Bank Math

PrepBank · পাতা ৫৬ / ১৬১ · ৫,৫০১–৫,৬০০ / ১৬,১২৪

৫,৫০১.

If H > M = D > P and K = H > T > Z, then which of the following options is not correct?

ক
H > D
খ
Z < H
গ
P < M
ঘ
Z > K

সঠিক উত্তর: ঘ

Z > K

উত্তর

সঠিক উত্তর: ঘ

Z > K

ঘ

ব্যাখ্যা

Question: If H > M = D > P and K = H > T > Z, then which of the following options is not correct?

Solution:
H > M = D > P and K = H > T > Z
By combining: Z < T< K = H > M = D > P

1) P < M True (as, M = D > P → M > P)

2) H > D True (as, H > M = D → H > D)

3) Z < H → True (as, Z < T< K = H → H > Z)

4) Z > K → False (as, Z < T< K, implies Z < K)

৫,৫০২.

In the equation: 45(p - q) - 18(p - q) - 27(p - q) = ?

ক
p - q
খ
0
গ
45(p - q)
ঘ
p

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In the equation: 45(p - q) - 18(p - q) - 27(p - q) = ?

Solution:
45(p - q) - 18(p - q) - 27(p - q)
= (p - q)(45 - 18 - 27)
= (p - q)(45 - 45)
= (p - q) × 0
= 0

৫,৫০৩.

If y/x = 1/5 and x + 2y = 21 then x is -

ক
12
খ
15
গ
18
ঘ
24

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

দেয়া আছে, y/x = 1/5
∴ x = 5y

এবং x + 2y = 21
⇒ 5y + 2y = 21
⇒ 7y = 21
∴ y = 3

∴ x = 5y
= 5 × 3
= 15
Answer: 15

৫,৫০৪.

A boat goes 8 km in one hour along the stream and 2 km in one hour against the stream. The speed in km/hr of the stream is _____

ক
ক) 2
খ
খ) 4
গ
গ) 3
ঘ
ঘ) 5

সঠিক উত্তর: গ

গ) 3

উত্তর

সঠিক উত্তর: গ

গ) 3

গ

ব্যাখ্যা

Question: A boat goes 8 km in one hour along the stream and 2 km in one hour against the stream. The speed in km/hr of the stream is _____

Solution:
এখানে,
নৌকার বেগ + স্রোতের বেগ = ৮ কি.মি.
নৌকার বেগ - স্রোতের বেগ = ২ কি.মি
২ × স্রোতের বেগ = ৬ কি.মি.
∴ স্রোতের বেগ = ৩ কি.মি.

৫,৫০৫.

If the area of a square is 676 square meters, what is the perimeter of the square?

ক
96 meters.
খ
104 meters
গ
92 meters.
ঘ
86 meters.

সঠিক উত্তর: খ

104 meters

উত্তর

সঠিক উত্তর: খ

104 meters

খ

ব্যাখ্যা

Question: If the area of a square is 676 square meters, what is the perimeter of the square?

Solution:
Given,
The area of the square = 676 square meters.

Therefore,
The length of one side of the square = √676 meters = 26 meters.

We know,
The perimeter of a square = 4 × length of one side
= 26 × 4 meters
= 104 meters

Thus, the perimeter of the square is 104 meters.

৫,৫০৬.

A train 108 m long moving at a speed of 50 km/hr crosses a train 112m long coming from opposite direction in 6 seconds. The speed of the second train is-

ক
64 km/hr
খ
76 km/hr
গ
82 km/hr
ঘ
90 km/hr

সঠিক উত্তর: গ

82 km/hr

উত্তর

সঠিক উত্তর: গ

82 km/hr

গ

ব্যাখ্যা

Question: A train 108 m long moving at a speed of 50 km/hr crosses a train 112m long coming from opposite direction in 6 seconds. The speed of the second train is-

Solution:
Distance covered = (108 + 112)
= 220 meter.
and Time = 6 seconds.

∴ Relative speed = (220/6) = (110/3) m/s.
= (110 × 3600)/(3 × 1000) km/hr
= 132 km/hr

Now,
50 + Speed of second train = 132 km/hr

∴ Speed of second train = (132 - 50) km/hr
= 82 km/hr.

৫,৫০৭.

How many years will it take for an investment of Tk. 7500 to earn Tk. 2250 in simple interest rate of 6%?

ক
3 years
খ
4 years
গ
5 years
ঘ
8 years

সঠিক উত্তর: গ

5 years

উত্তর

সঠিক উত্তর: গ

5 years

গ

ব্যাখ্যা

Question: How many years will it take for an investment of Tk. 7500 to earn Tk. 2250 in simple interest rate of 6%?

Solution:
Given that,
Principal, P = 7500
Simple Interest, SI = 2250
Rate of interest, r = 6%
Time, n = ?

We know,
SI = Pnr/100
⇒ n = (S × 100)/(P × r)
= (2250 × 100)/(7500 × 6)
= 5 years

So, it will take 5 years for the investment to earn Tk. 2250 at 6% simple interest.

৫,৫০৮.

The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volume is-

ক
4 : 9
খ
9 : 4
গ
20 : 27
ঘ
20 : 25

সঠিক উত্তর: গ

20 : 27

উত্তর

সঠিক উত্তর: গ

20 : 27

গ

ব্যাখ্যা

Question: The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volume is-

Solution:
Let the radius of both cylinders be 2x and 3x.
Let the height of both cylinders be 5y and 3y.

Ratio of the volume of two cylinders = {π × (2x)² × (5y)}/{π × (3x)² × (3y)}
= (4x² × 5)/(9x² × 3)
= 20/27

∴ Ratio = 20 : 27

৫,৫০৯.

How much interest will Tk. 2,000 earn in one year at an annual rate of 8% if interest is compounded every 6 months?

ক
Tk. 164.8
খ
Tk. 164.0
গ
Tk. 163.2
ঘ
Tk. 160.0

সঠিক উত্তর: গ

Tk. 163.2

উত্তর

সঠিক উত্তর: গ

Tk. 163.2

গ

ব্যাখ্যা

Question: How much interest will Tk. 2,000 earn in one year at an annual rate of 8% if interest is compounded every 6 months?

Solution:
interest = 2000 {1 + (8/(2 × 100))}^{1 × 2} - 2000
= 2000 (1 + (1/25))² - 2000
= 2000 × (26/25)² - 2000
= 2000 × 1.04 × 1.04 - 2000
= 2163.2 - 2000
= 163.2

৫,৫১০.

Which one is incorrect?

ক
cosec²θ - cot²θ = 1
খ
sec²θ - tan²θ = 1
গ
tan²θ + 1 = cot²θ
ঘ
sin²θ + cos²θ = 1

সঠিক উত্তর: গ

tan²θ + 1 = cot²θ

উত্তর

সঠিক উত্তর: গ

tan²θ + 1 = cot²θ

গ

ব্যাখ্যা

Question: Which one is incorrect?

Solution:
ত্রিকোনোমিতিক অনুপাতগুলোর সম্পর্ক:
sin²θ + cos²θ = 1
sec²θ - tan²θ = 1
cosec²θ - cot²θ = 1

৫,৫১১.

Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

ক
2 : 3
খ
3 : 4
গ
4 : 3
ঘ
4 : 5
ঙ
None

সঠিক উত্তর: গ

4 : 3

উত্তর

সঠিক উত্তর: গ

4 : 3

গ

ব্যাখ্যা

Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.

Solution:
5% of A + 4% of B = (2/3) (6% of A + 8% of B)
⇒ A/20 + B/25 = A/25 + 4B/75
⇒ (A/20) - (A/25) = (4B/75) - (B/25)
⇒ A/100 = B/75
⇒ A/B = 100/75 = 4/3
∴ A : B = 4 : 3

৫,৫১২.

The square root of (3 + 2√5)(3 - 2√5) is:

ক
i√3
খ
√10
গ
i√7
ঘ
√11
ঙ
i√11

সঠিক উত্তর: ঙ

i√11

উত্তর

সঠিক উত্তর: ঙ

i√11

ঙ

ব্যাখ্যা

Question: The square root of (3 + 2√5)(3 - 2√5) is:

Solution:
√{(3 + 2√5)(3 - 2√5)}
= √{3² - (2√5)²}
= √{9 - (4 × 5)}
= √{9 - 20}
= √(- 11)
= √{11(- 1)}
= √11 × √(- 1)
= i√11 [যেখানে i² = - 1]

৫,৫১৩.

∠B is the right angle of a right angles triangle ABC. If tanA = 3/4, then 5sinACosA =?

ক
5/3
খ
12/3
গ
1
ঘ
12/5

সঠিক উত্তর: ঘ

12/5

উত্তর

সঠিক উত্তর: ঘ

12/5

ঘ

ব্যাখ্যা

Question: ∠B is the right angle of a right angles triangle ABC. If tanA = 3/4, then 5sinACosA = ?

Solution:

দেওয়া আছে,
tanA = 3/4

∴ অতিভুজ = √(3² + 4²) = √(9 + 16) = 5

∴ sinA = AB/AC = 3/5
cosA = BC/AC = 4/5

∴ 5sinACosA = 5 × (3/5) × (4/5)
= 12/5

৫,৫১৪.

Find out the odd-one: 8, 27, 64, 100, 125, 216, 343

ক
ক) 100
খ
খ) 64
গ
গ) 125
ঘ
ঘ) 216

সঠিক উত্তর: ক

ক) 100

উত্তর

সঠিক উত্তর: ক

ক) 100

ক

ব্যাখ্যা

Question: Find out the odd-one:
8, 27, 64, 100, 125, 216, 343

Solution:
Here,
8 = 2³
27 = 3³
64 = 4³
100 = 10²
125 = 5³
216 = 6³
343 = 7³

∴ 100 is the odd-one.

৫,৫১৫.

If HCRAES is code SEARCH, which word has the code LATIPAC?

