লগ ইননিবন্ধন
বিষয়সমূহ

PrepBank · বিষয়ভিত্তিক প্রশ্ন

Bank Math

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

Bank Math

PrepBank · পাতা ১১৭ / ১৬১ · ১১,৬০১–১১,৭০০ / ১৬,১২৪

১১,৬০১.
If C is the midpoint of the points A(2, - 1) and B(8, 5), find the length of AC.
  1. ক
    8√2
  2. খ
    3√2
  3. গ
    3√5
  4. ঘ
    5
ব্যাখ্যা

Question: If C is the midpoint of the points A(2, - 1) and B(8, 5), find the length of AC.

Solution:
দেওয়া আছে,
 A(2, - 1) এবং B(8, 5), 
এবং C হলো AB-এর মধ্যবিন্দু।

দূরত্বের সূত্র ব্যবহার করে AB-এর দৈর্ঘ্য নির্ণয় করি,
AB = √(x2 - x1)2 + (y2 - y1)2)
= √(8 - 2)2 + {5 - (-1)}2
= √(62 + 62)
= √(36 + 36)
= √72
= √(36 × 2)
= 6√2

C হলো AB এর মধ্যবিন্দু, তাই AC = AB/2
 = 6√2/2
 = 3√2

১১,৬০২.
What is the largest number that divides 43, 91, and 183, leaving the same remainder in all three cases?
  1. ক
    4
  2. খ
    6
  3. গ
    11
  4. ঘ
    12
ব্যাখ্যা

Question: What is the largest number that divides 43, 91, and 183, leaving the same remainder in all three cases?

Solution:
এখানে বৃহত্তম সংখ্যা হচ্ছে সংখ্যাগুলোর পার্থক্যগুলোর H.C.F. (গ.সা.গু)।

প্রথম দুটি সংখ্যার পার্থক্য: 91 - 43 = 48
পরের দুটি সংখ্যার পার্থক্য: 183 - 91 = 92

48 এবং 92 এর মৌলিক উৎপাদক:
48 = 2 × 2 × 2 × 2 × 3 = 24 × 3
92 = 2 × 2 × 23 = 22 × 23

H.C.F. = 22 = 4

∴ নির্ণীত বৃহত্তম সংখ্যা = 4

১১,৬০৩.
25% of A's income is equal to 35% of B's income. The ratio of the incomes of A and B is-
  1. ক
    ক) 5 : 7
  2. খ
    খ) 7 : 5
  3. গ
    গ) 13 : 15
  4. ঘ
    ঘ) 15 : 13
  5. ঙ
    ঙ) 7 : 13
ব্যাখ্যা

25% of A = 35% of B
⇒ (25/100)A = (35/100)B
⇒ A/4 = 7B/20
⇒ A/B = (7/20)×4 = 7/5
⇒ A:B = 7:5

১১,৬০৪.
Find the value of ,
  1. ক
    3/4
  2. খ
    5/3
  3. গ
    5/4
  4. ঘ
    2
ব্যাখ্যা
Question: Find the value of ,


Solution:
১১,৬০৫.
If a + b = √5 and a - b = √3 the, 8ab(a2 + b2) = ?
  1. ক
    8
  2. খ
    10
  3. গ
    16
  4. ঘ
    24
ব্যাখ্যা
Question: If a + b = √5 and a - b = √3 the, 8ab(a2 + b2) = ?

Solution:
Given,
a + b = √5
and a - b = √3

∴ 8ab(a2 + b2)
= 4ab × 2(a2 + b2)
= {(a + b)2 - (a - b)2}{(a + b)2 + (a - b)2}
= {(√5)2 - (√3)2}{(√5)2 + (√3)2}
= (5 - 3)(5 + 3)
= 2 × 8
= 16
১১,৬০৬.
The ratio of the present ages of Riya and her mother is 3 : 7. The mother’s age at the time of Riya’s birth was 20 years. Find the mother’s present age.
  1. ক
    35 years
  2. খ
    30 years
  3. গ
    38 years
  4. ঘ
    None of these
ব্যাখ্যা
Question: The ratio of the present ages of Riya and her mother is 3 : 7. The mother’s age at the time of Riya’s birth was 20 years. Find the mother’s present age.

Solution:
Present ratio is 7 : 3.
Let actual ages are 7x and 3x.

∴ 7x - 3x = 20
⇒ 4x = 20
∴ x = 5

Hence the mother’s present age 7 × 5 = 35 years
১১,৬০৭.
A man is now 3 times as old as his son. In 10 years' time, the sum of their ages will be 76. How old was the man when his son was born?
  1. ক
    ক) 24 years
  2. খ
    খ) 42 years
  3. গ
    গ) 28 years
  4. ঘ
    ঘ) 32 years
ব্যাখ্যা
ধরি,
বর্তমানে পুত্রের বয়স = x বছর 
পিতার বয়স 3x বছর

প্রশ্নমতে,
10 + x + 10 + 3x = 76
4x =76 - 20
4x =56
 x=14 
 পুত্রের বয়স 14 বছর
পিতার বয়স = 3 × 14 = 42 বছর

জন্মের সময় পিতার বয়স ছিলো = 42 - 14 = 28 বছর 
১১,৬০৮.
If the perimeter of a certain rectangle is 76 m and its area is 360 m2, then what is the length of its shortest side?
  1. ক
    ক) 13
  2. খ
    খ) 15
  3. গ
    গ) 18
  4. ঘ
    ঘ) 10
ব্যাখ্যা

We know, Perimeter = 2(l+b) = 76
⇒ (l+b) = 38
⇒ l = 38 - b .....(1)
Given, the area, lb = 360 .....(2)
From (2)
(38 – b)b = 360
⇒ 38b – b2 = 360
⇒ b2 – 38b + 360 = 0
⇒ (b – 20)(b – 18) = 0
So, b = 20 or b = 18
When b = 20, l = 18 and when b = 18, l = 20.
∴ the shorter side is 18.

১১,৬০৯.
A jacket is sold after providing two successive discounts of 15%. If the marked price of the jacket is Tk. 400, find the selling price.
  1. ক
    Tk. 270
  2. খ
    Tk. 276
  3. গ
    Tk. 281
  4. ঘ
    Tk. 289
ব্যাখ্যা
Question: A jacket is sold after providing two successive discounts of 15%. If the marked price of the jacket is Tk. 400, find the selling price.

Solution:
First Discount:
Discount 1 = 400 × (15/100) = Tk. 60
Selling Price after 1st Discount = 400 - 60 = Tk. 340

Second Discount:
Discount 2 = 340 × (15/100) = Tk. 51
Selling Price after 2nd Discount = 340 - 51 = Tk. 289

So, the selling price of the jacket after two successive discounts of 15% is Tk. 289.
১১,৬১০.
4, -8, 16, -32, 64, (...)
  1. ক
    ক) 128
  2. খ
    খ) -128
  3. গ
    গ) 192
  4. ঘ
    ঘ) -192
  5. ঙ
    ঙ) 156
ব্যাখ্যা
Each number is the preceding number multiplied by -2. So, the required number is -128.
১১,৬১১.
Which of the following is divisible by 2 and 7?
  1. ক
    ক) 365
  2. খ
    খ) 362
  3. গ
    গ) 361
  4. ঘ
    ঘ) None
ব্যাখ্যা
Question: Which of the following is divisible by 2 and 7?

Solution: 
২, ৭ এর ল. সা. গু = ১৪ 

৩৬৫, ৩৬২, ৩৬১ ; ১৪ দ্বারা বিভাজ্য নয়। 
১১,৬১২.
Three unbiased coins are tossed. What is the probability of getting at least 2 tails?
  1. ক
    1/2
  2. খ
    3/4
  3. গ
    1/8
  4. ঘ
    2/3
ব্যাখ্যা

Question: Three unbiased coins are tossed. What is the probability of getting at least 2 tails?

Solution:
When three fair (unbiased) coins are tossed, the total number of possible outcomes = 2 × 2 × 2 = 8.
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} 

And all possible outcomes are, {HTT, THT, TTH, TTT} = 4

∴ Probability = (number of favorable outcomes)/(total possible outcomes)
= 4/8
= 1/2

So the probability of getting at least 2 tails is 1/2.

১১,৬১৩.
A can complete a work in 6 days while B can complete the same work in 12 days. If they work together and complete it, the portion of the work done by B is-
  1. ক
    1/3
  2. খ
    1/4
  3. গ
    1/2
  4. ঘ
    2/3
ব্যাখ্যা
Question: A can complete a work in 6 days while B can complete the same work in 12 days. If they work together and complete it, the portion of the work done by B is-

Solution:
A এর 1 দিনের কাজ = 1/6 অংশ
B এর 1 দিনের কাজ = 1/12 অংশ

তারা একত্রে 1 দিনের কাজ = (1/6) + (1/12) 
= (2 + 1)/12
= 3/12
= 1/4

তারা একত্রে 1/4 অংশ কাজ করে = 1 দিনে
তারা 1 বা সম্পূর্ণ অংশ  কাজ করে = 1/(1/4) = 4 দিনে

∴ B এর দ্বারা সম্পূর্ণ কাজের অংশ = 4 × (1/12) = 1/3
১১,৬১৪.
Lex has Tk. 1780.80 in his savings account that he opened 6 years ago. His account has an annual interest rate of 6.8% compounded annually. How much money did Lex use to open his savings account?
  1. ক
    Tk. 1000
  2. খ
    Tk. 1100
  3. গ
    Tk. 1200
  4. ঘ
    Tk. 1300
ব্যাখ্যা
Question: Lex has Tk. 1780.80 in his savings account that he opened 6 years ago. His account has an annual interest rate of 6.8% compounded annually. How much money did Lex use to open his savings account?

