155000
  4. ঘ
    Tk. 165000
সঠিক উত্তর: ক
Tk. 135000
উত্তর
সঠিক উত্তর: ক
Tk. 135000
ক
ব্যাখ্যা
Question: The price of a motorbike is 1,50,000. How much do you need to pay if you get a 10% discount?

Solution:
For 10% discount,
Original price 100 paid price 90
∴ Original price 1 paid price 90/100
∴ Original price 150000 paid price (90 × 150000)/100
= 135000
৩,৪৮০.
A rectangular fish tank 25m by 9m has water in it to a level of 2m. This water is carefully poured into a cylindrical container with a diameter of 10m. How high will the water reach in the cylindrical container?
  1. ক
    ক) 18π
  2. খ
    খ) 18/π
  3. গ
    গ) π/18
  4. ঘ
    ঘ) 9/2π
সঠিক উত্তর: খ
খ) 18/π
উত্তর
সঠিক উত্তর: খ
খ) 18/π
খ
ব্যাখ্যা

The volume of the fish tank = 25×9×2 = 450 m3
Let height of the cylindrical container is = h
So, πr2h = 450
⇒ h = 450/πr2
= 450/π52 [As, Diameter of the cylinder is 10 m, so its radius is 5 m]
= 18/π

৩,৪৮১.
If 43x + 5 = 1/16x + 1, Find the value of x.
  1. ক
    - 2
  2. খ
    5/3
  3. গ
    4
  4. ঘ
    - 7/5
সঠিক উত্তর: ঘ
- 7/5
উত্তর
সঠিক উত্তর: ঘ
- 7/5
ঘ
ব্যাখ্যা

Question: If 43x + 5 = 1/16x + 1, Find the value of x.

Solution
43x + 5 = 1/16x + 1
⇒ 22(3x + 5) = 1/24(x + 1)
⇒ 26x + 10 = 2- 4(x + 1)
⇒ 6x + 10 = - 4(x + 1)
⇒ 6x + 10 = - 4x - 4
⇒ 6x + 4x = - 4 - 10
⇒ 10x = - 14
⇒ x = - 14/10
∴ x = - 7/5

৩,৪৮২.
When a diagonal of a square is 24 cm then find out of its perimeter.
  1. ক
    36√2 cm
  2. খ
    12√2 cm
  3. গ
    52√2 cm
  4. ঘ
    48√2 cm
সঠিক উত্তর: ঘ
48√2 cm
উত্তর
সঠিক উত্তর: ঘ
48√2 cm
ঘ
ব্যাখ্যা

Question: When a diagonal of a square is 24 cm then find out of its perimeter.

solution:
Given that,
Diagonal of the square = 24 cm

We know, 
Diagonal of the square, d = √2 × a
a = d/√2 = 24/√2 = 12√2 
∴ a = 12√2 

∴ Perimeter of square = 4a = 4 × 12√2 = 48√2 cm

৩,৪৮৩.
Through what angle does the minute hand of a clock turn in 12 minutes?
  1. ক
    60°
  2. খ
    72°
  3. গ
    75°
  4. ঘ
    80°
সঠিক উত্তর: খ
72°
উত্তর
সঠিক উত্তর: খ
72°
খ
ব্যাখ্যা

Question: Through what angle does the minute hand of a clock turn in 12 minutes?

Solution:
আমরা জানি,
মিনিটের কাঁটা 60 মিনিটে ঘোরে 360° 
∴ 1 মিনিটে ঘোরে 360°/60 = 6° 
∴ 12 মিনিটে ঘোরে (12 × 6°) = 72° 

অতএব, মিনিটের কাঁটা 12 মিনিটে 72° ঘুরবে।

৩,৪৮৪.
Rahim's expenditures and savings are in the ratio of 3 : 2. His income increases by 10%. His expenditure also increases by 12%. How much percent does his savings increase?
  1. ক
    ক) 10%
  2. খ
    খ) 5%
  3. গ
    গ) 7%
  4. ঘ
    ঘ) 12%
সঠিক উত্তর: গ
গ) 7%
উত্তর
সঠিক উত্তর: গ
গ) 7%
গ
ব্যাখ্যা
Question: Rahim's expenditures and savings are in the ratio of 3 : 2. His income increases by 10%. His expenditure also increases by 12%. How much percent does his savings increase?