ক
CONFIND
খ
CAPITAL
গ
CONFLIC
ঘ
CONCERN

সঠিক উত্তর: খ

CAPITAL

উত্তর

সঠিক উত্তর: খ

CAPITAL

খ

ব্যাখ্যা

Question: If HCRAES is code SEARCH, which word has the code LATIPAC?

Solution:
Reversed HCRAES = SEARCH

So the code is just the reverse of the given word

Let’s reverse LATIPAC → CAPITAL

৫,৫১৬.

Compound interest on a certain sum at the rate of 25% per annum after 2 years is Tk. 5,625. Find the simple interest on that sum at the rate of 12% per annum for 5 years.

ক
Tk. 6,000
খ
Tk. 6,250
গ
Tk. 6,500
ঘ
Tk. 7,000

সঠিক উত্তর: ক

Tk. 6,000

উত্তর

সঠিক উত্তর: ক

Tk. 6,000

ক

ব্যাখ্যা

Question: Compound interest on a certain sum at the rate of 25% per annum after 2 years is Tk. 5,625. Find the simple interest on that sum at the rate of 12% per annum for 5 years.

Solution:

Let the sum be, P = x.
Rate of interest, r = 25%
Period, n = 2 years

We know,
Compound Principal, C = P(1 + r)ⁿ

∴ Compound interest = P(1 + r)ⁿ - P

Hence, compound interest = x(1 + 25/100)² - x = 5,625
⇒ x(5/4)² - x = 5,625
⇒ x(25/16) - x = 5,625
⇒ x(9/16) = 5,625
⇒ x = (5,625 × 16)/9
∴ x = 10,000 Tk.

Again,
Principal, P = 10,000 Tk.
Rate of interest, r = 12%
Period, n = 5 years

We know,
Simple Interest, I = Pnr/100

Hence, simple interest = 10,000 × 5 × 12/100
= 6,000 Tk.

৫,৫১৭.

An iron rod that weight 28 kg is cut into two pieces so that one of these pieces weight 18 kg and is 36 m long. If the weight of each pieces is proportional to its length, how long is the other pieces?

ক
34m
খ
10m
গ
20m
ঘ
72m

সঠিক উত্তর: গ

20m

উত্তর

সঠিক উত্তর: গ

20m

গ

ব্যাখ্যা

Question: An iron rod that weight 28 kg is cut into two pieces so that one of these pieces weight 18 kg and is 36 m long. If the weight of each pieces is proportional to its length, how long is the other pieces?

Solution:
Weight of second piece = 28 − 18 = 10 kg

Let x is the length of the second piece.

According to the Question,
⇒ 18/36 = 10/x
⇒ x = (36 × 10)/18
⇒ x = 20

∴ The length of the other piece is 20 meters.

৫,৫১৮.

Before anybody could notice Rifat took one third of the chocolates from a box. Later his three sisters arrived and the remaining chocolates where distributed equally among the four of them. Rifat received a total of 36 chocolates. how many did of his each sister receive?

ক
16
খ
12
গ
8
ঘ
18
ঙ
10

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: Before anybody could notice Rifat took one third of the chocolates from a box. Later his three sisters arrived and the remaining chocolates where distributed equally among the four of them. Rifat received a total of 36 chocolates. how many did of his each sister receive?

Solution:
Let,
Total Chocolates = x
First time Rifat took = x/3
Rest Amount = x - (x/3) = 2x/3
Amount of Chocolate when it divided equally = (2x/3) × (1/4)
= x/6

ATQ,
⇒ (x/6) + (x/3) = 36
⇒ (x + 2x)/6 = 36
⇒ 3x/6 = 36
⇒ x/2 = 36
∴ x = 72

So, each sister got = 72/6 = 12

৫,৫১৯.

X's age 3 years ago was three times the present age of Y. At present Z's age is twice the age of Y. Also Z is 12 years younger than X. What is the present age of Z?

ক
15 years
খ
24 years
গ
12 years
ঘ
18 years

সঠিক উত্তর: ঘ

18 years

উত্তর

সঠিক উত্তর: ঘ

18 years

ঘ

ব্যাখ্যা

Question: X's age 3 years ago was three times the present age of Y. At present Z's age is twice the age of Y. Also Z is 12 years younger than X. What is the present age of Z?

Solution:
Let the present age of Y be a years
Three years ago X's age = 3a years
Then, present age of X is (3a + 3)
Z's present age = 2a

According to question
(3a + 3) - 2a = 12
a = 9 year

∴ Present age of Z = 2a = 2 × 9 = 18 years

৫,৫২০.

The next number in the sequence 3, 8, 18, 33, 53, ... ... ... is

ক
78
খ
83
গ
88
ঘ
83

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

3, 8, 18, 33, 53, ... ... ...
8 - 3 = 5
18 - 8 = 10
33 - 18 = 15
53 - 33 = 20
The next number is 53 + 25 = 78

৫,৫২১.

Find the number in the place of sign `?'.

ক
9
খ
21
গ
27
ঘ
81

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Find the number in the place of sign `?'.

Solution:
Let, the number be x
So,
9/x = x/81
⇒ x² = 81 × 9
⇒ x² = 729
⇒ x² = 27²
∴ x = 27

৫,৫২২.

A motorcyclist completes a certain journey in 5 hours. He covers one-third distance at 60 km/hour and the rest 80 km/hour. The length of the journey is-

ক
240 km
খ
270 km
গ
300 km
ঘ
360 km

সঠিক উত্তর: ঘ

360 km

উত্তর

সঠিক উত্তর: ঘ

360 km

ঘ

ব্যাখ্যা

Question: A motorcyclist completes a certain journey in 5 hours. He covers one-third distance at 60 km/hour and the rest 80 km/hour. The length of the journey is-

Solution:
Let the length of the journey be x km.

Now
{(x/3)/60} + {(2x/3)/80} = 5
(x/180) + (x/120) = 5
(2x + 3x)/360 = 5
5x/360 = 5
x/360 = 1
x = 360

৫,৫২৩.

If Sohel was 35 years old 7 years ago, how old was he x years ago?

ক
45 - x
খ
40 - x
গ
47- x
ঘ
42 - x

সঠিক উত্তর: ঘ

42 - x

উত্তর

সঠিক উত্তর: ঘ

42 - x

ঘ

ব্যাখ্যা

Sohel was 35 years old 7 years ago
Therefore, Mario's present age = 35 + 7 = 42 years
x years ago, his age = (42 - x) years

৫,৫২৪.

If the radius of a cylinder is 4cm and height is 10cm, then the total surface area of a cylinder is:

ক
ক) 440 sq.cm
খ
খ) 352 sq.cm.
গ
গ) 400 sq.cm
ঘ
ঘ) 412 sq.cm
ঙ
ঙ) 395 s.q. cm

সঠিক উত্তর: খ

খ) 352 sq.cm.

উত্তর

সঠিক উত্তর: খ

খ) 352 sq.cm.

খ

ব্যাখ্যা

Total Surface Area of a Cylinder = 2πr(r + h)
TSA = 2 × 22/7 × 4(4 + 10)
= (2 × 22 × 4 × 14)/7
= (2 × 22 × 4 × 2)
= 352 sq.cm

৫,৫২৫.

Kamal gets 3 marks for each correctly done question but loses 2 marks for each wrongly done question. He attempts 30 questions and gets 40 marks. How many questions he has attempted correctly?

ক
20
খ
25
গ
26
ঘ
30
ঙ
32

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Kamal gets 3 marks for each correctly done question but loses 2 marks for each wrongly done question. He attempts 30 questions and gets 40 marks. How many questions he has attempted correctly?

Solution:
Marks for a correct answer = 3
Marks lost for a wrong answer = 2
Total questions attempted = 30
Total marks obtained = 40

Let the number of correct answers be x,
and the number of wrong answers be (30 - x).
Total marks = 3x - 2(30 - x)
∴ 3x - 2(30 - x) = 40
⇒ 3x - 60 + 2x = 40
⇒ 5x - 60 = 40
⇒ 5x = 100
⇒ x = 100/5
⇒ x = 20
∴ Kamal attempted 20 questions correctly.

৫,৫২৬.

Two ships are sailing in the sea on the two sides of the lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 45° and 45° respectively. If the lighthouse is 120 m high, the distance between the two ships is?

ক
250 m
খ
150 m
গ
300 m
ঘ
240 m

সঠিক উত্তর: ঘ

240 m

উত্তর

সঠিক উত্তর: ঘ

240 m

ঘ

ব্যাখ্যা

Question: Two ships are sailing in the sea on the two sides of the lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 45° and 45° respectively. If the lighthouse is 120 m high, the distance between the two ships is?

Solution:

Given that,
Height of the lighthouse = 120m
Now,
In triangle ADC,
AD/DC = tan 45°
⇒ AD/DC = 1 [tan 45° = 1]
⇒ AD = DC = 120m
Again,
In triangle ABD,
AD/BD = tan 45°
⇒ 120/BD = 1 [tan 45° = 1]
⇒ BD = 120 m

Now,
BC = BD + DC
= 120 + 120 = 240 m
∴ Total distance = 240 m

৫,৫২৭.

A factory produces 300 units in 15 days with 10 machines working 8 hours a day. How many machines are needed to produce 500 units in 10 days working 6 hours a day?

ক
20 machines
খ
24 machines
গ
30 machines
ঘ
34 machines

সঠিক উত্তর: ঘ

34 machines

উত্তর

সঠিক উত্তর: ঘ

34 machines

ঘ

ব্যাখ্যা

Question: A factory produces 300 units in 15 days with 10 machines working 8 hours a day. How many machines are needed to produce 500 units in 10 days working 6 hours a day?