Solution:
We know that,
A = P[1+(R/100)]n
⇒ 1780.80 = P[1 + 6.8/100]6
⇒ 1780.80 = P[1 + 0.068]6
⇒ 1780.80 = 1.484P
⇒ P = 1780.80/1.484
∴ P = 1200
১১,৬১৫.
What smallest number should be added to 4456 so that the sum is completely divisible by 6?
  1. ক
    2
  2. খ
    3
  3. গ
    4
  4. ঘ
    None of these
ব্যাখ্যা
Question: What smallest number should be added to 4456 so that the sum is completely divisible by 6?

Solution: 
4456 divided by 6 leaves a remainder of 4. Therefore, we need to add 2 to 4456 to make the sum divisible by 6.

4456 + 2 = 4458, and when divided by 6, this results in a remainder of 0.
১১,৬১৬.
Rakesh borrows 3500 taka from a Leasing Company at 5% compound interest per year. Calculate the total must be paid after 36 months?
  1. ক
    ক) 4,150.69
  2. খ
    খ) 4,105.69
  3. গ
    গ) 4,051.69
  4. ঘ
    ঘ) 4,015.69
ব্যাখ্যা
Question: Rakesh borrows 3500 taka from a Leasing Company at 5% compound interest per year. Calculate the total must be paid after 36 months?

Solution: 
দেওয়া আছে,
মূলধন P = 3500 টাকা
সময়, n = 36 মাস = 3 বছর
সুদের হার, r = 5% = 5/100 


চক্রবৃদ্ধি মুনাফায় সবৃদ্ধিমূল,
C = P(1 + r)n
= 3500(1 + 5/100)3
= 3500 × (105/100)3
= 3500 × (1.05)3
= 3500 × 1.157625
= 4,051.6875
= 4,051.69
১১,৬১৭.
In a bank clients stand in a queue. If Sami is 21th in order from both ends, how many clients are there in the queue?
  1. ক
    42
  2. খ
    43
  3. গ
    41
  4. ঘ
    40
ব্যাখ্যা
Question: In a bank clients stand in a queue. If Sami is 21th in order from both ends, how many clients are there in the queue?

Solution:
এক দিক থেকে সামির অবস্থান ২১ তম অর্থাৎ সে সহ ২১ জন।
অপর দিক থেকে তার অবস্থান ২১ তম অর্থাৎ সে বাদে আরও ২০ জন আছে।
∴ ঐ সারিতে মোট ক্লায়েন্ট আছে (২১ + ২০) জন = ৪১ জন 
১১,৬১৮.
A cylindrical water tank has a radius of 35 inches and a height of 120 inches. Calculate the total surface area.
  1. ক
    35120 sq. inches.
  2. খ
    34100 sq. inches.
  3. গ
    32321 sq. inches.
  4. ঘ
    34155 sq. inches.
ব্যাখ্যা
Question: A cylindrical water tank has a radius of 35 inches and a height of 120 inches. Calculate the total surface area.

Solution:
Water tank is cylindrical in nature.
Total Surface Area of a cylinder is given by, 2πr(h + r)

∴ Total Surface Area = 2 × (22/7) × 35(120 + 35)
= 2 × 22 × 5 × 155
= 34100

∴ Total Surface Area = 34100 sq. inches.
১১,৬১৯.
Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is-
  1. ক
    10
  2. খ
    16
  3. গ
    12
  4. ঘ
    14
ব্যাখ্যা
Question: Three pipes A, B and C can fill a tank in 6 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 7 hours. The number of hours taken by C alone to fill the tank is-

Solution:
Part time in 2 hours = 6/2 = 1/3
Remaining part = (1 - 1/3) = 2/3
∴ (A + B)'s 7 hour's work = 2/3
(A + B)'s 1 hour's work = 2/21

∴ C's hour's work= {(A + B + C)'s 1 hour's work} - {(A + B)'s 1 hour's work}
= 1/6 - 2/21
= (7 - 4)/42
= 3/42
= 1/14
 
∴ C alone can fill the tank in 14 hours.
১১,৬২০.
The difference between the length and the perimeter of a rectangle is 100 cms. What is the breadth of the rectangle?
  1. ক
    80 cms
  2. খ
    60 cms
  3. গ
    100 cms
  4. ঘ
    Data Inadequate
ব্যাখ্যা
Question: The difference between the length and the perimeter of a rectangle is 100 cms. What is the breadth of the rectangle?

Solution:
Let the length of the rectangle be 'x' and breadth of the rectangle be 'y'
According to the question:
2(x + y) - x = 100
⇒ 2x + 2y - x = 100
⇒ x + 2y = 100

From this we cannot find 'y' (breadth), so the given data is inadequate.
১১,৬২১.
Mr. Rifat divides Tk. 1573 such that 4 times the 1st share, thrice the 2nd share and twice the third share amount to the same. Then the value of the 2nd share is-
  1. ক
    Tk. 484
  2. খ
    Tk. 242
  3. গ
    Tk. 363
  4. ঘ
    Tk. 726
ব্যাখ্যা
Question: Mr. Rifat divides Tk. 1573 such that 4 times the 1st share, thrice the 2nd share and twice the third share amount to the same. Then the value of the 2nd share is-

Solution:
Total amount = Tk. 1573
Let,
The shares are A, B and C 
Here,
4A = 3B = 2C.
Now,
4A = 3B
∴ B = 4A/3

4A = 2C
∴ C = 2A

∴ A : B : C = A : 4A/3 : 2A
= 1 : 4/3 : 2
= 3 : 4 : 6

The value of the 2nd share = (4/13) × 1573 = Tk. 484
১১,৬২২.
The area of the right angle triangle is 80 square cm one of its leg is 16 cm long. Find the length of the other leg.
  1. ক
    23 cm
  2. খ
    36 cm
  3. গ
    10 cm
  4. ঘ
    28 cm
ব্যাখ্যা
Area of the triangle = 1/2 × base × height
⇒ 80 = 1/2 × 16 × other leg
So,
other leg = (80 × 2)/16
= 10 cm
১১,৬২৩.
If x2 - 3x + 1 = 0, what is the value of x2 - 1/x2?
  1. ক
    ক) 4√3
  2. খ
    খ) 3√5
  3. গ
    গ) 4√5
  4. ঘ
    ঘ) 2√3
ব্যাখ্যা
Question: If x2 - 3x + 1 = 0, what is the value of x2 - 1/x2?

Solution:
Given that,
x2 - 3x + 1 = 0
⇒ x2 + 1 = 3x
⇒ x + 1/x = 3 [Divided by x]

Now, 
x - 1/x = √{(x + 1/x)2 - 4.x.(1/x)}
= √{32 - 4}
= √(9 - 4)
= √5

So,
x2 - 1/x2 = (x + 1/x)(x - 1/x)
= 3√5
১১,৬২৪.
A group of boys and girls are participating in a tennis tournament. In Round 1, each boy plays against every other boy. In Round 2, each girl competes with all other girls. In the following round, each boy plays a match against every girl. If the number of matches played in Rounds 1 and 2 were 120 and 91 respectively, how many matches will be played in this third round?
  1. ক
    224
  2. খ
    320
  3. গ
    580
  4. ঘ
    210
  5. ঙ
    624
ব্যাখ্যা
Question: A group of boys and girls are participating in a tennis tournament. In Round 1, each boy plays against every other boy. In Round 2, each girl competes with all other girls. In the following round, each boy plays a match against every girl. If the number of matches played in Rounds 1 and 2 were 120 and 91 respectively, how many matches will be played in this third round?

Solution:
Let x be the number of girl players.
Let y be the number of boy players.

Now,
xC2 = 91
⇒ x!/2!(x - 2)!) = 91
⇒ x(x - 1) = 182
⇒ x2 - x - 182 = 0
⇒ x2 - 14x + 13x - 182 = 0
⇒ x(x - 14) + 13(x - 14) = 0
⇒ (x - 14)(x + 13) = 0
∴ x = 14
There are 14 girl players.

And
yC2 = 120
⇒ y!/2!(y - 2)! = 120
⇒ y2 - y - 240 = 0
⇒ y2 - 16y + 15y - 240 = 0
⇒ y(y - 16) + 15(y - 16) = 0
⇒ (y - 16)(y + 15) = 0
∴ y = 16
There are 16 boy players.

Number of matches between each boy and each girl = 14C1 × 16C1 = 14 × 16 = 224
Therefore, the required answer is 224.
১১,৬২৫.
The least number, Which when divided by 15, 20, 30, 40 leaves in each case a remainder of 6 is-
  1. ক
    114
  2. খ
    120
  3. গ
    146
  4. ঘ
    126
ব্যাখ্যা
Question: The least number, Which when divided by 15, 20, 30, 40 leaves in each case a remainder of 6 is-

Solution:
We first find the LCM of 15, 20, 30, and 40 by factoring them,
15 = 3 × 5
20 = 2 × 2 × 5
30 = 2 × 3 × 5
40 = 2 × 2 × 2 × 5

So, the LCM is = 2 × 2 × 2 × 3 × 5 = 120

∴ The least number is = 120 + 6 = 126
১১,৬২৬.
A cube of side 4 cm is cut into cubes of side 1 cm. Calculate the total surface area of all the small cubes.
  1. ক
    ক) 24 cm2
  2. খ
    খ) 384 cm2
  3. গ
    গ) 96 cm2
  4. ঘ
    ঘ) 196 cm2
ব্যাখ্যা
Question: A cube of side 4 cm is cut into cubes of side 1 cm. Calculate the total surface area of all the small cubes.

Solution: 
Side of original cube = 4 cm.

Number of cubes of side 1 cm
= (Volume of the bigger cube)/(Volume of the smaller cube)
= (4 × 4 × 4)/(1 × 1 × 1)
= 64

Now, the surface area of one cube = 6(side)2
= 6 × 12
= 6 cm2

∴ The surface area of 64 cubes = 6 × 64 cm2
= 384 cm2
১১,৬২৭.
The diameter of a circle is 14 cm. What is the circumference of the circle?
  1. ক
    44 m
  2. খ
    0.44 m
  3. গ
    22 cm
  4. ঘ
    2.2 cm
ব্যাখ্যা
Question: The diameter of a circle is 14 cm. What is the circumference of the circle?