Solution:
Let Rahim's expenditures be 3x and his savings be 2x
So, his income = 3x + 2x = 5x

Increased income = 110% of 5x = 5.5x
Increased expenditures = 112% of 3x = 3.36x

New savings = 5.5x - 3.36x = 2.14x

Increased savings = 2.14x - 2x = 0.14x

So, increases in percentage = (0.14x/2x) × 100 = 7%
৩,৪৮৫.
If 4 carpet weavers can complete 4 carpets in 4 days, how many carpets can 8 weavers produce in 8 days, assuming they work at the same constant rate?
  1. ক
    11 carpets
  2. খ
    20 carpets
  3. গ
    12 carpets
  4. ঘ
    10 carpets
  5. ঙ
    The answer is not available
সঠিক উত্তর: ঙ
The answer is not available
উত্তর
সঠিক উত্তর: ঙ
The answer is not available
ঙ
ব্যাখ্যা

Question: If 4 carpet weavers can complete 4 carpets in 4 days, how many carpets can 8 weavers produce in 8 days, assuming they work at the same constant rate?

Solution:
4 carpet-weavers in 4 days weave 4 carpets
∴ 1 carpet-weaver in 1 day weaves 4/(4 × 4) = 1/4 carpet

∴ 8 carpet-weavers in 8 days weave = (1/4 × 8 × 8) carpets
= 16 carpets

৩,৪৮৬.
A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
  1. ক
    ক) 56
  2. খ
    খ) 78
  3. গ
    গ) 126
  4. ঘ
    ঘ) 134
সঠিক উত্তর: গ
গ) 126
উত্তর
সঠিক উত্তর: গ
গ) 126
গ
ব্যাখ্যা
There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows:

Case I:
5 students in the first car and 3 in the second.
Hence, 8 students are divided into groups of 5 and 3
in 8C3 = 56 ways.

Case II:
4 students in the first car and 4 in the second.
So, 8 students are divided into two groups of 4 and 4
in 8C4 = 70 ways.

Therefore, the total number of ways in which 8 students can travel is:
56 + 70 = 126
৩,৪৮৭.
If logx(xy) = m, the value of logy(xy) =?
  1. ক
    ক) m
  2. খ
    খ) (m - 1)
  3. গ
    গ) m/(m + 1)
  4. ঘ
    ঘ) m/(m - 1)
সঠিক উত্তর: ঘ
ঘ) m/(m - 1)
উত্তর
সঠিক উত্তর: ঘ
ঘ) m/(m - 1)
ঘ
ব্যাখ্যা
Question: If logx(xy) = m, the value of logy(xy) =?

solution: 
logx(xy) = m
⇒ xm = xy
⇒ xm/x = xy/x
⇒  x m - 1 = y 
∴ x = y 1/m -1 

logy(xy)
= logyx + logyy
= logy y1/(m -1) + 1
= 1/(m - 1) logyy + 1
= {1/(m - 1)} + 1
= (1 + m - 1)/(m - 1)
= m/(m - 1)
৩,৪৮৮.
The marked price of a ceiling fan is Tk. 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.
  1. ক
    Tk. 1200
  2. খ
    Tk. 1185
  3. গ
    Tk. 1175
  4. ঘ
    Tk. 1150
সঠিক উত্তর: গ
Tk. 1175
উত্তর
সঠিক উত্তর: গ
Tk. 1175
গ
ব্যাখ্যা
Question: The marked price of a ceiling fan is Tk. 1250 and the shopkeeper allows a discount of 6% on it. Find the selling price of the fan.

Solution:
Marked price = Tk. 1250 and discount = 6%. 

Discount = 6% of Marked Price 
= (6% of Tk. 1250) 
= Tk. {1250 × (6/100)} 
= Tk. 75 

Selling price = (Marked Price) - (discount) 
= Tk. (1250 - 75) 
= Tk. 1175. 