Solution:
দৈনিক ৮ ঘণ্টা কাজ করে ১৫ দিনে ৩০০ ইউনিট বানায় ১০ টি মেশিন
দৈনিক ১ ঘণ্টা কাজ করে ১৫ দিনে ৩০০ ইউনিট বানায় ১০ × ৮ টি মেশিন
দৈনিক ১ ঘণ্টা কাজ করে ১ দিনে ৩০০ ইউনিট বানায় ১০ × ৮ × ১৫ টি মেশিন
দৈনিক ১ ঘণ্টা কাজ করে ১ দিনে ১ ইউনিট বানায় ১২০০/৩০০ টি মেশিন
দৈনিক ৬ ঘণ্টা কাজ করে ১ দিনে ১ ইউনিট বানায় ১২০০/(৩০০ × ৬) টি মেশিন
দৈনিক ৬ ঘণ্টা কাজ করে ১০ দিনে ১ ইউনিট বানায় ১২০০/(৩০০ × ৬ × ১০) টি মেশিন
দৈনিক ৬ ঘণ্টা কাজ করে ১০ দিনে ৫০০ ইউনিট বানায় (১২০০ × ৫০০)/(৩০০ × ৬ × ১০) টি মেশিন
= ৩৩.৩৩ টি মেশিন
≈ ৩৪ টি মেশিন

৫,৫২৮.

The sum of three consecutive integers is equal to their product. How many such possibilities are there?

ক
ক) Only one
খ
খ) Only two
গ
গ) Only three
ঘ
ঘ) No such possibility is there

সঠিক উত্তর: গ

গ) Only three

উত্তর

সঠিক উত্তর: গ

গ) Only three

গ

ব্যাখ্যা

Let the three consecutive numbers are x - 1, x, and x + 1.

(x - 1) + x + (x + 1) = (x - 1) (x) (x + 1)
3x = x³ - x
3 = x² -1
x² = 4

x= +2 or x = -2 or x = 0

So two sets are (1,2,3), (-1,0,1) and (-3,-2,-1)

Hence, the correct answer is an option(3) i.e., only three.

৫,৫২৯.

Find the value of sin(7π/6).

ক
- 1/2
খ
√3/2
গ
- √3/2
ঘ
1/√2

সঠিক উত্তর: ক

- 1/2

উত্তর

সঠিক উত্তর: ক

- 1/2

ক

ব্যাখ্যা

Question: Find the value of sin(7π/6).

Solution:
sin(7π/6)
= sin(π + π/6) [যেহেতু (π + θ) তৃতীয় চতুর্ভাগে পড়ে এবং তৃতীয় চতুর্ভাগে sin ঋণাত্মক, তাই sin(π + θ) = - sinθ]
= - sin(π/6)
= - sin(30°)
= - 1/2

৫,৫৩০.

The ratio of the present ages of A and B is 3 : 4. If the difference between their ages is 6 years, what is B’s present age?

ক
18 years
খ
24 years
গ
30 years
ঘ
36 years

সঠিক উত্তর: খ

24 years

উত্তর

সঠিক উত্তর: খ

24 years

খ

ব্যাখ্যা

Question: The ratio of the present ages of A and B is 3 : 4. If the difference between their ages is 6 years, what is B’s present age?

Solution:
Let,
Present age of A = 3x
Present age of B = 4x

ATQ,
4x - 3x = 6
∴ x = 6

∴ B's present age is 4 × 6 = 24 years

৫,৫৩১.

What is the sum of the roots of the equation x² - 6x + 9 = 0.

ক
0
খ
6
গ
9
ঘ
3

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: What is the sum of the roots of the equation x² - 6x + 9 = 0.

Solution:
x² - 6x + 9 = 0
⇒ x² - 2.x.3 + 3² = 0
⇒ (x - 3)² = 0
⇒ (x - 3)(x - 3) = 0
∴ x = 3 or x = 3

∴ The sum of the roots = 3 + 3 = 6

৫,৫৩২.

The number 25 is 2.5% of which of the following?

ক
10
খ
62.5
গ
100
ঘ
625
ঙ
1000

সঠিক উত্তর: ঙ

1000

উত্তর

সঠিক উত্তর: ঙ

1000

ঙ

ব্যাখ্যা

Question: The number 25 is 2.5% of which of the following?

Solution:
Let,
25 is 2.5% of x

2.5% of x = 25
⇒ (2.5/100) × x = 25
⇒ 2.5x = 2500
⇒ x = 2500/2.5
∴ x = 1000

৫,৫৩৩.

If θ is said to be an acute angle, and 7sin²θ + 3cos²θ = 4, then what is the value of tanθ?

ক
1
খ
1/√3
গ
2/√3
ঘ
1/√2

সঠিক উত্তর: খ

1/√3

উত্তর

সঠিক উত্তর: খ

1/√3

খ

ব্যাখ্যা

Question: If θ is said to be an acute angle, and 7sin²θ + 3cos²θ = 4, then what is the value of tanθ?

Solution:
7sin²θ + 3cos²θ = 4
⇒ 7sin²θ + 3(1 - sin²θ) = 4
⇒ 7sin²θ + 3 - 3sin²θ = 4

Then, 4sin²θ = 1
⇒ sinθ = 1/2
⇒ θ = 30°

Now, put θ = 30° in tanθ, we will get,
tanθ = tan 30° = 1/√3

৫,৫৩৪.

A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cms and its width is increased also by x cms so as to make it a square, then its area changes by:

ক
ক) 4
খ
খ) 144
গ
গ) 12
ঘ
ঘ) 2
ঙ
ঙ) None of these

সঠিক উত্তর: ক

ক) 4

উত্তর

সঠিক উত্তর: ক

ক) 4

ক

ব্যাখ্যা

Question: A rectangle is 14 cm long and 10 cm wide. If the length is reduced by x cm and its width is increased also by x cm so as to make it a square, then its area changes by:

Solution:
ATQ,
14 - x = 10 + x
⇒ x + x = 14 - 10
⇒ 2x = 4
∴ x = 2

Area of rectangle = 14 × 10 cm²
= 140 cm²

Area of square = 12²
= 144 cm²

∴ Area changes by = 144 - 140 cm²
= 4 cm²

৫,৫৩৫.

The radius of a wire is decreased to one-fourth and its volume remains the same. The new length is how many times the original length?

ক
ক) 9 times
খ
খ) 16 times
গ
গ) 4 times
ঘ
ঘ) 3 times

সঠিক উত্তর: খ

খ) 16 times

উত্তর

সঠিক উত্তর: খ

খ) 16 times

খ

ব্যাখ্যা

Wire is in the shape of a cylinder.
Let the radius of the original cylinder =r cm and height =h cm
Original volume =πr²h

New radius after decrease = r/4

Let the new height be H.
Now
πr²h = π(r/4)²H
h = H/16
16h = H

the height becomes 16 times.

৫,৫৩৬.

5p - 3q = 42; 5p + 3q = 18 Given this system of equations, what is the value of |p| + |q|?

ক
ক) 2
খ
খ) 4
গ
গ) 6
ঘ
ঘ) 10

সঠিক উত্তর: ঘ

ঘ) 10

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10

ঘ

ব্যাখ্যা

5p - 3q = 42
5p + 3q = 18
____________
10p = 60
⇒ p = 6

So, Value of q = -4

∴ |p| + |q| = |6| + |-4| = 6 + 4 = 10

৫,৫৩৭.

If a square region has area n, what is the length of the diagonal of the square in terms of n?

ক
ক) √(2n)
খ
খ) √n
গ
গ) 2√n
ঘ
ঘ) 2n

সঠিক উত্তর: ক

ক) √(2n)

উত্তর

সঠিক উত্তর: ক

ক) √(2n)

ক

ব্যাখ্যা

Question: If a square region has area n, what is the length of the diagonal of the square in terms of n?

Solution:
বর্গক্ষেত্রের ক্ষেত্রফল = n
বর্গক্ষেত্রের এক বাহুর দৈর্ঘ্য = √n
বর্গক্ষেত্রের কর্ণের দৈর্ঘ্য = √n × √2
= √(2n)

৫,৫৩৮.

The marked price is 20% higher than cost price. A discount of 20% is given on the marked price. By this type of sale, there is = ?

ক
ক) 4% loss
খ
খ) 2% loss
গ
গ) No loss no gain
ঘ
ঘ) 4% gain

সঠিক উত্তর: ক

ক) 4% loss

উত্তর

সঠিক উত্তর: ক

ক) 4% loss

ক

ব্যাখ্যা

Let the cost price = 100 units
Marked price = 120 units
Selling price = 120 × 80/100 = 96 units
There will be loss
Loss% = 100−96 /100 × 100 = 4%

৫,৫৩৯.

If θ + Φ = π/2 and sinθ = 1/2, then the value of cosΦ is?

ক
ক) 0
খ
খ) √3/2
গ
গ) 1/√2
ঘ
ঘ) 1/2

সঠিক উত্তর: ঘ

ঘ) 1/2

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1/2

ঘ

ব্যাখ্যা

Question: If θ + Φ = π/2 and sinθ = 1/2, then the value of cosΦ is?

Solution:
sinθ = 1/2
⇒ sinθ = sin (π/6)
∴ θ = π/6

θ + Φ = π/2
⇒ π/6 + Φ = π/2
⇒ Φ = π/2 - π/6
∴ Φ = π/3

cosΦ
= cos(π/3)
= 1/2

৫,৫৪০.

The ratio of X : Y is 2 : 5, and the ratio of Y : Z is 3 : 4. If X = 12, what is the value of Z?

ক
40
খ
30
গ
25
ঘ
32

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: The ratio of X : Y is 2 : 5, and the ratio of Y : Z is 3 : 4. If X = 12, what is the value of Z?

Solution:
Given:
X : Y = 2 : 5 -------(1)
Y : Z = 3 : 4 -------(2)
X = 12

From equation (1):
X/Y = 2/5
⇒ 2Y = 5X
⇒ Y = (5 × 12)/2 = 30
∴ Y = 30

From equation (2):
Y/Z = 3/4
⇒ 3Z = 4Y
⇒ Z = (4 × 30)/3 = 40

Therefore, the value of Z is 40.