Solution: 
Radius of the circle r = 14/2 = 7
The circumference of the circle = 2πr
= 2 × (22/7) × 7
= 44 cm
= 44/100 m
= 0.44 m
১১,৬২৮.
The number, whose square is equal to the difference of the squares of 75.15 and 60.12, is = ?
  1. ক
    ক) 56.39
  2. খ
    খ) 88.06
  3. গ
    গ) 45.09
  4. ঘ
    ঘ) 47.06
ব্যাখ্যা

Let the number be = x
According to question,
x2=(75.15)2−(60.12)2
⇒x2=(75.15+60.12)(75.15−60.12)
⇒x2=135.27×15.03
⇒x2=2033.1081
⇒x=45.09

১১,৬২৯.
A boat running downstream covers a distance of 24 km in 3 hours while for covering the same distance upstream, it takes 6 hours. What is the speed of the boat in still water?
  1. ক
    ক) 4 km/hr
  2. খ
    খ) 6 km/hr
  3. গ
    গ) 8 km/hr
  4. ঘ
    ঘ) 10 km/hr
ব্যাখ্যা
Question: A boat running downstream covers a distance of 24 km in 3 hours while for covering the same distance upstream, it takes 6 hours. What is the speed of the boat in still water?

Solution:
speed downstream = 24/3  km/hr = 8 km/hr
speed upstream = 24/6 km/hr = 4 km/hr 

∴ Speed in still water = (8 + 4)/2 km/hr = 6 km/hr.
১১,৬৩০.
In a factory, there are workers, executives and clerks. 70% of the employees are workers, 596 are executives and the remaining 334 employees are clerks. How many employees are there in the factory?
  1. ক
    3100 
  2. খ
    2100 
  3. গ
    2720 
  4. ঘ
    3390 
ব্যাখ্যা

Question: In a factory, there are workers, executives and clerks. 70% of the employees are workers, 596 are executives and the remaining 334 employees are clerks. How many employees are there in the factory?

Solution: 
Let
Total employee 100%
Executive and clerks (100 - 70)% = 30%

executive and clerks employee = 596 + 334 = 930 

Now
30% employee = 930
∴ 1% employee = 930/30
∴ 100% employee = ( 930 × 100)/30 = 3100 

১১,৬৩১.
Mr. Expert can do a job in 8 days and his son can do it 12 days. How many days will it take them to complete the job if they worked together?
  1. ক
    5
  2. খ
    (24/5)
  3. গ
    5.
  4. ঘ
    None
ব্যাখ্যা
Question: Mr. Expert can do a job in 8 days and his son can do it 12 days. How many days will it take them to complete the job if they worked together?

Solution: 
Mr. Expert 1 দিনে করতে পারে কাজটির = 1/8 অংশ
তার পুত্র 1 দিনে করতে পারে কাজটির = 1/12 অংশ

তারা একত্রে 1 দিনে করতে পারে কাজটির = (1/8) + (1/12) অংশ
= (3 + 2)/24 অংশ
= 5/24 অংশ

তারা একত্রে কাজটির 5/24 অংশ করতে পারে = 1 দিনে
তারা একত্রে কাজটির 1 অংশ করতে পারে = (1 × 24)/5 দিনে
= 24/5 দিনে
১১,৬৩২.
Identify the smallest integer that, when doubled, can be evenly divided by 18, 24, 28, and 36.
  1. ক
    252
  2. খ
    360
  3. গ
    504
  4. ঘ
    1008
ব্যাখ্যা

Question: Identify the smallest integer that, when doubled, can be evenly divided by 18, 24, 28, and 36.

Solution:
LCM of 18, 24, 28, and 36 is = 504
So, the number will be half of 504 = 504/2 = 252

১১,৬৩৩.
The average of 18 observations was calculated and it was 124. Later on it was discovered that two observations 46 and 82 were incorrect. The correct values are 64 and 28. The correct average of 18 observations is -
  1. ক
    ক) 123
  2. খ
    খ) 137
  3. গ
    গ) 121
  4. ঘ
    ঘ) 122
ব্যাখ্যা

Sum of 18 observations = 18 x 124
=2232

Correct sum of 18 observations = 2232 - 46 - 82 + 64 + 28
= 2196
Therefore,
Correct average =2196/18
= 122.

১১,৬৩৪.
Man could not decide between discount of 30% or two successive discounts of 25% and 5%, both given on a shopping of Tk. 2,000. What is the difference between both the discounts?
  1. ক
    ক) Tk.54
  2. খ
    খ) Tk.37
  3. গ
    গ) Tk.25
  4. ঘ
    ঘ) Tk.21
ব্যাখ্যা
Question:  Man could not decide between discount of 30% or two successive discounts of 25% and 5%, both given on a shopping of Tk. 2,000. What is the difference between both the discounts?
Solution: 
বাজার খরচ = Tk. 2000

১ম শর্তমতে∶
শতকরা ছাড় = 30%
ছাড়  = 30% of 2000 = 30/100 × 2000 = Tk. 600

২য় শর্তমতে ∶
১ম শতাংশ ছাড় = 25%
১ম ছাড় = 25% of 2000 = 25/100 × 2000 = Tk. 500

প্রথম ছাড়ের পর বাজার খরচ = 2000 – 500 = Tk. 1500

২য় শতাংশ ছাড় = 5%
২য় ছাড় = 5/100 × 1500 = Tk. 75

সম্পূর্ণ ছাড় = 500 + 75 = Tk. 575

∴ উভয় শর্তে ছাড়  = 600 – 575 = Tk.25
১১,৬৩৫.
Three partners shared the profit in a business in the ratio 3 : 4 : 5. They had partnered for 8 months, 6 months and 4 months respectively. What was the ratio of their investments?
  1. ক
    9 : 16 : 30
  2. খ
    9 : 18 : 30
  3. গ
    8 : 16 : 30
  4. ঘ
    9 : 16 : 24
  5. ঙ
    9 : 16 : 8
ব্যাখ্যা
Let their investments be x taka for 8 months,
                                        y taka for 6 months
                                 and z taka for 4 months respectively.

Then, 8x : 6y : 4z = 3 : 4 : 5.
or, 8x/6y = 3/4
or, y = 16x/9
and 8x/4z = 3/5.
or, z = 10x/3

x : y : z = x : 16x/9 : 10x/3 = 9 : 16 : 30
১১,৬৩৬.
A square is inscribed in a circle of diameter 2a and another square is a circumscribing circle. The difference between the areas of outer and inner squares is -
  1. ক
    ক) a2
  2. খ
    খ) 2a2
  3. গ
    গ) 3a2
  4. ঘ
    ঘ) 4a2
ব্যাখ্যা

Area or outer space = 2a x 2a = 4a2
From ABCD rectangle, In ΔBAD,
BD2 = (AD)2 + (AB)2
⇒ (2a)2 = x2 + x2
⇒ 4a2 = 2x2 
⇒ 2a2 = x2 
∴ x = √2a

Area of inner square = √2a × √2a = 2a2 

∴ The difference between the areas of outer and inner squares is = 4a2 - 2a2 = 2a2 

১১,৬৩৭.
Three fair coins are tossed simultaneously. What is the probability of getting at least two head and one tail?
  1. ক
    ক) 1/4
  2. খ
    খ) 3/8
  3. গ
    গ) 1/2
  4. ঘ
    ঘ) 5/8
ব্যাখ্যা
When three coins are tossed, total possible outcomes = 8
S = {HHH, HHT, HTT, THH, TTH, THT, HTH,TTT}
Favorable cases = {HHT, THH, HTH} 

P(getting at least one head, one tail) = 3/8
                                                           
∴ The probability is 3/8
১১,৬৩৮.
Three pipes A, B and C can fill a cistern in 8 minutes,12 minutes and 16 minutes respectively. What is the time taken by three pipes to fill the cistern when they are opened together?
  1. ক
    3.7 minutes
  2. খ
    4 minutes
  3. গ
    4.5 minutes
  4. ঘ
    5 minutes
ব্যাখ্যা
Question: Three pipes A, B and C can fill a cistern in 8 minutes,12 minutes and 16 minutes respectively. What is the time taken by three pipes to fill the cistern when they are opened together?

Solution:
Part of the tank filled by A in one minute = 1/8
Part of the tank filled by B in one minute = 1/12
Part of the tank filled by C in one minute = 1/16

Net part of the tank filled by A + B + C in one minute = 1/8 + 1/12 + 1/16
= (6 + 4 + 3)/48
= 13/48

13/48 part filled in 1 minute
Full part filled in 48/13  minutes
= 3.69 minutes 
≈ 3.7 minutes
১১,৬৩৯.
The length of a rectangle is thrice its breath, and its perimeter is 120 meters. What is its area?
  1. ক
    688 sq. m.
  2. খ
    720 sq. m.
  3. গ
    580 sq. m.
  4. ঘ
    None of these 
ব্যাখ্যা

Question: The length of a rectangle is thrice its breath, and its perimeter is 120 meters. What is its area?

Solution:
Let the breath = x
So, the Length = 3x

Perimeter of a rectangle = 2 (Length + Breadth)
So, 2(3x + x) = 120
⇒ 6x + 2x = 120
⇒ 8x = 120
∴ x = 120/8 = 15

Now, Breadth = 15
so, length = 15 × 3 = 45

So, its area = Length × Breadth = 45 × 15 = 675 sq. m.

১১,৬৪০.
In seven given numbers, the average of the first four numbers is 4 and the last four numbers is also 4. If the average of these given seven numbers is 3, the fourth number is -
  1. ক
    ক) 3
  2. খ
    খ) 4
  3. গ
    গ) 11
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
Question: In seven given numbers, the average of the first four numbers is 4 and the last four numbers is also 4. If the average of these given seven numbers is 3, the fourth number is - 


Solution:
Sum of first four numbers = 4 × 4 = 16
Sum of last four numbers = 4 × 4 = 16
Sum of first four numbers and last four numbers = 16 + 16 = 32

Again, Sum of seven numbers = 7 × 3 = 21

So, fourth number is = 32 - 21 = 11
১১,৬৪১.
If TOPIC is written as POITC, then how would FINAL be written in the same code?
  1. ক
    IAFLN
  2. খ
    LNIAF
  3. গ
    NIAFL
  4. ঘ
    INAFL
ব্যাখ্যা

Question: If TOPIC is written as POITC, then how would FINAL be written in the same code?