∴ Hence, the selling price of the fan is Tk. 1175. 
৩,৪৮৯.
If log3x+log9x2+log27x3 =9, then x equals to -
  1. ক
    3
  2. খ
    9
  3. গ
    27
  4. ঘ
    81
  5. ঙ
    243
সঠিক উত্তর: গ
27
উত্তর
সঠিক উত্তর: গ
27
গ
ব্যাখ্যা

[ log(xa)(yb) = b/a logxy ]
৩,৪৯০.
In a two-digit number, the difference of its digits is 2. If the digits are interchanged, the new number is 6 less than twice the original. What is the number?
  1. ক
    13
  2. খ
    24
  3. গ
    46
  4. ঘ
    57
সঠিক উত্তর: খ
24
উত্তর
সঠিক উত্তর: খ
24
খ
ব্যাখ্যা

Question: In a two-digit number, the difference of its digits is 2. If the digits are interchanged, the new number is 6 less than twice the original. What is the number?

Solution:
ধরি, 
একক স্থানীয় অঙ্ক = x
এবং দশক স্থানীয় অঙ্ক = y
∴ সংখ্যাটি = 10y + x

১ম শর্তমতে, 
x - y = 2 
বা, x = y + 2 ................(i) 

২য় শর্তমতে, 
(10x + y) = 2(10y + x) - 6
বা, 10x + y = 20y + 2x - 6 
বা, 10x - 2x - 20y + y = - 6
বা, 8x - 19y = - 6 
বা, 8(y + 2) - 19y = - 6   [যেহেতু x = y + 2]
বা, 8y + 16 - 19y = - 6 
বা, - 11y = - 6 - 16 
বা, - 11y = - 22
বা, y = (- 22)/(- 11)
∴ y = 2 

(i) নং সমীকরণে y = 2 বসিয়ে পাই, 
x = y + 2
বা, x = 2 + 2 
∴ x = 4

∴ নির্ণেয় সংখ্যাটি = 10y + x
= (10 × 2) + 4
= 20 + 4
= 24

৩,৪৯১.
The least number by which 150 must be multiplied to make it a perfect square is-
  1. ক
    2
  2. খ
    3
  3. গ
    5
  4. ঘ
    6
  5. ঙ
    9
সঠিক উত্তর: ঘ
6
উত্তর
সঠিক উত্তর: ঘ
6
ঘ
ব্যাখ্যা

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

Solution:
একটি সংখ্যা পূর্ণবর্গ সংখ্যা হতে হলে তার মৌলিক গুণনীয়কগুলোকে অবশ্যই জোড় সংখ্যায় (even power) থাকতে হবে।

150 = 2 × 3 × 5 × 5 = 21 × 31 × 52

জোড়া গঠন করে পাই, 2 × 3 × (5 × 5)
এখানে জোড়া বিহীন সংখ্যা 2 এবং 3

∴ 150 কে (2 × 3) = 6 দ্বারা গুণ করলে এটি পূর্ণবর্গ সংখ্যা হবে।

৩,৪৯২.
A man can row 12 km/hr in still water. If the speed of the current is 4 km/hr, he takes 4 hours more upstream than downstream. What is the distance (in km)?
  1. ক
    ক) 32 km
  2. খ
    খ) 48 km
  3. গ
    গ) 50 km
  4. ঘ
    ঘ) 64 km
সঠিক উত্তর: ঘ
ঘ) 64 km
উত্তর
সঠিক উত্তর: ঘ
ঘ) 64 km
ঘ
ব্যাখ্যা
Question: A man can row 12 km/hr in still water. If the speed of the current is 4 km/hr, he takes 4 hours more upstream than downstream. What is the distance (in km)?

Solution: 
Speed of the man in still water = 12 km/h
Speed of the current = 4 km/h
Speed of the man along the current = (12 + 4) km/h = 16 km/h
Speed of the man against the current = (12 -  4) km/h = 8 km/h


Let, The distance is x km
Now
 x/8 - x/16 = 4
⇒ (2x - x)/16 = 4
⇒ x/16 = 4 
∴ x = 64 km
৩,৪৯৩.
Let U = {1,2,3,4,5,6,7,8}, A = {2,3,6}, and B = {1,4,5}. Find Ac∪Bc.
  1. ক
    {1,2,3,4,5,6,7,8}
  2. খ
    { }
  3. গ
    {2,3,6}
  4. ঘ
    {1,4,5,7,8}
  5. ঙ
    {7,8}
সঠিক উত্তর: ক
{1,2,3,4,5,6,7,8}
উত্তর
সঠিক উত্তর: ক
{1,2,3,4,5,6,7,8}
ক
ব্যাখ্যা

Question: Let U = {1,2,3,4,5,6,7,8}, A = {2,3,6}, and B = {1,4,5}. Find Ac ∪ Bc.