৫,৫৪১.

At what rate of compound interest per annum will a sum of Tk. 5000 become Tk. 7200 in 2 years?

ক
5%
খ
10%
গ
15%
ঘ
20%

সঠিক উত্তর: ঘ

20%

উত্তর

সঠিক উত্তর: ঘ

20%

ঘ

ব্যাখ্যা

প্রশ্ন: At what rate of compound interest per annum will a sum of Tk. 5000 become Tk. 7200 in 2 years?

সমাধান:
দেওয়া আছে,
মূলধন (Principal), P = 5000 টাকা
চক্রবৃদ্ধি মূল (Compound Amount), C = 7200 টাকা
সময় (Time), n = 2 বছর
মুনাফার হার (Rate), r = ?

আমরা জানি,
চক্রবৃদ্ধি মূল, C = P(1 + r/100)ⁿ
⇒ 7200 = 5000(1 + r/100)²
⇒ (1 + r/100)² = 7200/5000
⇒ (1 + r/100)² = 72/50
⇒ (1 + r/100)² = 36/25
⇒ (1 + r/100) = 6/5
⇒ (100 + r)/100 = 6/5
⇒ (100 + r) = 600/5
⇒ r = 120 - 100
∴ r = 20
সুতরাং, বার্ষিক চক্রবৃদ্ধি সুদের হার 20%।

৫,৫৪২.

What is the greatest number that can be subtracted from 10,000 so that the remainder may be divisible by 32, 36, 48, and 54?

ক
ক) 8200
খ
খ) 9136
গ
গ) 9200
ঘ
ঘ) 9228

সঠিক উত্তর: খ

খ) 9136

উত্তর

সঠিক উত্তর: খ

খ) 9136

খ

ব্যাখ্যা

Question: What is the greatest number that can be subtracted from 10,000 so that the remainder may be divisible by 32, 36, 48, and 54?

Solution:
L.C.M of 32, 36, 48, and 54 is = 864

So, required number is = 10000 - 864 = 9136

৫,৫৪৩.

As a salesperson, Rahim can choose one of two methods of annual payment: either an annual salary of Tk. 50,000 with no commission or an annual salary of Tk. 20,000 plus a 25 percent commission on his total annual sales. What must his total annual sales be to give him the same annual pay with either method?

ক
Tk. 1,00,000
খ
Tk. 1,20,000
গ
Tk. 1,50,000
ঘ
Tk. 80,000

সঠিক উত্তর: খ

Tk. 1,20,000

উত্তর

সঠিক উত্তর: খ

Tk. 1,20,000

খ

ব্যাখ্যা

Question: As a salesperson, Rahim can choose one of two methods of annual payment: either an annual salary of Tk. 50,000 with no commission or an annual salary of Tk. 20,000 plus a 25 percent commission on his total annual sales. What must his total annual sales be to give him the same annual pay with either method?

Solution:
ধরি,
রহিমের মোট বার্ষিক বিক্রয় = x টাকা

প্রথম পদ্ধতি অনুযায়ী রহিমের বেতন = 50,000 টাকা
দ্বিতীয় পদ্ধতি অনুযায়ী রহিমের বেতন = 20,000 + x এর 25%

প্রশ্নমতে,
50000 = 20000 + (x এর 25%)
⇒ 50000 - 20000 = 25x/100
⇒ 30000 = x/4
⇒ x = 30000 × 4
∴ x = 120000

সুতরাং, রহিমের মোট বার্ষিক বিক্রয় 1,20,000 টাকা হতে হবে।

৫,৫৪৪.

How many degrees are between the hands of a clock at 3:30?

ক
105°
খ
90°
গ
75°
ঘ
70°

সঠিক উত্তর: গ

75°

উত্তর

সঠিক উত্তর: গ

75°

গ

ব্যাখ্যা

Question: How many degrees are between the hands of a clock at 3:30?
Solution:
Value of angle = {(11 × 30) - (60 × 3)}/2
= (330 - 180)/2
= 150/2
= 75°

৫,৫৪৫.

After distributing the chocolates equally among 25 kids, 8 chocolates remain. Had the number of children been 28, 22 chocolates would have been left after equally distributing. Find the total number of chocolates?

ক
ক) 315
খ
খ) 358
গ
গ) 368
ঘ
ঘ) 322

সঠিক উত্তর: খ

খ) 358

উত্তর

সঠিক উত্তর: খ

খ) 358

খ

ব্যাখ্যা

Question: After distributing the chocolates equally among 25 kids, 8 chocolates remain. Had the number of children been 28, 22 chocolates would have been left after equally distributing. Find the total number of chocolates?

Solution:
Let M number of the chocolates distributing each student. Therefore,
total number of chocolates is 25M + 8 when it distributing among 25 children and 28M - 22 when it distributing among 28 children.

Therefore,
28M - 22 = 25M + 8
=> 28M - 25M = 8 + 22
=> 3M = 30
=> M = 10

Therefore total number of sweets is 25 × 10 + 8 = 258

৫,৫৪৬.

A certain principal amount, invested at simple interest, grows to Tk. 815 after 3 years and Tk. 854 after 4 years. What is the original principal amount?

ক
Tk. 658
খ
Tk. 612
গ
Tk. 698
ঘ
Tk. 710

সঠিক উত্তর: গ

Tk. 698

উত্তর

সঠিক উত্তর: গ

Tk. 698

গ

ব্যাখ্যা

Question: A certain principal amount, invested at simple interest, grows to Tk. 815 after 3 years and Tk. 854 after 4 years. What is the original principal amount?

Solution:
Given,
Amount after 3 years = Tk. 815
Amount after 4 years = Tk. 854
∴ Interest for 1 year = 854 - 815 = Tk. 39
∴ Interest for 3 years = 39 × 3 = Tk. 117
∴ Principal = 815 - 117 = Tk. 698

৫,৫৪৭.

Average of six non-zero positive integers is 15 and the median is 18. The modal value is less than the median. What is the maximum possible value of the largest of the six integers?

ক
28
খ
29
গ
30
ঘ
31
ঙ
32

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Question: Average of six non-zero positive integers is 15 and the median is 18. The modal value is less than the median. What is the maximum possible value of the largest of the six integers?

Solution:
দেওয়া আছে,
শূণ্য নয় এমন ৬ টি সংখ্যার গড় = ১৫

∴ ৬ টি সংখ্যার সমষ্টি = (১৫ × ৬) = ৯০

আবার, মধ্যমা = ১৮
∴ ৬টি সংখ্যাকে ছোট থেকে বড় ক্রমে সাজালে, ৩য় ও ৪র্থ সংখ্যার গড় হবে ১৮।
∴ ৩য় ও ৪র্থ সংখ্যা দুটি হবে = ১৭ ও ১৯

যেহেতু, প্রচুরক মধ্যমা হতে ছোট হবে,

প্রদত্ত তথ্যের ভিত্তিতে সর্বনিম্ন মান নিয়ে ৫ টি সংখ্যা হবে = ১, ১, ১৭, ১৯, ২০ [যেহেতু ৩য় ও ৪র্থ সংখ্যা ১৭ ও ১৯]

তাদের সমষ্টি = ১ + ১ + ১৭ + ১৯ + ২০ = ৫৮

∴ বৃহত্তম সংখ্যাটি হবে = ৯০ - ৫৮ = ৩২

৫,৫৪৮.

A takes thrice as long to do a piece of work, as B takes. A & B together can finish a piece of work in 15 days. A alone can do it in -

ক
ক) 15 days
খ
খ) 25 days
গ
গ) 45 days
ঘ
ঘ) 60 days

সঠিক উত্তর: ঘ

ঘ) 60 days

উত্তর

সঠিক উত্তর: ঘ

ঘ) 60 days

ঘ

ব্যাখ্যা

ধরি,
B কাজটি করতে সময় নেয় = x দিন
A কাজটি করতে সময় নেয় = 3x দিন

A এবং B 1 দিনে করতে পারে কাজটির = (1/x) + (1/3x) অংশ
= (3 + 1)/3x
= 4/3x
A এবং B 4/3x অংশ কাজ করতে সময় লাগে = 1 দিন
A এবং B 1 অংশ কাজ করতে সময় লাগে = 1/(4/3x) দিন
= 3x/4

প্রশ্নমতে,
3x/4 = 15
x = (15 × 4)/3
x = 20

A কাজটি করতে সময় নেয় = 3× 20 দিন = 60 দিন

৫,৫৪৯.

A dice is thrown randomly. What is the probability that the number shown on the dice is not divisible by 3?

ক
1/3
খ
2/3
গ
1/4
ঘ
1/2

সঠিক উত্তর: খ

2/3

উত্তর

সঠিক উত্তর: খ

2/3

খ

ব্যাখ্যা

Question: A dice is thrown randomly. What is the probability that the number shown on the dice is not divisible by 3?

Solution:
Numbers on dice are {1, 2, 3, 4, 5, 6}
Numbers on dice not divisible by 3 are {1, 2, 4, 5}
Number of favorable outcomes = 4
Total possible outcomes = 6

∴ The probability that the number shown on the dice is not divisible by 3 is 4/6 = 2/3

৫,৫৫০.

A sum of Tk. 4950 is distributed among A, B and C such that the ratio of amount received by A and B is 5 : 4 and that of B and C is 6 : 3 respectively. Find the share of B ?

ক
1800
খ
1500
গ
1200
ঘ
900

সঠিক উত্তর: ক

1800

উত্তর

সঠিক উত্তর: ক

1800

ক

ব্যাখ্যা

Question: A sum of Tk. 4950 is distributed among A, B and C such that the ratio of amount received by A and B is 5 : 4 and that of B and C is 6 : 3 respectively. Find the share of B ?

Solution:
A : B = 5 : 4
B : C = 6 : 3

A : B = 15 : 12 ( multiply by 3 )
B : C = 12 : 6 ( multiply by 2 )

∴ A : B : C = 15 : 12 : 6

ATQ,
15X + 12X + 6X = 4950
33X = 4950
X = 150

∴ Share of B is = 12 × 150 = 1800

৫,৫৫১.