Solution:
The code contains the letters of the word in the order- third,second, fourth, first and fifth

১১,৬৪২.
A coin is thrown 3 times in the air. What is the probability that one head is followed by two tails?
  1. ক
    ক) 1/2
  2. খ
    খ) 1/4
  3. গ
    গ) 1/8
  4. ঘ
    ঘ) 5/6
ব্যাখ্যা
মোট নমুনা বিন্দু = {HHH, HHT, HTT, HTH, THH, TTH, THT, TTT}
= 8টি
প্রথমে  Head এবং পরে দুইবার Tail হওয়ার অনুকূল ফলাফল = HTT = 1টি 

নির্ণেয় সম্ভাব্যতা = 1/8
১১,৬৪৩.
How much will it cost to fence in a field that is 3000 cm long and 600 cm wide with fence that costs Tk. 50 a meter?
  1. ক
    ক) 720 Tk.
  2. খ
    খ) 1800 Tk.
  3. গ
    গ) 9000 Tk.
  4. ঘ
    ঘ) 3600 Tk.
ব্যাখ্যা
Question: How much will it cost to fence in a field that is 3000 cm long and 600 cm wide with fence that costs Tk. 50 a meter?

Solution: 
The perimeter of the field is 2(3000 + 600) cm
= 2 × 3600 cm
= 7200 cm
= 72 m

Total cost = 72 × 50 = 3600 Tk. 
১১,৬৪৪.
If tan 6A = √3, then find A. 
  1. ক
    15°
  2. খ
    10°
  3. গ
    25°
  4. ঘ
    30°
ব্যাখ্যা

Question: If tan 6A = √3, then find A.

Solution:
tan 6A = √3
⇒ tan 6A = tan60°
⇒ 6A = 60°
⇒ A = 60°/6
∴ A = 10°

১১,৬৪৫.
√(0.25/0.0009) × √(0.09/0.36) is equal to?
  1. ক
    ক) 5/6
  2. খ
    খ) 7(1/6)
  3. গ
    গ) 7(1/3)
  4. ঘ
    ঘ) 2(5/3)
  5. ঙ
    ঙ) 8(1/3)
ব্যাখ্যা

According to question,
√(0.25/0.0009) × √(0.09/0.36)
⇒ √((25/9)×100) × √(9/36)
⇒ ((5×10)/3) × (3/6)
⇒ 25/3
⇒ 8(1/3)

১১,৬৪৬.
Find the value of 6(-3)(1/3)(-0.25)
  1. ক
    ক) 6
  2. খ
    খ) 4.5
  3. গ
    গ) 1.5
  4. ঘ
    ঘ) -0.5
ব্যাখ্যা

6(-3)(1/3)(-0.25)
= 6×0.25
= 1.5

১১,৬৪৭.
What is the ratio of 3/4 to the product 4(3/4)?
  1. ক
    ক) 1/3
  2. খ
    খ) 1/4
  3. গ
    গ) 4/9
  4. ঘ
    ঘ) 9/4
ব্যাখ্যা
Question: What is the ratio of 3/4 to the product 4(3/4)? 

Solution:
ratio = (3/4)/{4(3/4)}
         = (3/4)/{(4 × 3)/4}
         = (3/4)/(3/1)
         = (3/4) × (1/3)
         = 1/4
১১,৬৪৮.
A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is.
  1. ক
    49 m2
  2. খ
    36 m2
  3. গ
    42 m2
  4. ঘ
    48 m2
ব্যাখ্যা
Question: A cistern 6 m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is.

Solution: 
The upper part of the calf is open. Here the area of ​​the wetted part is asked.
Therefore, the upper opening has to be excluded from the total area.
Here,
Length = 6 m
Width = 4 m
Height = 1 m 25 cm = 1.25 m

So, the area of total wet surface = 2{(6 × 4) + (4 × 1.25) + (6 × 1.25)} - (6 × 4)
= (2 × 36.5) - 24 
= 73 - 24
= 49 m2
১১,৬৪৯.
Ratul and Sajib were classmates. Their earnings now are in the ratio 5:6. The ratio of their expenses is 7:9. Sajib saves Tk. 3,000 every month while Ratul saves Tk. 1000/- more than Somesh. Find the total earnings and expenses of each of them.
  1. ক
    ক) Ratul - 25000, 21000; Sajib - 30000, 27000
  2. খ
    খ) Ratul - 30000, 27000; Sajib - 36000, 32000
  3. গ
    গ) Ratul - 36000, 32000; Sajib - 30000, 27000
  4. ঘ
    ঘ) None of the above
ব্যাখ্যা

Income ratio = Ratul : Sajib = 5 : 6 = 5/6
Common factor helps in finding actual values easily
So, take 'A' as a common factor.
Income of Ratul = 5A; Income of Sajib = 6A
(Expenses of Ratul)/(Expenses of Sajib) = (Ratul Income - Ratul Saving)/(Sajib Income -Sajib Saving) = 7/9
Since Ratul save, Tk. 1000/- more than Sajib, Ratul's savings = Tk. 4000/-
5A - 4000/6A - 3000 = 7/9
∴ 9(5A-4000) = 7(6A-3000)
∴ A = 5000
Income of Ratul = 5A = 25000 ; Income of Sajib = 6A = 30000
Spending of Ratul =25000 - 4000 = 21000
Spending of Sajib = 30000 - 3000 = 27000.

১১,৬৫০.
A, B and C play cricket. The ratio of A’s runs to B’s runs and B’s runs to C’s is 3 ∶ 2. They make altogether 342 runs. How many runs did A make?
  1. ক
    ক) 108
  2. খ
    খ) 72
  3. গ
    গ) 162
  4. ঘ
    ঘ) 99
ব্যাখ্যা
A + B + C = 342

A : B = 3 : 2 = 9 : 6
B : C = 3 : 2 = 6 : 4
A : B : C = 9 : 6 : 4

∴ Runs made by A = 9/19 × 342 = 162

১১,৬৫১.
A line intersecting a circle in two points is called a _______.
  1. ক
    ক) Secant
  2. খ
    খ) Chord
  3. গ
    গ) Diameter
  4. ঘ
    ঘ) Tangent
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
A line intersecting a circle in two points is called a Secant.
১১,৬৫২.
If α and β are positive acute angles, sin(4α - β) = 1 and cos(2α + β) = 1/2, then the value of (α + 2β) is?
  1. ক
    40°
  2. খ
    55°
  3. গ
    45°
  4. ঘ
    50°
ব্যাখ্যা
Question: If α and β are positive acute angles, sin(4α - β) = 1 and cos(2α + β) = 1/2, then the value of (α + 2β) is?

Solution:
Given,
sin(4α - β) = 1
⇒ sin(4α - β) = sin 90°
⇒ 4α - β = 90° ..... (1)

again, cos(2α + β) = 1/2
⇒ cos(2α + β) = cos 60°
⇒ 2α + β = 60° .... (2)

(1) + (2) ⇒ 4α - β + 2α + β = 90° + 60°
⇒ 6α = 150°
⇒ α = 25°
From (2), β = 60° - (2 × 25°) = 10°
∴ (α + 2β) = 25° + (2 × 10°) = 45°
১১,৬৫৩.
A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?
  1. ক
    2/7
  2. খ
    3/7
  3. গ
    11/27
  4. ঘ
    30/112
ব্যাখ্যা
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 2 women?

Solution: 
the ways of choosing 4 from 8 employs = 8C4 = 70
choosing 2 women from 5 women = 5C2 = 10
choosing 2 men from 3 men = 3C2 = 3

probability = (3 × 10)/70 = 3/7
১১,৬৫৪.
The distance between A and B is 30 km. A boat makes a return journey from point A to point B and back in 10 hours 30 minutes. One way it travels with the stream and on the return it travels against the stream. If the speed of the stream increases by 2 km/hr, the return journey takes 17 hours 30 minutes. What is the speed of the boat in still water?
  1. ক
    ক) 5 km/hr
  2. খ
    খ) 6 km/hr
  3. গ
    গ) 7 km/hr
  4. ঘ
    ঘ) 8 km/hr
ব্যাখ্যা
Question: The distance between A and B is 30 km. A boat makes a return journey from point A to point B and back in 10 hours 30 minutes. One way it travels with the stream and on the return it travels against the stream. If the speed of the stream increases by 2 km/hr, the return journey takes 17 hours 30 minutes. What is the speed of the boat in still water?

