Bank Math

PrepBank · পাতা ১৯ / ১৬১ · ১,৮০১–১,৯০০ / ১৬,১২৪

১,৮০১.

If the simple interest on Tk. N at N% per annum for 5 years is Tk. N, what is the value of N?

ক
20
খ
25
গ
30
ঘ
15

ব্যাখ্যা

Question: If the simple interest on Tk. N at N% per annum for 5 years is Tk. N, what is the value of N?

Solution:
Given,
P = N
r = N% = N/100
n = 5 years
I = N

We know,
I = Prn
⇒ N = N × (N/100) × 5
⇒ N = (N² × 5)/100
⇒ N = N²/20
⇒ N² = 20N
⇒ N²/N = 20
∴ N = 20

সুতরাং, N এর মান হলো 20

১,৮০২.

A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 175, how much must C pay as his share of rent?

ক
Tk. 45
খ
Tk. 50
গ
Tk. 55
ঘ
Tk. 60

ব্যাখ্যা

Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Tk. 175, how much must C pay as his share of rent?

Solution:
A : B : C = (10 × 7) : (12 × 5) : (15 × 3)
= 70 : 60 : 45
= 14 : 12 : 9

∴ C's rent = 175 × (9/35)
= Tk. 45

১,৮০৩.

A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC is 10 Find the value of CB.

ক
10.5 cm
খ
(20/7)√58 cm
গ
23/2 cm
ঘ
None of these

ব্যাখ্যা

Solution: A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC is 10 Find the value of CB.

Solution:

(Tangents from the external point are equal)
(x + 7)² = 10² + (x + 3)²
⇒ x² + 14x + 49 = 100 + x² + 6x + 9
⇒ 8x = 60
∴ x = 7.5cm

∴ CB = x + 3 = 7.5 + 3 = 10.5 cm

১,৮০৪.

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is-

ক
276
খ
299
গ
322
ঘ
345

ব্যাখ্যা

Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is-

Solution:
Clearly, the numbers are (23 × 13) and (23 × 14).

∴ Larger number = (23 × 14) = 322.

১,৮০৫.

If debater A is in the team, which other debaters must be in the team as well?

ক
ক) X, Z and D
খ
খ) X, Y and B
গ
গ) X, Z and B
ঘ
ঘ) X, Z and C

ব্যাখ্যা

64-66): Answer the questions on the busis of the information given below
City High School must put together a debating team consisting of four debaters. There are candidates of equal ability: X, Y and Z who are all seniors; and A, B, C and D who are all juniors. The school requires that there should be two seniors and two juniors the team. It is also necessary that all of THE debaters be able to work with one another.
i) Debaters Y and A cannot work together.
ii) Debaters Z and C cannot work together.
iii) Debaters A and B cannot work together.

Question: If debater A is in the team, which other debaters must be in the team as well?

Solution:
X, Y, Z = সিনিয়র এবং সমান পারদর্শী।
A, B, C, D = জুনিয়র

৪ জনের টিমে, দুই জন সিনিয়র এবং ২ জন জুনিয়র থাকবে এবং
১) Y এবং A এক সাথে থাকতে পারবে না।
২) Z এবং C এক সাথে থাকতে পারবে না।
৩) A এবং B এক সাথে থাকতে পারবে না।

তাহলে A যদি টিমে থাকে বাকি সদস্য গুলো হবে,
সিনিয়র থাকবে X, Z
জুনিয়র থাকবে D

১,৮০৬.

If a committee of 3 people is to be selected from among 6 married couples such that the committee does not include two people who are married to each other, how many such committees are possible?

ক
160
খ
220
গ
960
ঘ
480

ব্যাখ্যা

Question: If a committee of 3 people is to be selected from among 6 married couples such that the committee does not include two people who are married to each other, how many such committees are possible?

Solution:
Number of ways 3 people can be chosen from 12 = ¹²C₃ = 220

Number of ways a couple can be chosen = 6
Number of ways the third person can be chosen = ¹⁰C₁ = 10

Hence total number of ways a couple with another person can be chosen = 6 × 10 = 60

Therefore total number of ways a couple cannot be chosen = 220 - 60 = 160

১,৮০৭.

In a triangle the length of the sides are 5, 9 and x. Which statement is always true?