A pole is broken such that the broken part makes an angle of 30° with the ground and touches it at a point 30 meters from the base. What is the length of the broken part?

ক
20√2
খ
20√3
গ
25
ঘ
40√2
ঙ
10√3

সঠিক উত্তর: খ

20√3

উত্তর

সঠিক উত্তর: খ

20√3

খ

ব্যাখ্যা

Question: A pole is broken such that the broken part makes an angle of 30° with the ground and touches it at a point 30 meters from the base. What is the length of the broken part?

Solution:

To find the length of the broken part of the pole, we can model this as a right-angled triangle:

The broken part of the pole is the hypotenuse.
The horizontal distance from the base of the pole to where the top touches the ground is 30 meters.
The angle between the broken part and the ground is 30°.
let the hypotenuse = x

Using the cosine function:
cos(30°) = Adjacent(base)/hypotenuse
⇒ √3/2 = 30/x
⇒ √3x = 60
⇒ x = 60/√3 = (60√3)/(√3 × √3)
⇒ x = 60√3/3
∴ x = 20√3

৫,৫৫২.

One-fourth percent, written as a decimal, is-

ক
0.25
খ
0.00025
গ
0.025
ঘ
0.0025

সঠিক উত্তর: ঘ

0.0025

উত্তর

সঠিক উত্তর: ঘ

0.0025

ঘ

ব্যাখ্যা

Question: One-fourth percent, written as a decimal, is-

Solution:
As we know,1% =1/100
Hence,
(1/4)% = (1/4) × (1/100)
= 1/400
= 0.0025

৫,৫৫৩.

The number of students in 3 classes is in the ratio 3 : 4 : 5. If 10 students are increased in each class this ratio changes to 4 : 5 : 6. The total number of students in the three classes in the beginning was

ক
ক) 135
খ
খ) 120
গ
গ) 110
ঘ
ঘ) 100

সঠিক উত্তর: খ

খ) 120

উত্তর

সঠিক উত্তর: খ

খ) 120

খ

ব্যাখ্যা

Question: The number of students in 3 classes is in the ratio 3 : 4 : 5. If 10 students are increased in each class this ratio changes to 4 : 5 : 6. The total number of students in the three classes in the beginning was

Solution:
Let the number of students in the classes be 3x, 4x and 5x respectively;
Total students = 3x + 4x + 5x = 12x
According to the question,
(3x + 10) : (4x + 10) = 4 : 5
or, 5(3x + 10) = 4(4x+10)
or, 15x + 50 = 16x + 40
or, x = 10

Hence,
Original number of students,
12x = 12 × 10
= 120

৫,৫৫৪.

A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:

ক
39
খ
42
গ
40
ঘ
50
ঙ
35

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

After 10 days: 150 men had food for 35 days.

Suppose 125 men had food for x days.

Now, Less men, More days (Indirect Proportion)

∴ 125 : 150 :: 35 : x

⇒ 125 × x = 150 × 35

⇒ x = (150 × 35)/125

= 42

৫,৫৫৫.

How many 4-digit numbers can be formed from the digits 1, 3, 4, 6, 9, which are divisible by 2 and have no digit repeated?

ক
24 ways
খ
36 ways
গ
48 ways
ঘ
60 ways
ঙ
None of the above

সঠিক উত্তর: গ

48 ways

উত্তর

সঠিক উত্তর: গ

48 ways

গ

ব্যাখ্যা

Question: How many 4-digit numbers can be formed from the digits 1, 3, 4, 6, 9, which are divisible by 2 and have no digit repeated?

Solution:
We know,
A number is divisible by 2 if its last digit is even.
The available digits are: 1, 3, 4, 6, 9
Even digits here are: 4, 6
So, the last digit must be one of these 2 digits.

So, last digit can be chosen in 2 ways.

As the digit is not repeated,
First digit (thousands place) can be chosen in = 4 ways

As the digit is not repeated,
Second digit (hundreds place) can be chosen in = 3 ways

As the digit is not repeated,
Third digit (tens place) can be chosen in = 2 ways

∴ Total ways = 2 × 4 × 3 × 2 ways
= 48 ways

৫,৫৫৬.

12 years ago the difference in age between Puja and Sejan was 6 years. What is the difference now?

ক
6 years
খ
12 years
গ
2 years
ঘ
none of the above

সঠিক উত্তর: ক

6 years

উত্তর

সঠিক উত্তর: ক

6 years

ক

ব্যাখ্যা

Question: 12 years ago the difference in age between Puja and Sejan was 6 years. What is the difference now?

Solution:
The difference in age remains the same as they both pass the same period of time together.
so, at present, their age difference is 6 years.

৫,৫৫৭.

A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is-

ক
400 kg
খ
560 kg
গ
600 kg
ঘ
640 kg

সঠিক উত্তর: গ

600 kg

উত্তর

সঠিক উত্তর: গ

600 kg

গ

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is -

Solution:

⇒ Quantity of cheaper : Quantity of Dearer = (CP of of Dearer - Mean Price) : (Mean Price - CP of Cheaper)
⇒ Quantity of cheaper : Quantity of Dearer = (18 - 14) : ( 14 - 8) = 4 : 6 = 2 : 3

∴ Quantity of suger sold at 18% profit = (3/5) × 1000
= 600 Kg

৫,৫৫৮.

If 9x² - qx + 16 is a square number, then q =?

ক
ক) 12
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 24

সঠিক উত্তর: ঘ

ঘ) 24

উত্তর

সঠিক উত্তর: ঘ

ঘ) 24

ঘ

ব্যাখ্যা

Question: If 9x² - qx + 16 is a square number, then q =?

Solution:
Given that,
9x² - qx + 16
= (3x)² - 2.3.4x + (4)²
= (3x)² - 24x + (4)²

∴ q = 24

৫,৫৫৯.

A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?

ক
ক) 8 hours
খ
খ) 12 hours
গ
গ) 10 hours
ঘ
ঘ) 24 hours

সঠিক উত্তর: খ

খ) 12 hours

উত্তর

সঠিক উত্তর: খ

খ) 12 hours

খ

ব্যাখ্যা

Question: A can do a piece of work in 4 hours, B and C together in 3 hours, and A and C together in 2 hours. How long will B alone take to do it?

Solution:
A's 1 hour's work = 1/4
(B + C)'s 1 hour's work = 1/3
(A + C)'s 1 hour's work = 1/2

∴C's 1 hour's work = (1/2) - (1/4) = 1/4

B's 1 hour's work = (1/3) - (1/4) = 1/12

Hence, B will complete the whole work in 12 hours.

৫,৫৬০.

When 52416 is divided by 312, the quotient is 168. What will be the quotient when 52.416 is divided by 0.0168 ?

ক
2740
খ
2850
গ
2980
ঘ
3120
ঙ
None of these

সঠিক উত্তর: ঘ

3120

উত্তর

সঠিক উত্তর: ঘ

3120

ঘ

ব্যাখ্যা

Question: When 52416 is divided by 312, the quotient is 168. What will be the quotient when 52.416 is divided by 0.0168?

Solution:

৫,৫৬১.

Two men and three boy can repair a bridge in 10 days while three men and two boy can do same work in 8 days. If two men and one boy are used to finish this work, in how many a they will complete it?

ক
ক) 15.0 days
খ
খ) 13.5 days
গ
গ) 11.0 days
ঘ
ঘ) 12.5 days

সঠিক উত্তর: ঘ

ঘ) 12.5 days

উত্তর

সঠিক উত্তর: ঘ

ঘ) 12.5 days

ঘ

ব্যাখ্যা

2 men and 3 boys can do a piece of work in 10 days.
Thus, 20 men and 30 boys can do a piece of work in 1 day......(i)

3 men and 2 boys can do the same work in 8 days.
Thus, 24 men and 16 boys can do the same work in 1 day....(ii)

Equating (i) and (ii) we get -
20 men + 30 boys = 24 men + 16 boys
4 men = 14 boys
2 men = 7 boys

• Substituting this in equation (i) we get

10 boys can do a piece of work in 10 days.
But we need to find out in how many days 2 men and 1 boy can do the work, which is equivalent to 8 boys.

8 boys can do the same work in (10 × 10/8) = 12.5 days.

৫,৫৬২.

The income of Asim, Shakil and Riaz is in the ratio of 12 : 9 : 7 and their spendings are in the ratio 15 : 9 : 8. If Asim saves 25% of his income. What is the ratio of the savings of Asim, Shakil and Riaz?

ক
ক) 15 : 18 : 11
খ
খ) 5 : 8 : 7
গ
গ) 23 : 18 : 11
ঘ
ঘ) 25 : 16 : 13

সঠিক উত্তর: ক

ক) 15 : 18 : 11

উত্তর

সঠিক উত্তর: ক

ক) 15 : 18 : 11

ক

ব্যাখ্যা

Income = Expenditure + Saving
Asim : 12x = 15y + 3x (3x = 25% of 12x)
Shakil : 9x = 9y + (9x – 9y)
Riaz : 7x = 8y + (7x – 8y)
Therefore, 12x – 3x = 15y
x/y = 5/3
y = 3x/5
Therefore, savings = (income – expenditure)
Asim = 12x – 9x = 3x
Shakil = 9x - 9y = 9x - (27x/5)
= 18x/5
Riaz = 7x - 8y = 7x - (24x/5)
= 11x/5
i.e., the ratio of savings of Asim : Shakil : Riaz
= 3x : 18x/5 : 11x/5
= 15 : 18 : 11.

৫,৫৬৩.

The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average is increased by 0.2 years. The average age of new students is?