Solution:
Let, 
x km/hr be the speed of boat upstream
y km/hr be the speed of boat downstream

∴ 30/x + 30/y = 10 hours 30 minutes = 10.5 hour = 105/10 hour = 21/2
⇒ 30/x + 30/y = 21/2
⇒ 60/x + 60/y = 21
⇒ 20/x + 20/y = 7
⇒ 20/x = 7 - 20/y
⇒  20/x = (7y - 20)/y
⇒ x/20 = y/(7y - 20)
∴ x = 20y/(7y - 20) ............(1)


If the speed of the stream increases by 2 km/hr
30/(x - 2) + 30/(y + 2) = 17 hours 30 minutes = 17.5 hour = 175/10 = 35/2
⇒ 30/(x - 2) + 30/(y + 2) = 35/2
⇒ 60/(x - 2) + 60/(y + 2) = 35
⇒ 12/(x - 2) + 12/(y + 2) = 7
⇒ 12/(x - 2) = 7 - 12/(y + 2)
⇒ 12/(x - 2) = (7y + 14 -12)/(y + 2)
⇒ 12/(x - 2) = (7y + 2)/(y + 2)
⇒ (x - 2)/12 = (y + 2)/(7y + 2)
⇒ x - 2 = (12y + 24)/(7y + 2)
⇒ x = (12y + 24)/(7y + 2) + 2
⇒ x = (12y + 24 + 14y + 4)/(7y + 2)
∴ x = (26y + 28)/(7y + 2) ...............(2)

From (1) and (2) we get,
20y/(7y - 20) = (26y + 28)/(7y + 2)
⇒ 20y(7y + 2) = (26y + 28)(7y - 20)
⇒ 140y2 + 40y = 182y2 - 324y - 560
⇒ 42y2 - 364y - 560 = 0
⇒ 3y2 - 26y - 40 = 0
⇒ 3y2 - 30y + 4y - 40 = 0
⇒ 3y(y - 10) + 4(y - 10) = 0
⇒ (y - 10)(3y + 4) = 0
∴ y = 10 or  y = - 4/3 [which is not acceptable]
∴ y =10

From (1) we get 
x = 20y/(7y - 20)
= 200/(70 - 20)
= 4 
 
∴ The speed of the boat in still water = (10 + 4)/2 km/hr
= 7 km/hr
১১,৬৫৫.
Three unbiased coins are tossed. What is the probability of getting at least two heads?
  1. ক
    3/4
  2. খ
    1/4
  3. গ
    1/3
  4. ঘ
    1/2
ব্যাখ্যা
Question: Three unbiased coins are tossed. What is the probability of getting at least two heads?

Solution:
The events when three unbiased coins are tossed = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Total number of events 8

The events of getting at least two heads {HHH, HHT, HTH, THH}

Number of expected events = 4

∴ The probability of getting at least two heads is = 4/8 = 1/2
১১,৬৫৬.
If x2 + y2 + z2 = 16 and xy + yz + zx = 10, find the value of x + y + z.
  1. ক
    ± 5
  2. খ
    ± 6
  3. গ
    ± 7
  4. ঘ
    ± 8
  5. ঙ
    None
ব্যাখ্যা
Question: If x2 + y2 + z2 = 16 and xy + yz + zx = 10, find the value of x + y + z.

Solution:
x2 + y2 + z2 = 16 
xy + yz + zx = 10

We know that,
(x + y + z)2 = x2 + y2 + z2 + 2(xy + yz + zx )
⇒ (x + y + z)2 = 16 + 2 × 10
⇒ (x + y + z)2 = 36
⇒ x + y + z = √36
⇒ x + y + z = ± 6

∴ The value of (x + y + z) is ± 6.
১১,৬৫৭.
If y = sin(sinx) then what is the value of dy/dx?
  1. ক
    cos(sinx)
  2. খ
    cosx.cos(cosx)
  3. গ
    cos2x
  4. ঘ
    cosx.cos(sinx)
ব্যাখ্যা

Question: If y = sin(sinx) then what is the value of dy/dx?

Solution:

১১,৬৫৮.
If x = 7 -  4√3, then √x + 1/√x =?
  1. ক
    3
  2. খ
    4
  3. গ
    6
  4. ঘ
    8
ব্যাখ্যা
Question: If x = 7 -  4√3, then √x + 1/√x =?

Solution:
Given that,
x = 7 -  4√3
⇒ x = 4 - 4√3 + 3
⇒ x = (2)2 - 2 . 2 . √3 + (√3)2
⇒ x = (2 - √3)2
∴  √x = 2 - √3

∴ 1/√x = 1/(2 - √3)
= {1(2 + √3)}/{(2 - √3)(2 + √3)}
= (2 + √3)/{22 - (√3)2}
= (2 + √3)/(4 - 3)
= 2 + √3

∴ √x + 1/√x = 2 - √3 + 2 + √3
= 4
১১,৬৫৯.
The value of a machine depreciates every year by 10%. If its present value is Tk. 50000 then the value of the machine after 2 years is?
  1. ক
    Tk. 40000
  2. খ
    Tk. 45500
  3. গ
    Tk. 35500
  4. ঘ
    Tk. 40500
ব্যাখ্যা
Question: The value of a machine depreciates every year by 10%. If its present value is Tk. 50000 then the value of the machine after 2 years is?

solution:
Given that,
Present value of machine = 50000
Depreciation rate = 10%
And year = 2

Now,
After first year value of machine = (100 - 10)% of 50000 = (90/100) × 50000 = Tk. 45000
And after 2 years value of machine = (100 - 10)% of 45000 = (90/100) × 45000 = Tk. 40500

∴ value of machine after 2 years is Tk. 40500
১১,৬৬০.
Asif bought 5 apples at Taka 15 and sold 3 apples at Taka 15. What will be the rate of profit-
  1. ক
    66.67%
  2. খ
    26.75%
  3. গ
    50%
  4. ঘ
    33.33%
ব্যাখ্যা
Question: Asif bought 5 apples at Taka 15 and sold 3 apples at Taka 15. What will be the rate of profit-

Solution:
5 টি আপেলের ক্রয়মূল্য 15 টাকা
1 টি আপেলের ক্রয়মূল্য 15/5 = 3 টাকা

আবার,
3 টি আপেলের বিক্রয়মূল্য 15 টাকা
1 টি আপেলের বিক্রয়মূল্য 15/3 = 5 টাকা

∴ লাভ = 5 - 3 = 2 টাকা

∴ 3 টাকায় লাভ হয় 2 টাকা
1 টাকায় লাভ হয় 2/3 টাকা
100 টাকায় লাভ হয় 200/3 = 66.67 টাকা

∴  লাভ 66.67%
১১,৬৬১.
A swimmer can swim at a speed of 4 km/h in still water. If the river current flows at 2 km/h, how long will it take to swim 12 km downstream and then return to the starting point?
  1. ক
    6 hours
  2. খ
    7 hours
  3. গ
    5 hours
  4. ঘ
    8 hours
ব্যাখ্যা

Question: A swimmer can swim at a speed of 4 km/h in still water. If the river current flows at 2 km/h, how long will it take to swim 12 km downstream and then return to the starting point?

Solution: 
Speed of the swimmer in still water = 4 km/h
Speed of the current = 2 km/h
Distance one way = 12 km

Downstream Speed = 4 + 2 = 6 km/h
Upstream Speed = 4 - 2 = 2 km/h 

Time taken downstream = 12/6 = 2 hours
Time taken upstream = 12/2 = 6 hours

∴ Total time = 6 + 2 
= 8 hours

১১,৬৬২.
একটি হীরার কোম্পানির মালিক চুরি রোধ করার জন্য তিন স্তর বিশিষ্ট সুরক্ষা গ্রহণ করলো, যেখানে হীরা পর্যন্ত পৌঁছাতে বা হীরা নিয়ে বের হতে একটি চোরকে তিন দরজার তিন জন দাড়োয়ানকে অতিক্রম করতে হয়। কৌশলে একটি চোর কোম্পানিতে ঢুকে কিছু হীরার রিং চুরি করে বের হওয়ার সময় প্রত্যেক দাড়োয়ানকে তার কাছে থাকা রিং-এর ১/২ অংশের চেয়ে ২টি বেশি রিং দিতে হলো। চোরটি একটি রিং নিয়ে পালালে, কতগুলো হীরার রিং চুরি করেছিল?
  1. ক
    ৩২ টি
  2. খ
    ২৪ টি
  3. গ
    ৪৮ টি
  4. ঘ
    ৩৬ টি
  5. ঙ
    কোনটিই নয়
ব্যাখ্যা
প্রশ্ন: একটি হীরার কোম্পানির মালিক চুরি রোধ করার জন্য তিন স্তর বিশিষ্ট সুরক্ষা গ্রহণ করলো, যেখানে হীরা পর্যন্ত পৌঁছাতে বা হীরা নিয়ে বের হতে একটি চোরকে তিন দরজার তিন জন দাড়োয়ানকে অতিক্রম করতে হয়। কৌশলে একটি চোর কোম্পানিতে ঢুকে কিছু হীরার রিং চুরি করে বের হওয়ার সময় প্রত্যেক দাড়োয়ানকে তার কাছে থাকা রিং-এর ১/২ অংশের চেয়ে ২টি বেশি রিং দিতে হলো। চোরটি একটি রিং নিয়ে পালালে, কতগুলো হীরার রিং চুরি করেছিল?

সমাধান:
 ধরি,
সে হীরা চুরি করেছিল = ক টি

তাহলে, ১ম দাড়োয়ানকে দিল = (ক/২) + ২ = (ক + ৪)/২ টি
অবশিষ্ট থাকলো = ক - {(ক + ৪)/২} = (ক - ৪)/২ টি

২য় দাড়োয়ানকে দিল = {(ক - ৪)/৪} + ২ = (ক + ৪)/৪ টি
অবশিষ্ট রইলো = {(ক - ৪)/২} - {(ক + ৪)/৪} = (ক - ১২)/৪ টি

৩য় দাড়োয়ানকে দিল = {(ক - ১২)/৮} + ২ = (ক + ৪)/৮ টি
অবশিষ্ট রইলো = {(ক - ১২)/৪} - {(ক + ৪)/৮} = (ক - ২৮)/৮

প্রশ্নমতে,
(ক - ২৮)/৮ = ১
⇒ ক - ২৮ = ৮
⇒ ক = ৩৬
সুতরাং, সে ৩৬ টি হীরার রিং চুরি করেছিল।
১১,৬৬৩.
A committee of 5 members is to be formed by selecting out of 6 men and 7 women. What is the probability that the committee has exactly 2 men and 3 women?
  1. ক
    175/429
  2. খ
    223/429
  3. গ
    1/2
  4. ঘ
    11/120
ব্যাখ্যা
Question: A committee of 5 members is to be formed by selecting out of 6 men and 7 women. What is the probability that the committee has exactly 2 men and 3 women?