ক
ক) x > 5
খ
খ) x < 9
গ
গ) 5 < x < 9
ঘ
ঘ) 4 < x < 14

ব্যাখ্যা

আমরা জানি
ত্রিভুজের যেকোনো দুই বাহুর সমষ্টি তৃতীয় বাহু অপেক্ষা বৃহত্তর।
এখন
9 + 5 > x
14 > x
এবং
x + 5 > 9
x + 5 - 5 > 9 - 5
x > 4
সুতরাং
4 < x < 14

১,৮০৮.

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

ক
14 years
খ
18 years
গ
20 years
ঘ
22 years

ব্যাখ্যা

Question: A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

Solution:
Let,
The son's present age is x years.
Then, the man's present age is = (x + 24)
∴ (x + 24) + 2 = 2(x+ 2)
⇒ x + 26 = 2x + 4
⇒ x = 22

১,৮০৯.

In an examination, a student's average marks was 67 per paper. If he had obtained 19 more marks for his Biology paper and 5 more marks for his Economics paper, his average per paper would have been 70. How many papers were there in the examination?

ক
ক) 8
খ
খ) 9
গ
গ) 10
ঘ
ঘ) 11

ব্যাখ্যা

Question: In an examination, a student's average marks was 67 per paper. If he had obtained 19 more marks for his Biology paper and 5 more marks for his Economics paper, his average per paper would have been 70. How many papers were there in the examination?

Solution:
Let the number of papers be x
Then student's total number = 67x
ATQ,
(67x + 19 + 5)/x = 70
⇒ 70x - 67x = 24
⇒ 3x = 24
∴ x = 8

১,৮১০.

What is the greatest number of 3 digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

ক
903
খ
996
গ
975
ঘ
939

ব্যাখ্যা

Questions: What is the greatest number of 3 digits which when divided by 6, 9 and 12 leaves a remainder of 3 in each case?

Solution:
৬, ৯, ১২ এর ল.সা.গু = ৩৬

তিন অঙ্কের বৃহত্তম সংখ্যা = ৯৯৯
৯৯৯ কে ৩৬ দ্বারা ভাগ করলে অবশিষ্ট থাকে ২৭
৯৯৯ - ২৭ = ৯৭২ ; ৩৬ দ্বারা নিঃশেষে বিভাজ্য।

নির্ণেয় সংখ্যা = ৯৭২ + ৩ = ৯৭৫

১,৮১১.

Walking at the rate of 4 kmph a man cover certain distance in 2 hr 45 min. Running at a speed of 16.5 kmph the man will cover the same distance in.

ক
ক) 49 min
খ
খ) 40 min
গ
গ) 34 min
ঘ
ঘ) 48 min

ব্যাখ্যা

Distance = Speed × time
Here time = 2hr 45 min = 11/4 hr
Distance = 4× (11/4)= 11 km
New Speed =16.5 kmph
Therefore time = D/S = 11/16.5 = 40 min

১,৮১২.

Parimal rented a car for Tk. 1800 plus Tk. 10 per mile driven. Maruf rented a car for Tk. 2500 plus Tk. 5 per mile driven. If each drove d miles and each was charged exactly the same amount for the rental, then d equals-

ক
100
খ
120
গ
135
ঘ
140
ঙ
150

ব্যাখ্যা

Question: Parimal rented a car for Tk. 1800 plus Tk. 10 per mile driven. Maruf rented a car for Tk. 2500 plus Tk. 5 per mile driven. If each drove d miles and each was charged exactly the same amount for the rental, then d equals-

Solution:
For d miles Parimal's cost would be: 1800 + 10d
And Maruf's cost would be: 2500 + 5d

Since we are told that each was charged exactly the same amount then:
1800 + 10d = 2500 + 5d
⇒ 5d = 700
∴ d = 140

১,৮১৩.

x - y = 2 এবং x + y = 60 হলে, x² - y² এর মান কত?

ক
130
খ
30
গ
120
ঘ
60

ব্যাখ্যা

প্রশ্ন: x - y = 2 এবং x + y = 60 হলে, x² - y² এর মান কত?

সমাধান:
দেওয়া আছে,
x - y = 2
এবং x + y = 60

আমরা জানি,
x² - y² = (x + y)(x - y)
= 60 × 2
= 120

১,৮১৪.

A box contains 4 red, 5 green and 6 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or black?