ক
8 years
খ
25 years
গ
18 years
ঘ
15 years
ঙ
16 years

সঠিক উত্তর: ঙ

16 years

উত্তর

সঠিক উত্তর: ঙ

16 years

ঙ

ব্যাখ্যা

Question: The average age of 40 students of a class is 15 years. When 10 new students are admitted, the average is increased by 0.2 years. The average age of new students is?

Solution:
40 জনের মোট বয়স = 40 × 15 = 600 বছর
10 জন নতুন student ভর্তি হওয়ায় মোট = 40 + 10 = 50 জন

∴ গড় বয়স = 15 + 0.2 = 15.2 বছর

∴ 50 জনের মোট বয়স = 15.2 × 50 = 760 বছর

∴ নতুন 10 জনের বয়স = 760 - 600 = 160 বছর
∴ নতুন 10 জনের গড় বয়স 160 ÷ 10 = 16 বছর

৫,৫৬৪.

To produce an annual income of Tk. 900 from a 9% stock at 90, the amount of stock needed is -

ক
ক) Tk. 10500
খ
খ) Tk. 10000
গ
গ) Tk. 10060
ঘ
ঘ) Tk. 18000

সঠিক উত্তর: খ

খ) Tk. 10000

উত্তর

সঠিক উত্তর: খ

খ) Tk. 10000

খ

ব্যাখ্যা

Since face value is not given, take it as Tk. 100.
As it is an 9% stock, income (dividend) per stock = Tk. 9
ie, For an income of Tk. 9, the amount of stock needed = Tk. 100
For an income of Tk. 900, the amount of stock needed = (100 × 900)/9 = 10000

৫,৫৬৫.

Find the least five-digit number which can be divided by 8, 12, 16 and 20 leaving remainders 1, 5, 9 and 13 respectively.

ক
ক) 10003
খ
খ) 10093
গ
গ) 10073
ঘ
ঘ) 10013

সঠিক উত্তর: গ

গ) 10073

উত্তর

সঠিক উত্তর: গ

গ) 10073

গ

ব্যাখ্যা

Difference between divisors and remainders = (8 - 1) / ( 12 - 5) / (16 - 9) / (20 - 13) = 7
LCM of 8,12,16,20 is 240
Least 5 digit number is = 10000
240)10000(41
9840
____________
160
So, the number is = 10000 + 240 - 160 - 7 = 10073

৫,৫৬৬.

How many zeros will be required to number the pages of a book containing 1000 pages?

ক
ক) 168
খ
খ) 192
গ
গ) 84
ঘ
ঘ) 216

সঠিক উত্তর: খ

খ) 192

উত্তর

সঠিক উত্তর: খ

খ) 192

খ

ব্যাখ্যা

The pages of the book may be divided into 10 groups;
(1 -100), (101 - 200), (201 -300),......, (901 - 1000).
Clearly, for the first group, one needs 11 zeros,
For second to ninth groups, one needs 20 zeros each.
So, total number of zeros required = 11 + 8 × 20 + 21 = 192
Answer : 192

৫,৫৬৭.

If x + 4/x = 4, then x/(x² + x - 1) =?

ক
1/5
খ
2/3
গ
2/7
ঘ
2/5

সঠিক উত্তর: ঘ

2/5

উত্তর

সঠিক উত্তর: ঘ

2/5

ঘ

ব্যাখ্যা

প্রশ্ন: If x + 4/x = 4, then x/(x² + x - 1) =?

সমাধান:
দেওয়া আছে
x + 4/x = 4
⇒ (x² + 4)/x = 4
⇒ x² + 4 = 4x
⇒ x²- 4x + 4 = 0
⇒ (x - 2)² = 0
⇒ x - 2 = 0
⇒ x = 2

প্রদত্ত রাশি
x/(x² + x - 1)
= 2(2² + 2 - 1)
= 2/(4 + 2 - 1)
= 2/5

৫,৫৬৮.

What is the measure of each interior angle in a regular hexagon?

ক
100°
খ
115°
গ
120°
ঘ
125°

সঠিক উত্তর: গ

120°

উত্তর

সঠিক উত্তর: গ

120°

গ

ব্যাখ্যা

Question: What is the measure of each interior angle in a regular hexagon?

Solution:
সুষম বহুভুজের বাহুর সংখ্যা n হলে তার কোণগুলোর সমষ্টি (2n - 4) সমকোণ।
সুতরাং সুষম ষড়ভুজের ছয় কোণের সমষ্টি = (2 × 6 - 4) সমকোণ
= (12 - 4) × 90°
= 8 × 90°
= 720°

সুতরাং সুষম ষড়ভুজের একটি শীর্ষ কোণ = 720°/6
= 120°

৫,৫৬৯.

If a² + b² = 45 and ab = 18, find (1/a) + (1/b)

ক
ক) 1/3
খ
খ) 1/2
গ
গ) 2/3
ঘ
ঘ) 1/4

সঠিক উত্তর: খ

খ) 1/2

উত্তর

সঠিক উত্তর: খ

খ) 1/2

খ

ব্যাখ্যা

Question: If a² + b² = 45 and ab = 18, find (1/a) + (1/b)

Solution:
দেওয়া আছে,
ab = 18
a² + b² = 45
⇒ (a + b)² - 2ab = 45
⇒ (a + b)² - 36 = 45
⇒ (a + b)² = 81
∴ a + b = 9

এখন,
(1/a) + (1/b)
=(b + a)/ab
= 9/18
= 1/2

৫,৫৭০.

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question:

Solution:

৫,৫৭১.

Pipes A and B take 36 seconds and 45 seconds, respectively, to fill the tank when used separately. Pipe C, which can empty the tank in 30 seconds, starts operating after 7 seconds of A and B being open. How much additional time will be needed to fill the tank completely?

ক
43 seconds
খ
39 seconds
গ
46 seconds
ঘ
51 seconds
ঙ
None of the above

সঠিক উত্তর: খ

39 seconds

উত্তর

সঠিক উত্তর: খ

39 seconds

খ

ব্যাখ্যা

Question: Pipes A and B take 36 seconds and 45 seconds, respectively, to fill the tank when used separately. Pipe C, which can empty the tank in 30 seconds, starts operating after 7 seconds of A and B being open. How much additional time will be needed to fill the tank completely?
(পাইপ A এবং B আলাদাভাবে ৩৬ সেকেন্ড এবং ৪৫ সেকেন্ডে ট্যাংকটি পূর্ণ করতে পারে। পাইপ C, যা ৩০ সেকেন্ডে ট্যাংকটি খালি করে, A এবং B খোলা থাকা অবস্থায় ৭ সেকেন্ড পরে কাজ শুরু করে। ট্যাংকটি সম্পূর্ণ পূর্ণ করতে কত অতিরিক্ত সময় প্রয়োজন?)

Solution:
এখানে, ট্যাঙ্কের ধারণক্ষমতা (ল.সা.গু) LCM (36, 45, 30) = 180 units
∴ অতএব, পাইপ A এর দক্ষতা = 180/36 = 5 units/second
পাইপ B এর দক্ষতা = 180/45 = 4 units/second
পাইপ C এর দক্ষতা = - 180 / 30 = - 6 units/second

এখন,
প্রথম ৭ সেকেন্ডে, A এবং B খুলে রাখা হয়েছিল।
A এবং B এর যৌথ দক্ষতা = 5 + 4 = 9 units/second
অতএব, ৭ সেকেন্ডে ট্যাঙ্কের যে অংশটি পূর্ণ হয়েছে তা হচ্ছে = 7 × 9 = 63 units

ট্যাঙ্কের খালি অংশ = 180 - 63 = 117 units

এখন, সব পাইপ খুলে দেওয়া হয়েছে।
সব পাইপের যৌথ দক্ষতা = 5 + 4 - 6 = 3 units/second
অতএব, আরও সময় প্রয়োজন = 117/3 = 39 seconds.

৫,৫৭২.

If 3^{x + y} = 81 and 3^{x - y} = 9, then what are the values of x and y respectively?

ক
(2, 5)
খ
(3, 1)
গ
(3, 4)
ঘ
(5, 2)

সঠিক উত্তর: খ

(3, 1)

উত্তর

সঠিক উত্তর: খ

(3, 1)

খ

ব্যাখ্যা

Question: If 3^{x + y} = 81 and 3^{x - y} = 9, then what are the values of x and y respectively?

Solution:
Given,
3^{x + y} = 81
⇒ 3^{x + y} = 3⁴⇒ x + y = 4 .......(1)

Again,
3^{x - y} = 9
⇒ 3^{x - y} = 3²⇒ x - y = 2 ........(2)

Now, solving (1) and (2) we get,
x + y + x - y = 4 + 2
⇒ 2x = 6
⇒ x = 3

Now, x + y = 4
⇒ 3 + y = 4
⇒ y = 4 - 3
⇒ y = 1

∴ (x, y) = (3, 1)

৫,৫৭৩.

Tk. 1,000 becomes Tk. 1,200 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 2%, what amount will Tk. 1,000 become in 4 years?

ক
Tk. 1240
খ
Tk. 1280
গ
Tk. 1300
ঘ
Tk. 1340

সঠিক উত্তর: খ

Tk. 1280

উত্তর

সঠিক উত্তর: খ

Tk. 1280

খ

ব্যাখ্যা

Question: Tk. 1,000 becomes Tk. 1,200 in 4 years at a certain rate of simple interest. If the rate of interest is increased by 2%, what amount will Tk. 1,000 become in 4 years?

Solution:
Principal, P = 1000
Interest, I = 1,200 - 1,000 = 200
Time, T = 4 years

SI = PRT/100
⇒ R = (SI × 100)/(P × n)
⇒ R = (200 × 100)/(1000 × 4)
⇒ R = 20000/4000
⇒ R = 5

∴ Interest rate, R = 5%

∴ New Interest rate = 5% + 2% = 7%

New interest at 7% for 4 years:
New interest = (1,000 × 7 × 4)/100
= (28,000)/100
= 280 Tk.

New amount = Principal + Interest
= 1,000 + 280
= Tk. 1,280

৫,৫৭৪.