Solution:
Total member = 6 + 7 = 13
2 men can be selected out of 6 men in  6C2 ways
3 women can be selected out of 7 women in 7C3 ways
Required number of ways = 6C2 × 7C3 = 15 × 35 = 525

The total number of ways to make committee with all members = 13C5 = 1287

∴ The probability that the committee has exactly 2 men and 3 women = 525/1287
= 175/429
১১,৬৬৪.
A man bought 40 shares of Tk 100 each at Tk 95 and sold them at Tk 110. What is his total gain?
  1. ক
    Tk 600
  2. খ
    Tk 400
  3. গ
    Tk 800
  4. ঘ
    Tk 200
ব্যাখ্যা
Question: A man bought 40 shares of Tk 100 each at Tk 95 and sold them at Tk 110. What is his total gain?

Solution:
→ Buying price = 40 × 95 = Tk 3,800
→ Selling price = 40 × 110 = Tk 4,400
→ Profit = 4400 − 3800 = Tk 600
১১,৬৬৫.
Daud is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Daud?
  1. ক
    36 years
  2. খ
    23years
  3. গ
    29 years
  4. ঘ
    25 years
  5. ঙ
    Cannot be determined
ব্যাখ্যা
Question: Daud is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Daud?

Solution:
Let Rohan's age be x years.
Then,
Daud's age = (x - 9) years.

ATQ,
(x - 9)/x = 4/5
⇒ 5x - 45 = 4x
∴ x = 45

Hence, Daud's age = (x - 9) = 45 - 9 = 36 years.
১১,৬৬৬.
In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.
  1. ক
    40000
  2. খ
    45000
  3. গ
    55000
  4. ঘ
    50000
ব্যাখ্যা
Question: In an election 4% of votes cast are invalid. A candidate gets 55% of casted votes and wins the election by 4800 votes. Find the total number of votes casted.

Solution:
বিজয়ী প্রার্থী ভোট পায়= 55%
বৈধ ভোট = (100 - 4)% = 96%

বিজয়ী প্রার্থী বৈধ ভোটের শতকরা পায় = (55 × 96)/100
= 52.8%

পরাজিত প্রার্থী ভোট পায় = (96 - 52.8)%
= 43.2%

বিজয়ী প্রার্থী ও পরাজিত প্রার্থীর ভোটের পার্থক্য = (52.8 - 43.2)%
= 9.6%

প্রশ্নমতে
9.6% = 4800
1% = 4800/9.6
100% = (4800 × 100)/9.6
= 50000
১১,৬৬৭.
A batsman makes a score of 80 runs in the 16th innings and increases average by 3. What is his average after 16th innings?
  1. ক
    ক) 25
  2. খ
    খ) 29
  3. গ
    গ) 32
  4. ঘ
    ঘ) 35
ব্যাখ্যা

Question: A batsman makes a score of 80 runs in the 16th innings and increases average by 3. What is his average after 16th innings?

Solution: 
Assume his initial average after 15 innings = x
His total runs after 15 innings = 15x

After scoring 80 runs his average got increased by 3 to x + 3
So his total runs after 16 innings= 16 × (x +3)

But it was given that the difference in the total scores after 15 innings and 16 innings =80
16×(x + 3) - 15X=80
16x + 48 - 15x = 80 
x + 48 = 80
x = 32 

His average after 16th innings is = 32 + 3 = 3 = 35 

১১,৬৬৮.
The difference between two integers is 4. If their product is 221, then the sum of the two numbers is?
  1. ক
    30
  2. খ
    18
  3. গ
    26
  4. ঘ
    22
ব্যাখ্যা

Question: The difference between two integers is 4. If their product is 221, then the sum of the two numbers is?

Solution:
Let the two integers be x and y
The difference between the two integers is 4,
∴ x - y = 4 and their product is, xy = 221

We know,
⇒ (x + y)2 = (x - y)2 + 4xy
⇒ (x + y)2 = 42 + (4 × 221)
⇒ (x + y)2 = 16 + 884
⇒ (x + y)2 = 900
⇒ x + y = √900
∴ x + y = 30

∴ The sum of the two numbers is 30

১১,৬৬৯.
A person wants an annual income of Tk 2,400 from a stock paying 8% dividend. If the market price of the Tk 100 stock is Tk 120, how much should he invest?
  1. ক
    Tk 30,000
  2. খ
    Tk 32,000
  3. গ
    Tk 36,000
  4. ঘ
    Tk 40,000
ব্যাখ্যা
Question: A person wants an annual income of Tk 2,400 from a stock paying 8% dividend. If the market price of the Tk 100 stock is Tk 120, how much should he invest?

Solution:
→ Calculate Dividend per Share (প্রতি শেয়ারে লভ্যাংশ):
Dividend is paid on face value, not market price.
Dividend per share = Face value × Dividend rate
= Tk 100 × 8%
= Tk 8/share/year.

→ Determine Number of Shares Needed (প্রয়োজনীয় শেয়ার সংখ্যা):
To earn Tk 2,400/year with Tk 8/share/year:
Number of shares = Total desired income ÷ Dividend per share
= 2,400 ÷ 8
= 300 shares.

→ Calculate Total Investment (মোট বিনিয়োগ):
Each share costs Tk 120 (market price).
Total investment = Number of shares × Market price
= 300 × Tk 120
= Tk 36,000.
১১,৬৭০.
A man takes 6 hours 30 min in going by cycle and coming back by scooter. He would have lost 2 hours 10 min by going on cycle both ways. How long would it take him to go by scooter both ways?
  1. ক
    ক) 2 hr 40 min
  2. খ
    খ) 3 hr 20 min
  3. গ
    গ) 4 hr 20 min
  4. ঘ
    ঘ) 2 hr 20 min
ব্যাখ্যা

Let,
The distance be x km.
Then,
Time taken to cover x km by cycle + Time taken to cover x km by scooter = 6 hr 30 min
⇒ (Time taken to cover 2x km by cycle) + (Time taken to cover 2x km by scooter) = 13 hrs
But,
Time taken to cover 2x km by cycle = 8 hr 40 min.
∴ Time Taken to cover 2x km by scooter = 13 hrs - 8 hr 40 min
= 4 hr 20 min.
Hence, required time = 4 hours 20 min.

১১,৬৭১.
A median of a triangle divides it into two ___
  1. ক
    ক) congruent triangles
  2. খ
    খ) triangles of equal area
  3. গ
    গ) isosceles triangles
  4. ঘ
    ঘ) right triangles
ব্যাখ্যা

ত্রিভুজের যেকোন মধ্যমা ত্রিভুজটিকে সমান ক্ষেত্রফলবিশিষ্ট দুটি ত্রিভুজক্ষেত্রে বিভক্ত করে।

১১,৬৭২.
Nehal's regular pay is Tk 25 per hour up to 40 hours. Overtime is twice the payment for regular times. If he was paid Tk 1800, how many hours overtime did he work?
  1. ক
    8 hours.
  2. খ
    10 hours.
  3. গ
    12 hours.
  4. ঘ
    16 hours.
  5. ঙ
    20 hours.
ব্যাখ্যা
Question: Nehal's regular pay is Tk 25 per hour up to 40 hours. Overtime is twice the payment for regular times. If he was paid Tk 1800, how many hours overtime did he work?

Solution:
Nehal’s regular wage for 40 hours = (25 × 40) = 1000 Taka.
Amount earned from overtime = (1800 - 1000) Taka = 800 Taka.
Since the overtime rate is twice the regular hourly wage,
Total overtime hours worked = 800 ÷ (25 × 2) hours
= 16 hours.
১১,৬৭৩.
If tomorrow is Friday, what day of the week will it be after 46 days?
  1. ক
    Wednesday
  2. খ
    Saturday
  3. গ
    Friday
  4. ঘ
    Tuesday
  5. ঙ
    Monday
ব্যাখ্যা

Question: If tomorrow is Friday, what day of the week will it be after 46 days?

Solution: 
Given that,
Tomorrow is Friday, then today is Thursday

Days of the week repeat every 7 days. So, find the remainder when 46 is divided by 7.
So 46 ÷ 7 = 6 weeks + 4 days remainder.
So the day will move 4 days forward. 

Count 4 days from Thursday,
Thursday → Friday → Saturday → Sunday → Monday

Therefore, 46 days from today (Thursday) is Monday.

১১,৬৭৪.
In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is-
  1. ক
    29
  2. খ
    30
  3. গ
    31
  4. ঘ
    32
  5. ঙ
    33
ব্যাখ্যা
Question: In an examination, a candidate is required to pass all five different subjects. The number of ways he can fail is-

Solution:
The candidate will fail if he fails either in 1 or 2 or 3 or 4 or 5 subjects,
∴ Required number of ways 5C1 + 5C2 + 5C3 + 5C4 + 5C5
= 5 + 10 + 10 + 5 + 1
= 31
১১,৬৭৫.
If 10x = 1/2 then, 10- 8x = ?
  1. ক
    128
  2. খ
    64
  3. গ
    256
  4. ঘ
    16
  5. ঙ
    None
ব্যাখ্যা
Question: If 10x = 1/2 then, 10- 8x = ?