Solution:
Complement of A:
A = {2,3,6}
U = {1,2,3,4,5,6,7,8}
Ac = U - A = {1,4,5,7,8}

Complement of B:
B = {1,4,5}
Bc = U - B = {2,3,6,7,8}

Union of Complements:
Ac ∪ Bc = {1,4,5,7,8} ∪ {2,3,6,7,8} = {1,2,3,4,5,6,7,8} = U

∴Ac ∪ Bc = {1,2,3,4,5,6,7,8}

৩,৪৯৪.
The five individuals - A, B, C, D, and E - have an average age of 25 years. A and B together average 28 years, while C and D have an average of 32. Can you deduce the age of E?
  1. ক
    10 years
  2. খ
    8 years
  3. গ
    5 years
  4. ঘ
    None of the above
সঠিক উত্তর: গ
5 years
উত্তর
সঠিক উত্তর: গ
5 years
গ
ব্যাখ্যা
Question: The five individuals - A, B, C, D, and E - have an average age of 25 years. A and B together average 28 years, while C and D have an average of 32. Can you deduce the age of E?

Solution:
The average age of A, B, C, D and E is = 25 years.
The total age of A, B, C, D and E is = (25 × 5) = 125 years.

The average age of A and B is = 28 years
The total age of A and B is = (28 × 2) = 56 years

The average of C and D is = 32 years
The total age of C and D is = (32 × 2) = 64 years

∴ Age of E is = (125 - 56 - 64) = 5 years
৩,৪৯৫.
48 men can complete a piece of work in 18 days. In how many days can 36 men complete the same piece of work?
  1. ক
    20 days
  2. খ
    24 days
  3. গ
    26 days
  4. ঘ
    28 days
সঠিক উত্তর: খ
24 days
উত্তর
সঠিক উত্তর: খ
24 days
খ
ব্যাখ্যা

Question: 48 men can complete a piece of work in 18 days. In how many days can 36 men complete the same piece of work?

Solution:
Let the required number of days be x
Less men, More days (Indirect proportion)
∴ 36 : 48 : : 18 : x
⇔ 36/48 = 18/x
⇔ 36x = 18 × 48
⇔ x = (18 × 48)/36
∴ x = 24

৩,৪৯৬.
The average age of three men is 30 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest man is-
  1. ক
    12 years
  2. খ
    18 years
  3. গ
    30 years
  4. ঘ
    42 years
সঠিক উত্তর: খ
18 years
উত্তর
সঠিক উত্তর: খ
18 years
খ
ব্যাখ্যা

Question: The average age of three men is 30 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest man is-

Solution:
The sum of the ages of three men = (30 × 3) years
= 90 years

Let the ages be 3x, 5x and 7x

Now,
3x + 5x + 7x = 90
⇒ 15x = 90
⇒ x = 6

So, age of the youngest man = 3x
= 3 × 6
= 18 years

৩,৪৯৭.
A shopkeeper has two varieties of lentils priced at Taka 60 per kg and Taka 80 per kg. In what ratio should he mix them to get a mixture worth Taka 68 per kg?
  1. ক
    2 : 3
  2. খ
    3 : 2
  3. গ
    3 : 4
  4. ঘ
    4 : 3
সঠিক উত্তর: খ
3 : 2
উত্তর
সঠিক উত্তর: খ
3 : 2
খ
ব্যাখ্যা

Question: A shopkeeper has two varieties of lentils priced at Taka 60 per kg and Taka 80 per kg. In what ratio should he mix them to get a mixture worth Taka 68 per kg?