ক
ক) 1/3
খ
খ) 2/15
গ
গ) 2/3
ঘ
ঘ) 1/9

ব্যাখ্যা

Question: A box contains 4 red, 5 green and 6 black balls. A ball is drawn at random from the box. What is the probability that the ball drawn is either red or black?

Solution:
Total number of balls = (4 + 5 + 6) = 15
P(drawing a red ball or a black ball) = P(red) + P(black)
= (4/15) + (6/15)
= (4 + 6)/15
= 10/15
= 2/3
∴ The probability is 2/3.

১,৮১৫.

In a group of 60 people, 27 like coffee and 42 like tea and each person likes at least one of the two drinks. How many like both coffee and tea?

ক
15
খ
9
গ
12
ঘ
11

ব্যাখ্যা

Question: In a group of 60 people, 27 like coffee and 42 like tea and each person likes at least one of the two drinks. How many like both coffee and tea?

Solution:
Let,
A = Set of people who like coffee
B = Set of people who like tea

Given,
n(A ∪ B) = 60
n(A) = 27
n(B) = 42

then;
n(A ∩ B) = n(A) + n(B) - n(A ∪ B)
= 27 + 42 - 60
= 69 - 60
= 9

Therefore, 9 people like both tea and coffee.

১,৮১৬.

একটি সিলিন্ডারের ভূমির ক্ষেত্রফল 100π ব‍র্গমিটার এবং আয়তন 900π ঘনমিটার হলে সিলিন্ডারের উচ্চতা কত?

ক
3 মিটার
খ
6 মিটার
গ
9 মিটার
ঘ
12 মিটার
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: একটি সিলিন্ডারের ভূমির ক্ষেত্রফল 100π ব‍র্গমিটার এবং আয়তন 900π ঘনমিটার হলে সিলিন্ডারের উচ্চতা কত?

সমাধান:
ধরি,
সিলিন্ডারের ব্যাসা‍র্ধ = r
আমরা জানি,
সিলিন্ডারের ভূমির ক্ষেত্রফল = πr²

সিলিন্ডারের ভূমির আয়তন = πr²h

প্রশ্নমতে,
πr²h/πr² = 900π/100π
∴ h = 9

১,৮১৭.

The ratio of the cost price and selling price is 10 : 7, the loss percent is =?

ক
10%
খ
20%
গ
30%
ঘ
40%
ঙ
None of the above

ব্যাখ্যা

Question: The ratio of the cost price and selling price is 10 : 7, the loss percent is =?

Solution:
Let the cost price be Tk. 10x
The selling price is Tk. 7x

Hence, the loss percent = [(10x - 7x)/10x] × 100%
= (3/10) × 100%
= 30%

১,৮১৮.

A computer can perform 30 identical tasks in six hours. At that rate, what is the minimum number of computers that should be assigned to complete 80 tasks within three hours?

ক
ক) 12
খ
খ) 7
গ
গ) 9
ঘ
ঘ) 6
ঙ
ঙ) 8

ব্যাখ্যা

We Know
Total work = rate × Time

therefore
30 = Rate × 6
or Rate = 30/6 = 5

Now we need to find the number of computers
total work given = 80 and total time = 3 hrs

therefore
80 = 5 × 3 × No. of computers
or No. of computers = 80/15 = 5.333 , but no. of computers cannot be fraction i.e , so we have to consider as 1.

Total no. of computers = 5 + 1 = 6.

১,৮১৯.

A father said to his son, 'I was as old as you are at the present at the time of your birth'. Two years ago, the father's age was 48 years, the son's age in two years will be-

ক
ক) 23 years
খ
খ) 25 years
গ
গ) 27 years
ঘ
ঘ) 29 years

ব্যাখ্যা

Question: A father said to his son, 'I was as old as you are at the present at the time of your birth'. Two years ago, the father's age was 48 years, the son's age in two years will be-

Solution:
let, at present son is x years old
so, at time of his birth the father was x years old

∴ at present the age of father is = x + x year
= 2x year

Two years ago, the father's age was 48 years
fathers age at present = 48 + 2 years
= 50 years

2x = 50
⇒ x = 50/2
= 25 year

∴ the son's age in two years will be = 25 + 2
= 27 years

১,৮২০.

The speed of a boat in still water is 8 kmph. If it can travel 1 km upstream in 1 hr, what time would it take to travel the same distance downstream?