Solution:
10- 8x = (10x)- 8
= (1/2)- 8
= 28
= 256
১১,৬৭৬.
A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is -
  1. ক
    150 meters
  2. খ
    200 meters
  3. গ
    220 meters
  4. ঘ
    250 meters
ব্যাখ্যা
Question: A train passes two bridges of length 800 m and 400 m in 100 seconds and 60 seconds respectively. The length of the train is -

Solution:
Let length of the train be x m and speed of the train is s kmph.
Speed, s = (x + 800)/100 . . . . . (i)
Speed, s = (x + 400)/60. . . . . (ii) 

Equating equation (i) and (ii),
we get,
(x + 800)/100 = (x + 400)/60
Or, (x + 800)/5 = (x + 400)/3
Or, 5x + 2000 = 3x + 2400
Or, 2x = 400
∴ x = 200m

∴ The length of the train is 200 meters.
১১,৬৭৭.
A man on tour travels first 60 km at 20 km/hr and the next 60 km at 30 km/hr. The average speed for the first 120 km of the tour is :
  1. ক
    28 km/hr
  2. খ
    18 km/hr
  3. গ
    27 km/hr
  4. ঘ
    24 km/hr
ব্যাখ্যা

Question: A man on tour travels first 60 km at 20 km/hr and the next 60 km at 30 km/hr. The average speed for the first 120 km of the tour is :

সমাধান:
প্রথম অংশের জন্য সময় = দূরত্ব/গতিবেগ
= 60 কিমি/20 কিমি/ঘন্টা
= 3 ঘন্টা

দ্বিতীয় অংশের জন্য সময় = দূরত্ব/গতিবেগ
= 60 কিমি/30 কিমি/ঘন্টা
= 2 ঘন্টা

মোট অতিক্রান্ত দূরত্ব = 60 কিমি + 60 কিমি = 120 কিমি
মোট সময় = 3 ঘন্টা + 2 ঘন্টা = 5 ঘন্টা

∴ গড় গতিবেগ = মোট দূরত্ব/মোট সময় 
= 120 কিমি/5 ঘন্টা
= 24 কিমি/ঘন্টা

১১,৬৭৮.
The sum of ages of 5 children born at the intervals of 4 years each is 70 years. What is the age of the eldest child?
  1. ক
    22 years
  2. খ
    24 years
  3. গ
    20 years
  4. ঘ
    18 years
  5. ঙ
    Nonr of these
ব্যাখ্যা
Question: The sum of ages of 5 children born at the intervals of 4 years each is 70 years. What is the age of the eldest child?

Solution:
Let the ages of children be x, (x + 4), (x + 8), (x + 12) and (x + 16) years.
Then, 
x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 70
5x + 40 = 70
5x = 70 - 40
⇒ 5x = 30
⇒ x = 6
∴ Age of the eldest child = x + 16 = 6 + 16 = 22 years.
১১,৬৭৯.
The ratio between the ages of Mobin and Xami is 4:5 and that between the ages of Mobin and Faisal is 5:6. If the sum of the ages of the three is 69 years, what is Xami’s age?
  1. ক
    ক) 20
  2. খ
    খ) 24
  3. গ
    গ) 25
  4. ঘ
    ঘ) 30
ব্যাখ্যা

Mobin's age:Xam's age = 4:5 = 1:5/4
Mobin's age:Faisal's age = 5:6 = 1:6/5
Let, Mobin's age be x years. Then, Xami's age = 5x/4
And, Faisal's age = 6x/5 years
∴ x + 5x/4 + 6x/5 = 69
⇒ 20x + 25x + 24x = 69 × 20
⇒ 20x + 25x + 24x = 1380
⇒ 69x = 1380
⇒ x = 1380/69
= 20
Xami's age = 5x/4 = (5 × 20)/4
= 25 years

১১,৬৮০.
A computer is available for Tk. 39000 cash or Tk. 17000 as cash down payment followed by five monthly instalments of Tk. 4800 each. What is the rate of interest under the instalment plan?
  1. ক
    ক) 35.71% p.a.
  2. খ
    খ) 36.71% p.a.
  3. গ
    গ) 37.71% p.a.
  4. ঘ
    ঘ) 38.71% p.a.
ব্যাখ্যা

Total cost of the computer = Tk. 39000
Down payment = Tk. 17000
Balance = Tk. (39000 - 17000) = Tk. 22000.
Let the rate of interest be R% p.a.
Amount of Tk. 22000 for 5 months
= {22000 + 22000 × (5/12) × R/100}
= {22000 + (275R/3)}

The customer pays the shopkeeper Tk. 4800 after 1 month,
Tk. 4800 after 2 months, ...... and Tk. 4800 after 5 months.

Thus, the shopkeeper keeps Tk. 4800 for 4 months, Tk. 4800 for 3 months, Tk. 4800 for 2 months, Tk. 4800 for 1 months and Tk. 4800 at the end.

∴ sum of the amounts of these installments
= (Tk. 4800 + S.I. on Tk. 4800 for 4 months) + (Tk. 4800 + S.I. on Tk. 4800 for 3 months) + ...... + (Tk. 4800 + S.I. on Tk. 4800 for 1 month) + Tk. 4800
= Tk. (4800 × 5) + S.I. on Tk. 4800 for (4 + 3 + 2 + 1) months
= Tk. 24000 + S.I. on Tk. 4800 for 10 months
= 24000 × 4800 × R × (10/12) × (1/100)
= (24000 + 40 R)

∴ {22000 + (275R/3)} = (24000 + 40 R)
⇒ 155R/3 = 2000
⇒ R = (2000 × 3)/155
= 38.71

১১,৬৮১.
Rajib finishes his work in 15 days while Sagor takes 10 days. Find the number of days it will take them to complete the same work together?
  1. ক
    ক) 5 days
  2. খ
    খ) 6 days
  3. গ
    গ) 7 days
  4. ঘ
    ঘ) 8 days
ব্যাখ্যা
Question: Rajib finishes his work in 15 days while Sagor takes 10 days. Find the number of days it will take them to complete the same work together?

Solution: 
রাজিব, ১৫ দিনে করে ১ অংশ 
১ দিনে করে ১/১৫ অংশ  

সাগর, ১০ দিনে করে ১ অংশ 
১ দিনে করে ১/১০ অংশ 

একসাথে ১ দিনে করে = (১/১৫) + (১/১০)
= (২ + ৩)/৩০
= ৫/৩০ 
= ১/৬ অংশ 

সম্পূর্ণ কাজ করবে ৬ দিনে। 
১১,৬৮২.
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
    450 meter
  2. খ
    500 meter
  3. গ
    350 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
১১,৬৮৩.
If logx(1/125) = - 3, then x = ?
  1. ক
    1/4
  2. খ
    5
  3. গ
    10
  4. ঘ
    1/9
ব্যাখ্যা

Question: If logx(1/125) = - 3, then x = ?

Solution:
Given that,
logx(1/125) = - 3
⇒ x- 3 = 1/125  [loga(b) = c  ⇒ ac = b]
⇒ 1/x3 = 1/125
⇒ x3 = 125
∴ x = 5

১১,৬৮৪.
A team of 2 men and 5 women completed one-fourth of a project in 3 days. After 3 days one woman left the team and one man joined the team. The newly formed team took 2 days to complete another one fourth of the project. How many days will 4 men takes to complete the project alone?
  1. ক
    6
  2. খ
    8
  3. গ
    12
  4. ঘ
    24
  5. ঙ
    None
ব্যাখ্যা
Question: A team of 2 men and 5 women completed one-fourth of a project in 3 days. After 3 days one woman left the team and one man joined the team. The newly formed team took 2 days to complete another one fourth of the project. How many days will 4 men takes to complete the project alone?

Solution:
Let efficiency of one man = M
Let efficiency of one woman = W

ATQ,
(2M + 5W) × 3 = 1/4 of work
⇒ 6M + 15W = 1/4  ... (1)

and, (3M + 4W) × 2 = 1/4
⇒ 6M + 8W = 1/4 ...(2)

Subtracting these equations
7W = 0 ⇒ W = 0
Substituting in equation (2)
6M = 1/4
M = 1/24

For 4 men to complete full work, Time taken = 1/(4 × M)
= 1/{4 × (1/24)
= 24/4
= 6
∴ 4 men will take 6 days to complete the project alone.
১১,৬৮৫.
The roots of the quadratic equation 6x2 - x - 2 = o are -
  1. ক
    1/2, - 2/3
  2. খ
    - 1/2, 2/3
  3. গ
    - 1/2, 3/2
  4. ঘ
    None of the above
ব্যাখ্যা
Question: The roots of the quadratic equation 6x2 - x - 2 = o are -

Solution:
6x2 - x - 2 = o
⇒ 6x2 - 4x + 3x - 2 = o
⇒ 2x(3x - 2) + 1 (3x - 2) = o
⇒ (2x + 1)(3x - 2) = 0

So, 2x + 1 = 0
x = - 1/2

Or, 3x - 2 = 0
x = 2/3 
১১,৬৮৬.
If your car runs from A to B at 60 km/hr and on returning from B to A, it is 40 km/hr, then average speed in km/hr of the car will be-
  1. ক
    60 km/hr
  2. খ
    50 km/hr
  3. গ
    42 km/hr
  4. ঘ
    48 km/hr
ব্যাখ্যা

Question: If your car runs from A to B at 60 km/hr and on returning from B to A, it is 40 km/hr, then average speed in km/hr of the car will be-

Solution:
Given that,
The speed of the car is travelling and the returning are 60 km/hr and 40 km/hr

We know,
Average speed = Total distance/Total time

Time = Distance/Speed

Now,
Let the distance between A and B be x

∴ Total time = (x/60) + (x/40)
= (2x + 3x)/120
= 5x/120 = x/24
∴ Total time = x/24

And total distance = x + x = 2x 

∴ Average speed = 2x/(x/24) = 48 km/hr

১১,৬৮৭.
A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.
  1. ক
    Tk. 40
  2. খ
    Tk. 50
  3. গ
    Tk. 55
  4. ঘ
    Tk. 60
ব্যাখ্যা
Question: A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

Solution:
ধরি,
ক্রয়মূল্য = 100 টাকা
25% লাভে বিক্রয়মূল্য = 100 + 25 = 125 টাকা
25% কমে ক্রয়মূল্য = 100 - 25 = 75 টাকা

আবার,
40% লাভে বিক্রয়মূল্য = {75 + 75 × (40/100)}
= 105 টাকা
বিক্রয়মূল্য কম হয় = (125 - 105) টাকা
= 20 টাকা

এখন,
২০ টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = 100 টাকায়
∴ 10 টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = (100 × 10)/20 টাকায়
= 50 টাকা
১১,৬৮৮.
Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is
  1. ক
    30% 
  2. খ
    32.3% 
  3. গ
    37.5% 
  4. ঘ
    None of these
ব্যাখ্যা
Question: Alom invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is

Solution: 
let, Alom invest x taka at 15% per annum for 4 years and y taka at 12% per annum for 3 years

ATQ, 
x × 0.15 × 4 = y × 0.12 × 3
⇒ x/y = 0.36/.6 = 3/5 
 ⇒ x : y = 3 : 5

%percentage = (3/8) × 100% 
= 37.5% 
১১,৬৮৯.
A retailer bought a glass at wholesale and marked it up 80% to its initial retail price of Tk.45. By how many more taka does he need to increase the price to achieve a 100% markup?
  1. ক
    Tk. 3
  2. খ
    Tk. 5
  3. গ
    Tk. 7
  4. ঘ
    Tk. 9
ব্যাখ্যা
Question: A retailer bought a glass at wholesale and marked it up 80% to its initial retail price of Tk.45. By how many more taka does he need to increase the price to achieve a 100% markup?