7 is 5 percent of what number?

ক
ক) 35
খ
খ) 140
গ
গ) 75
ঘ
ঘ) 49

সঠিক উত্তর: খ

খ) 140

উত্তর

সঠিক উত্তর: খ

খ) 140

খ

ব্যাখ্যা

question: 7 is 5 percent of what number?

solution:
let the number is X

So,
5% of X = 7
X = 7 × 20
X = 140

৫,৫৭৫.

If log₁₀(x + 2) + log₁₀(x + 1) = log₁₀(x + 2) + 1, then what is the value of x?

ক
5
খ
- 3
গ
12
ঘ
- 6
ঙ
9

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Question: If log₁₀(x + 2) + log₁₀(x + 1) = log₁₀(x + 2) + 1, then what is the value of x?

Solution:
Given that,
log₁₀(x + 2) + log₁₀(x + 1) = log₁₀(x + 2) + 1
⇒ log₁₀(x + 2) + log₁₀(x + 1) = log₁₀(x + 2) + log₁₀10 ;[log_aa = 1]
⇒ log₁₀(x + 2) - log₁₀(x + 2) + log₁₀(x + 1) = log₁₀10
⇒ log₁₀(x + 1) = log₁₀10
⇒ x + 1 = 10
∴ x = 9

৫,৫৭৬.

Three vessels contain a milk mixture 30 litre each. When put in a big vessel, they result in a mixture of milk and water in the ratio 2:1. If the ratio is to be reversed to make it 1: 2, how much more water should be added to the mix?

ক
ক) 20L
খ
খ) 40L
গ
গ) 90L
ঘ
ঘ) 100L

সঠিক উত্তর: গ

গ) 90L

উত্তর

সঠিক উত্তর: গ

গ) 90L

গ

ব্যাখ্যা

3 vessels of 30 litres each = 3 X 30 = 90 ml milk mixture
Amount of milk in mixture = 2/(2 + 1) × 90 = 60L
Amount of water = 90 - 60 = 30L

To make milk to water ratio 1 : 2, we simply need to make water double of milk.
By direct observation,
we can say that we should have 60L x 2 = 120L water to make the required ratio

We already have 30L,
we need (120 - 30) = 90L more water.

৫,৫৭৭.

Three partners A, B, and C start a business. B's capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 16500 at the end of a year. Find out B's share in it.

ক
4000
খ
5000
গ
6000
ঘ
7000

সঠিক উত্তর: গ

6000

উত্তর

সঠিক উত্তর: গ

6000

গ

ব্যাখ্যা

Question: Three partners A, B, and C start a business. B's capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk. 16500 at the end of a year. Find out B's share in it.

Solution:
Suppose C's capital = x
then, B's capital = 4x (Since B's Capital is four times C's capital)
A's capital,
2 × A's capital = 3 × B's capital (Since twice A's capital is equal to thrice B's capital)
⇒ 2 × A = 3 × 4x
∴ A = 6x

Now,
A : B : C
= 6x : 4x : x
= 6 : 4 : 1

B's share = 16500 × (4/11)
= 1500 × 4
= 6000

৫,৫৭৮.

60% of 200 is what percent of 160?

ক
ক) 20
খ
খ) 50
গ
গ) 60
ঘ
ঘ) 75

সঠিক উত্তর: ঘ

ঘ) 75

উত্তর

সঠিক উত্তর: ঘ

ঘ) 75

ঘ

ব্যাখ্যা

Let 60% of 200 be x percent of 160.
that means, 60% of 200 = x% of 160.
⇒ 60 × 200/100 = 160x/100
⇒ 120 = 8x/5
⇒ 8x = 600
⇒ x = 75

৫,৫৭৯.

The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.

ক
80
খ
90
গ
100
ঘ
110

সঠিক উত্তর: গ

100

উত্তর

সঠিক উত্তর: গ

100

গ

ব্যাখ্যা

Question: The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.

Solution:
Length of the hall = 40 m
Breadth of hall= 25 m
Height of hall = 20 m
Volume of the hall = 40 × 25 × 20 = 20000 m³
Space occupied by each person = 200 m³
Number of person that can accommodate in the hall = 20000/200 = 100

৫,৫৮০.

If Amina’s salary is 60% more than Bina’s salary, then Bina’s salary is what percent less than Amina’s salary?

ক
37.5%
খ
40%
গ
24.5%
ঘ
50%

সঠিক উত্তর: ক

37.5%

উত্তর

সঠিক উত্তর: ক

37.5%

ক

ব্যাখ্যা

Question: If Amina’s salary is 60% more than Bina’s salary, then Bina’s salary is what percent less than Amina’s salary?

Solution:
Let,
Bina’s Salary is Tk. 100. Then,
Amina’s Salary = (100 + 60% of 100)
= 100 + (60× 100)/100
= 100 + 60
= 160

Difference between Amina’s Salary and Bina’s Salary = 160 - 100 = 60

∴ lower = (60/160) × 100 = 37.5%

∴ Bina’s salary is 37.5% lower than Amina’s salary.

৫,৫৮১.

In a kilometre race, A, B and C are three participants. A can give B start of 50 m and C a start of 69 m. The start which B can allow C, is -

ক
17 m
খ
18 m
গ
19 m
ঘ
20 m

সঠিক উত্তর: ঘ

20 m

উত্তর

সঠিক উত্তর: ঘ

20 m

ঘ

ব্যাখ্যা

A : B : C
= 1000 : (1000 - 50) : (1000 - 69)
= 1000 : 950 : 931

In a 950 m race, B can give C a start of
(950 - 931) m
= 19 m

In a 1000 m race, B can give C a start of
(19/950) × 1000 = 20 m

৫,৫৮২.

A man said to his son,"I was one-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son.

ক
25.7 years
খ
28 years
গ
29.3 years
ঘ
36 years
ঙ
None of these

সঠিক উত্তর: ঘ

36 years

উত্তর

সঠিক উত্তর: ঘ

36 years

ঘ

ব্যাখ্যা

Question: A man said to his son,"I was one-third of your present age when you were born". If the present age of the man is 48 years, find the present age of the son.

Solution:

Present age of the son be P, he was born P years ago.

The age of the man was: (48 - P).

His age when the son was born should be equal to 1/3 of P.

(48 - P) =P/3
⇒ 144 - 3P = P
⇒ 4P = 144
∴ P = 36

৫,৫৮৩.

A trader allows two successive discounts of 30% and 15% on selling an article. If he gets Tk. 476 for that article, find its marked price = ?

ক
ক) 700
খ
খ) 400
গ
গ) 900
ঘ
ঘ) 800

সঠিক উত্তর: ঘ

ঘ) 800

উত্তর

সঠিক উত্তর: ঘ

ঘ) 800

ঘ

ব্যাখ্যা

Let, Marked price = Tk. x
∴x× 70/100 × 85/100 =476
⇒ x = 476 × 100/70 ×100/85
⇒ x= Tk. 800

৫,৫৮৪.

A boy goes to school at a speed of 5 km/h and returns to the village at a speed of 4 km/h. If he takes 4 hours and 30 minutes in all, what is the distance between the village and the school?

ক
ক) 7 km
খ
খ) 10km
গ
গ) 4km
ঘ
ঘ) 5km

সঠিক উত্তর: খ

খ) 10km

উত্তর

সঠিক উত্তর: খ

খ) 10km

খ

ব্যাখ্যা

মনেকরি,
বাড়ি হতে স্কুলের দূরত্ব x km

প্রশ্নমতে,
x/5 +x/4 = 9/2 [ গতিবেগ = দূরত্ব/ সময় ]
(4x + 5x)/20 = 9/2
9x/20= 9/2
x/20 = 1/2
x = 20/2
x= 10

৫,৫৮৫.

A contractor undertook to finish a piece of work in 100 days and employed 75 men. After 50 days, 2/5 of the work was completed. How many additional men should be employed to complete the work on schedule?

ক
25 men
খ
38 men
গ
33 men
ঘ
43 men

সঠিক উত্তর: খ

38 men

উত্তর

সঠিক উত্তর: খ

38 men

খ

ব্যাখ্যা

Question: A contractor undertook to finish a piece of work in 100 days and employed 75 men. After 50 days, 2/5 of the work was completed. How many additional men should be employed to complete the work on schedule?

Solution:
We know that 75 men completed 2/5 of the work in 50 days. Therefore, the amount of work done by 1 man in 50 days is:
Work done by 1 man in 50 days = 2/(5×75) = 2/375

Remaining work = 1 - 2/5 = 3/5

Number of men required = Remaining work / Work done by 1 man in 50 days
= (3/5)/(2/375)
= 112.5

Since the number of workers must be an integer, round up to 113 workers.

Additional workers = 113 − 75 = 38

৫,৫৮৬.

P takes twice as much time as Q or three times as much time as R to finish a piece of work. Working together, they can finish the work in 2 days. Q can do the work alone in how many days?

ক
6 days
খ
4 days
গ
8 days
ঘ
10 days

সঠিক উত্তর: ক

6 days

উত্তর

সঠিক উত্তর: ক

6 days

ক

ব্যাখ্যা

Question: P takes twice as much time as Q or three times as much time as R to finish a piece of work. Working together, they can finish the work in 2 days. Q can do the work alone in how many days?

Solution:
ধরা যাক,
P, Q ও R এর যথাক্রমে কাজটি শেষ করতে সময় লাগে x, x/2, এবং x/3 দিন।

তারা একসাথে 2 দিনে কাজ শেষ করে।
অর্থাৎ তাদের একদিনের কাজ হলো 1/2 অংশ।

∴ P + Q + R এর একদিনের কাজ = (1/x) + (2/x) + (3/x)
= (1 + 2 + 3)/x
= 6/x

শর্তমতে,
6/x = 1/2
∴ x = 12

∴ Q একা কাজ শেষ করতে সময় নেবে = 12/2 = 6 দিন।

৫,৫৮৭.

sin135° + sin45° = ?