Solution: 
Cheaper variety price of lentils, p = 60 Taka
Expensive variety price of lentils, q = 80 Taka
mixture price, r = 68 Taka

Ratio = (q - r)/(r - p)
=(80 - 68)/(68 - 60)
=12/8
= 3 : 2

৩,৪৯৮.
A word consists of 9 letters; 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability that more than one vowel will be selected?
  1. ক
    ক) 13/42
  2. খ
    খ) 5/42
  3. গ
    গ) 17/42
  4. ঘ
    ঘ) 3/14
সঠিক উত্তর: গ
গ) 17/42
উত্তর
সঠিক উত্তর: গ
গ) 17/42
গ
ব্যাখ্যা
For solving this question,
we can find the probability of selecting at the most 1 vowel.
So list down the possibilities:
CCC, CCV, CVC, VCC
in all these situations, we have only selected 1 or no vowels.
So now let’s find out the probability of the above situations.
=(5/9 × 4/8 × 3/7) + [(5/9 × 4/8 × 4/7) × 3]
=(5 × 4 × 3)/(9 × 8 × 7) + [(5 × 4 × 4 × 3)/(9 × 8 × 7)]
=60/504 + 240/504
=300/504
=25/42
Now adhering to the question,
the probability which we found is of obtaining one or less vowels.
Thus we need to subtract this probability from 1 to get the final answer.
=1 − 25/42
=(42 − 25)/42
=17/42
৩,৪৯৯.
If 2x2 - 5x + 3 = 0 and 4x2 - (k + 1)x + 6 = 0, Then find the values of k for each of the following quadratic equations, so that they have a common root?
  1. ক
    9
  2. খ
    5
  3. গ
    - 3
  4. ঘ
    8
  5. ঙ
    12
সঠিক উত্তর: ক
9
উত্তর
সঠিক উত্তর: ক
9
ক
ব্যাখ্যা
Question: If 2x2 - 5x + 3 = 0 and 4x2 - (k + 1)x + 6 = 0, Then find the values of k for each of the following quadratic equations, so that they have a common root?

Solution:
দেওয়া আছে,
দ্বিঘাত সমীকরণ দুইটি,
2x2 - 5x + 3 = 0 .....(1)
এবং 4x2 - (k + 1)x + 6 = 0 ........(2)

যদি দুটি দ্বিঘাত সমীকরণের উভয় উৎপাদক সাধারণ হয়, তাহলে তাদের সহগগুলি সমানুপাতিক হবে। অর্থাৎ
a1/a2 = b1/b2 = c1/c2 .......(3)

এখন,
1 নং সমীকরণ হতে সহগগুলির তুলনা করে পাই,
a1 = 2 , b1 = - 5, c1 = 3
এবং 2 নং সমীকরণ হতে সহগগুলির তুলনা করে পাই,
a2 = 4, b2 = - (k + 1), c2 = 6

এখন,
3 নং সমীকরণ হতে সমানুপাতিকতার শর্ত ব্যবহার করে,
2/4 = - 5/- (k + 1) = 3/6

প্রথম দুইটি অনুপাত হতে পাই,
⇒ 2/4 = - 5/- (k + 1)
⇒ 2k + 2 = 20
⇒ 2k = 18
∴ k = 9

আবার, শেষ দুইটি অনুপাত হতে পাই,
⇒ - 5/- (k + 1) = 3/6
⇒ 3k + 3 = 30
⇒ 3k = 27
∴ k = 9

∴ উভয় সমীকরণে একটি সাধারণ মূল 9 থাকবে।

৩,৫০০.
In triangle PQR length of the side QR is less than twice the length of the side PQ by 2 cm. Length of the side PR exceeds the length of the side PQ by 10 cm. The perimeter is 40 cm. The length of the smallest side of the triangle PQR is :
  1. ক
    ক) 6 cm
  2. খ
    খ) 7 cm
  3. গ
    গ) 8 cm
  4. ঘ
    ঘ) 10 cm
সঠিক উত্তর: গ
গ) 8 cm
উত্তর
সঠিক উত্তর: গ
গ) 8 cm
গ
ব্যাখ্যা

In △PQR,
QR + 2 = 2PQ
QR = 2PQ - 2 ..........(1)
PR = PQ + 10 ......... (2)
Perimeter = 40 m
Or, PQ + QR + RP = 40
Putting the value of PQ and QR from equation (1) and (2),
PQ + 2PQ - 2 + PQ + 10 = 40
Or, 4PQ = 32
Or, PQ = 8 cm ,which is the smallest side of the triangle.