Solution: 
let, wholesale price x

1.8x = 45 
⇒ x = 45/1.8 
∴ x = 25 taka 

to achieve a 100% markup retail price  = 25 + 25 = 50 taka 

he needs to increase = 50 - 45 taka 
= Tk. 5
১১,৬৯০.
Find the compound interest at the rate of 20% for 3 years on that principal which in 2 years at the rate of 10% per annum gives Tk.10500 as compound interest. (when compounded annually)
  1. ক
    Tk. 36400
  2. খ
    Tk. 35000
  3. গ
    Tk. 36200
  4. ঘ
    Tk. 36000
ব্যাখ্যা
Question: Find the compound interest at the rate of 20% for 3 years on that principal which in 2 years at the rate of 10% per annum gives Tk.10500 as compound interest. (when compounded annually)

Solution:
Let,
P = Principal, R = rate of interest and T = time period

Annual compound interest formula is:
C.I. = P(1 + R/100)T - P
Given,
R = 10% and T = 2
⇒ 10500 = P(1 + 10/100)2 - P
⇒ 10500 = 0.21P
⇒ P = 50000

∴ Principal = Tk. 50000

Then,
R = 20% and T = 3
C.I. = 50000(1 + 20/100)3 - 50000
= 50000(1.2)3 - 50000
= 36400
১১,৬৯১.
A coat was sold for Tk 75. The coat was sold for 150% of the cost of the coat. How much did the coat cost?
  1. ক
    Tk. 150
  2. খ
    Tk. 45
  3. গ
    Tk. 50
  4. ঘ
    Tk. 60
  5. ঙ
    None of these
ব্যাখ্যা
Question: A coat was sold for Tk. 75. The coat was sold for 150% of the cost of the coat. How much did the coat cost?

Solution:
Let,
The cost price of coat = x

ATQ,
150% of x = 75
⇒ (150/100) × x = 75
⇒ x = (75 × 100)/150
∴ x = 50
১১,৬৯২.
If the sum of two numbers is 15 and their difference is 5. Find the two numbers.
  1. ক
    10, 5
  2. খ
    7, 8
  3. গ
    9, 6
  4. ঘ
    11, 4
ব্যাখ্যা
Question: If the sum of two numbers is 15 and their difference is 5. Find the two numbers.

Solution:
Let the two numbers be x and y. Then,
x + y = 15 .......(1)
x − y = 5 .......(2)

Adding equation (1) and (2), we get,
2x = 20
∴ x = 10

Thus, y = 5
Hence, the required numbers are 10 and 5.
১১,৬৯৩.
Traveling at 108 kilometers per hour, a 120-meter train will cross a railway platform that is 210 meters long in…
  1. ক
    12 sec
  2. খ
    15 sec
  3. গ
    13 sec
  4. ঘ
    11 sec
ব্যাখ্যা

Question: Traveling at 108 kilometers per hour, a 120-meter train will cross a railway platform that is 210 meters long in…

Solution:
Here,
Speed of the running train = 108 km/hr
= {108 × (5/18)} m/sec
= 30 m/sec

And length of the train is = 120 metres
Length of platform = 210 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (120 + 210)/30
= 330/30 
= 11 sec

১১,৬৯৪.
If a train stops on the way, its speed is 35 km/hr but if it doesn't, its speed is 40 km/hr. Find the number of minutes the train halts per hour.
  1. ক
    ক) 4 minutes
  2. খ
    খ) 6 minutes
  3. গ
    গ) 7.5 minutes
  4. ঘ
    ঘ) 8 minutes
ব্যাখ্যা

The difference in speed due to stopping = Speed without stoppage - Speed with stoppage
∴ Difference = 40-35 = 5km/hr
Thus, in 1-hour train covers 5 km less.

Time taken to cover 4km = 5km/(40 km/hr)
= 1/8 hours.
= (1/8 × 60) minutes.
= 7.5 minutes.

Hence, The train halts 7.5 minutes per hour.

১১,৬৯৫.
One year ago, the ratio between Fahim and Rohan's ages was 3 : 2. One year hence, the ratio of their age will be 4 : 3. What is the sum of their present ages in years?
  1. ক
    12 years
  2. খ
    14 years
  3. গ
    18 years
  4. ঘ
    21 years
  5. ঙ
    16 years
ব্যাখ্যা

Question: One year ago, the ratio between Fahim and Rohan's ages was 3 : 2. One year hence, the ratio of their age will be 4 : 3. What is the sum of their present ages in years?

Solution:
ধরি, এক বছর আগে ফাহিমের বয়স ছিল 3x বছর এবং রোহানের বয়স ছিল 2x বছর।
বর্তমানে ফাহিমের বয়স = (3x + 1) বছর
বর্তমানে রোহানের বয়স = (2x + 1) বছর

এক বছর পর তাদের বয়সের অনুপাত হবে 4 : 3
∴ এক বছর পর ফাহিমের বয়স হবে = (3x + 1) + 1 = (3x + 2) বছর
∴ এক বছর পর রোহানের বয়স হবে = (2x + 1) + 1 = (2x + 2) বছর

প্রশ্নমতে,
(3x + 2)/(2x + 2) = 4/3
⇒ 3(3x + 2) = 4(2x + 2)
⇒ 9x + 6 = 8x + 8
⇒ 9x - 8x = 8 - 6
⇒ x = 2

সুতরাং, বর্তমানে ফাহিমের বয়স = (3 × 2) + 1 = 6 + 1 = 7 বছর
এবং বর্তমানে রোহানের বয়স = (2 × 2) + 1 = 4 + 1 = 5 বছর
∴ তাদের বর্তমান বয়সের যোগফল = 7 + 5 = 12 বছর।

১১,৬৯৬.
A man can row 9 km/hr in still water and he finds that it takes him twice as long to row upstream as to row downstream the river. Find the rate of the stream.
  1. ক
    ক) 2 km/hr
  2. খ
    খ) 3 km/hr
  3. গ
    গ) 4 km/hr
  4. ঘ
    ঘ) 5 km/hr
ব্যাখ্যা
Question: A man can row 9 km/hr in still water and he finds that it takes him twice as long to row upstream as to row downstream the river. Find the rate of the stream.

Solution: 
Let, the speed of the current be x km/hr
Thus upstream speed = (9 - x) km/h and
downstream speed = (9 + x) km/hr

Let distance traveled be y

Then,
y/(9 - x) = 2y/(9 + x)
1/(9 - x) = 2/(9 + x)
9 + x = 18 - 2x
x + 2x = 18 - 9
3x = 9
x = 3 

the speed of the current be 3 km/hr.
= 3 km/hr.
১১,৬৯৭.
A shopkeeper sells a pen-drive by 5% discount. In 8% discount, he earns Tk.15. What is the marked price of the pen-drive?
  1. ক
    ক) Tk. 500
  2. খ
    খ) Tk. 750
  3. গ
    গ) Tk. 780
  4. ঘ
    ঘ) Tk. 820
ব্যাখ্যা
Suppose, marked price of the pen-drive is Tk. x
At 5% discount, selling price of pen-drive = (100 - 5)x = Tk. 95x
At 8% discount, selling price of pen-drive = (100 - 8)x = Tk. 92x
Therefore,
95% of x - 92% of x = 15
⇒ 95x/100 - 92x/100 = 15
⇒ 3x = 1500
⇒ x = 500
১১,৬৯৮.
What is the greatest number that divides 84, 144 or 18 without any remainder?
  1. ক
    ক) 6
  2. খ
    খ) 12
  3. গ
    গ) 18
  4. ঘ
    ঘ) 24
ব্যাখ্যা

HCF of the given numbers will be the greatest number which can divide 48, 84 and 144
18 = 2 × 3 × 3
84 = 2 × 2 × 3 × 7
144 = 2 × 2 × 2 × 2 × 3 × 3
∴ HCF = 2 × 3 = 6
Hence 6 is the greatest number which divides 18, 84 and 144 without leaving any remainder

১১,৬৯৯.
The area of a rectangle R with width 4 feet is equal to the area of a square S, which has a perimeter of 24 feet. The perimeter of the rectangle R is -
  1. ক
    9 ft
  2. খ
    16 ft
  3. গ
    24 ft
  4. ঘ
    26 ft
ব্যাখ্যা
Question: The area of a rectangle R with width 4 feet is equal to the area of a square S, which has a perimeter of 24 feet. The perimeter of the rectangle R is -

Solution:
ধরি,
চতুর্ভুজ, R এর দৈর্ঘ্য এবং প্রস্থ যথাক্রমে l, b.
বর্গের এক বাহু = a

প্রশ্নমতে,
4a = 24
a = 6

∴ চতুর্ভুজের ক্ষেত্রফল = বর্গের ক্ষেত্রফল
l × b = a2
l = a2/b
= 36/4
= 9

∴ চতুর্ভুজের পরিসীমা = 2(l + b)
= 2(9 + 4)
= 26 feet
১১,৭০০.
The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?
  1. ক
    30
  2. খ
    25
  3. গ
    45
  4. ঘ
    35
ব্যাখ্যা
Question: The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is?

Solution:
(27 × 5) - (25 × 4)
= 135 - 100
= 35