ক
√5
খ
√2
গ
√7
ঘ
None

সঠিক উত্তর: খ

√2

উত্তর

সঠিক উত্তর: খ

√2

খ

ব্যাখ্যা

Question: sin135° + sin45° = ?

Solution:

Given that,
sin135° + sin45°
= sin(180° - 45°) + sin45°
= sin45° + sin45°
= 2 × sin45°
= 2 × (1/√2)
= √2

∴ sin135° + sin45° = √2

৫,৫৮৮.

Find the value of k if (x - 1) is a factor of 4x² + 3x² − 4x + k

ক
ক) 1
খ
খ) - 3
গ
গ) 2
ঘ
ঘ) 3

সঠিক উত্তর: খ

খ) - 3

উত্তর

সঠিক উত্তর: খ

খ) - 3

খ

ব্যাখ্যা

4x² + 3x² − 4x + k = 0
⇒ 4(1)² + 3(1)² - 4(1) + k = 0 [As, x - 1 is a factor]
⇒ 4 + 3 - 4 + k = 0
⇒ k = - 3

৫,৫৮৯.

In 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race A beats B by:

ক
ক) 20 m
খ
খ) 25 m
গ
গ) 22.5 m
ঘ
ঘ) 9 m

সঠিক উত্তর: ক

ক) 20 m

উত্তর

সঠিক উত্তর: ক

ক) 20 m

ক

ব্যাখ্যা

Distance covered by B in 9 sec.
=(100/45)x 9m= 20 m.
A beats B by 20 metres.

৫,৫৯০.

Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

ক
30 days
খ
55/2 days
গ
75 days
ঘ
75/2 days

সঠিক উত্তর: ঘ

75/2 days

উত্তর

সঠিক উত্তর: ঘ

75/2 days

ঘ

ব্যাখ্যা

Question: Abir does 80% of a work in 20 days. He then calls in Belal and they together finish the remaining work in 3 days. How long Belal alone would take to do the whole work?

Solution:
abir does 80% or 4/5 work in 20 days
in one day, he does 1/25 work
in 3 days, he does 3/25 work

work remaining = 1/5 - 3/25
= 2/25 work

Belal does 2/25 parts in 3 days
he will complete the work 75/2 days

৫,৫৯১.

Five years ago, the average age of A and B was 18 years. At present the average age of A, B, and C is 24 years. What would be the age of C after 5 years?

ক
32 years
খ
31 years
গ
33 years
ঘ
36 years

সঠিক উত্তর: খ

31 years

উত্তর

সঠিক উত্তর: খ

31 years

খ

ব্যাখ্যা

Question: Five years ago, the average age of A and B was 18 years. At present the average age of A, B, and C is 24 years. What would be the age of C after 5 years?

Solution:
The sum of the ages of A and B, 5 years ago = 18 × 2 = 36 years.
The sum of the present age of A and B = 5 + 5 + 36 = 46 years.
Sum of the present ages of A, B, and C = 24 × 3 = 72 years.

∴ Present age of C = 72 - 46 = 26 years.

∴ C's age after 5 years = 26 + 5 = 31 years.

৫,৫৯২.

Rafiq and Abir start simultaneously from a place A towards B 50 km apart. Rafiq's speed is 3km/h less than that of Abir. Abir, after reaching B, turns back and meets Rafiq at a places 10 km away from B. Rafiq's speed is-

ক
2 kmph
খ
4 kmph
গ
6 kmph
ঘ
8 kmph

সঠিক উত্তর: গ

6 kmph

উত্তর

সঠিক উত্তর: গ

6 kmph

গ

ব্যাখ্যা

Question: Rafiq and Abir start simultaneously from a place A towards B 50 km apart. Rafiq's speed is 3km/h less than that of Abir. Abir, after reaching B, turns back and meets Rafiq at a places 10 km away from B. Rafiq's speed is-

Question:
Let, the speed of Rafiq be = a kmph
Now,
Abir's speed = (a + 3) kmph

∴ Distance covered by Abir = (50 + 10) = 60 km
∴ Distance covered by Rafiq = (50 - 10) = 40 km.

ATQ,
60/(a + 3) = 40/a
⇒ 60a = 40a + 120
⇒ 60a - 40a = 120
⇒ 20a = 120
⇒ a = 120/20
∴ a = 6 kmph

৫,৫৯৩.

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is?

ক
ক) 4%
খ
খ) 6(/4)%
গ
গ) 20%
ঘ
ঘ) 25%

সঠিক উত্তর: গ

গ) 20%

উত্তর

সঠিক উত্তর: গ

গ) 20%

গ

ব্যাখ্যা

Let C.P of 1 litre milk be Tk. 1.
Then, S.P of 1 litre of mixture = Tk. 1, Gain = 25%
C.P. of 1 litre mixture = Tk. (100/125) × 1
= Tk. 4/5
By the rule of alligation, we have:

∴ Ratio of the milk to water = 4/5 : 1/5
= 4 : 1.
Hence, percentage of water in the mixture
= {(1/5) × 100}%
= 20%

৫,৫৯৪.

0.5 × 0.01 × 0.002 = ?

ক
0.000001
খ
0.00005
গ
0.0001
ঘ
0.00001

সঠিক উত্তর: ঘ

0.00001

উত্তর

সঠিক উত্তর: ঘ

0.00001

ঘ

ব্যাখ্যা

0.5 × 0.01 × 0.002 = 0.00001

৫,৫৯৫.

If ‘A’ stands for ‘÷’, ‘B’ stands for ‘+’, ‘C’ stands for ‘×’ and ‘D’ stands for ‘-’, then what will come in place of the question mark (?)
7 C 11 B 12 A 6 D 18 = ?

ক
61
খ
76
গ
82
ঘ
53
ঙ
None

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If ‘A’ stands for ‘÷’, ‘B’ stands for ‘+’, ‘C’ stands for ‘×’ and ‘D’ stands for ‘-’, then what will come in place of the question mark (?)
7 C 11 B 12 A 6 D 18 = ?

Solution:
দেওয়া আছে
A = ÷
B = +
C = × এবং
D = -

প্রদত্ত শর্ত অনুসারে পাই
7 C 11 B 12 A 6 D 18 = 7 × 11 + 12 ÷ 6 - 18
= 7 × 11 + 2 - 18
= 77 + 2 - 18
= 79 - 18
= 61

৫,৫৯৬.

If 16% of 40% of a number is 8, then find the number.

ক
115
খ
120
গ
125
ঘ
130

সঠিক উত্তর: গ

125

উত্তর

সঠিক উত্তর: গ

125

গ

ব্যাখ্যা

Question: If 16% of 40% of a number is 8, then find the number.

Solution:

Let X be the required number.

Therefore, as per the given question,

(16/100) × (40/100) × X = 8

⇒ X = (8 × 100 × 100)/(16 × 40)

∴ X = 125

৫,৫৯৭.

A square is drawn inside of a circle with a perimeter of 42π. What is the perimeter of that square?

ক
84
খ
42√2
গ
126
ঘ
84√2

সঠিক উত্তর: ঘ

84√2

উত্তর

সঠিক উত্তর: ঘ

84√2

ঘ

ব্যাখ্যা

Question: A square is drawn inside of a circle with a perimeter of 42π. What is the perimeter of that square?

Solution:
Circumference of the circle 2πr = 42π
r = 42π/2π
r = 21
So, Diameter of a circle d = 2r
= 2 × 21
= 42
If the square’s side is a, its diagonal distance
d = a√2
⇒ a = d/√2
⇒ a = 42/√2
⇒ a = (42 × √2)/(√2 × √2)
⇒ a = (42 × √2)/2
a = 21√2

So, perimeter 4a = 21√2 × 4
= 84√2

∴ Perimeter of a that square is 84√2

৫,৫৯৮.

A man starts from a point and travels 12 km in the north direction. Again he went east for 6 km and changed direction and again went north for 8 km. Finally went west for 6 km. What is the direct distance between his destination and journey?

ক
14 km
খ
16 km
গ
18 km
ঘ
20 km

সঠিক উত্তর: ঘ

20 km

উত্তর

সঠিক উত্তর: ঘ

20 km

ঘ

ব্যাখ্যা

Question: A man starts from a point and travels 12 km in the north direction. Again he went east for 6 km and changed direction and again went north for 8 km. Finally went west for 6 km. What is the direct distance between his destination and journey?

Solution:

ঐ ব্যক্তির যাত্রাস্থান A এবং গন্তব্য স্থান = E
∴ তার গন্তব্য স্থান ও যাত্রা স্থানের সরাসরি দূরত্ব, AE = (12 + 8) কি.মি.
= 20 কি.মি.

৫,৫৯৯.

If √(2ⁿ) = 64, then the value of n is

ক
12
খ
8
গ
6
ঘ
16

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If √(2ⁿ) = 64, then the value of n is-

Solution:
Given that,
√(2ⁿ) = 64
⇒ (2ⁿ)^1/2 = 2⁶
⇒ 2^n/2 = 2⁶
⇒ n/2 = 6
⇒ n = 2 × 6
∴ n = 12

৫,৬০০.

The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being (1/4)% is -

ক
Tk. 119.75
খ
Tk. 121.75
গ
Tk. 125.75
ঘ
None of the above

সঠিক উত্তর: ঘ

None of the above

উত্তর

সঠিক উত্তর: ঘ

None of the above

ঘ

ব্যাখ্যা

Question: The market value of a 10.5% stock, in which an income of Tk. 756 is derived by investing Tk. 9000, brokerage being (1/4)% is -

Solution:
For an income of Tk. 756, investment = Tk. 9000
For an income of Tk. (21/2), investment = Tk. {(9000/756) × (21/2)}
= Tk. 125
∴ For a Tk. 100 stock, investment = Tk. 125
The market value of Tk. 100 stock = Tk. {125 - (1/4)}
= Tk. 124.75