ক
2 minute
খ
1 minute
গ
4 minute
ঘ
3 minute

ব্যাখ্যা

Speed of the boat in still water = 8 km/hr
Speed upstream = 1/1 = 1 km/hr.
Speed of the stream = 8 - 1 = 7 km/hr.
Speed downstream = (8 + 7) = 15 km/hr.
Time is taken to travel 1 km downstream = (1/15) hr
= (1 × 60)/15
= 4 minutes.

১,৮২১.

In a shop, the cost of 5 shirts, 5 pairs of trousers and 3 hats is Tk. 710. The cost of 11 shirts, 11 pairs of trousers and 8 hats is Tk. 1590. What is the total cost of 1 shirt, 1 pair of trousers and 1 hat?

ক
ক) Tk. 130
খ
খ) Tk. 150
গ
গ) Tk. 180
ঘ
ঘ) Tk. 200
ঙ
ঙ) None of these

ব্যাখ্যা

ধরি, একটি শার্টের দাম s টাকা, এক জোড়া ট্রাউজারের দাম t টাকা এবং একটি হ্যাটের দাম h টাকা। সুতরাং, প্রশ্নানুসারে, 5s + 5t + 3h = 710………(i) এবং 11s + 11t + 8h = 1590
বা, 11s + 11t = 1590 - 8z…….(ii)
এখন, (i) নং equation কে 5 দিয়ে ভাগ করলে পাওয়া যাবে, s + t + (3/5)h = 142
⇒ 11s + 11t + (33/5)z = 1562 [উভয় পক্ষকে 11দ্বারা গুন]
⇒ 1590 - 8z + (33/5)z = 1562
⇒ - 8z + (33/5)z = 1562 - 1590 = -28
⇒ -7z/5 = -28
⇒ z = 20
এবং 11x + 11y = 1590 - 8×20 = 1430…..(iii)
(iii) নং কে 11 দ্বারা ভাগ করে পাই, x + y = 130
∴ x + y + z = 130 + 20 = 150

১,৮২২.

A pole 6m high casts a shadow 2√3m long on the ground, then the Sun's elevation is-

ক
ক) 60°
খ
খ) 45°
গ
গ) 30°
ঘ
ঘ) 90°

ব্যাখ্যা

প্রশ্ন: A pole 6m high casts a shadow 2√3m long on the ground, then the Sun's elevation is-

সমাধান:

tanθ = লম্ব/ভূমি
বা, tanθ = 6/(2√3)
বা, tanθ = √3
বা, tanθ = tan60°
∴ θ = 60°

১,৮২৩.

A monkey climbs a 12 meters-high slippery pillar. In his first minute, he climbs 2 meters, and in the next minute, he slip one meter down. In this way, how much time will he take to reach the top of the pillar?

ক
ক) 10 minutes
খ
খ) 12 minutes
গ
গ) 11 minutes
ঘ
ঘ) 21 minutes

ব্যাখ্যা

Question: A monkey climbs a 12 meters-high slippery pillar. In his first minute, he climbs 2 meters, and in the next minute, he slip one meter down. In this way, how much time will he take to reach the top of the pillar?

Solution:
On first minute monkey climb = 2 m
On the second minute it slips = 1 m
For every two minute, it climbs 1 m
So, average speed = 1 m/2 min For 10 m,
time is taken = 20 min
For the last 2 m jump add 1 min
So time taken = 20 + 1 = 21 min

∴ Monkey takes 21 minutes to reach the top of the pole.

১,৮২৪.

Which number replace the question mark-

ক
60
খ
54
গ
50
ঘ
46

ব্যাখ্যা

Question: Which number replace the question mark-

Solution:
In 1st figure:
6 + 5 + 4 + 3 = 18
⇒ 18 × 2 = 36

In 2nd figure:
9 + 5 + 5 + 3 = 22
⇒ 22 × 2 = 44

In 3rd figure:
6 + 5 + 9 + 5 = 25
⇒ 25 × 2 = 50

১,৮২৫.

A salesman receives daily wage of Tk. 200 and earns a commission of 20% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1000?

ক
ক) Tk. 5000
খ
খ) Tk. 4000
গ
গ) Tk. 6000
ঘ
ঘ) None

ব্যাখ্যা

Question: A salesman receives daily wage of Tk. 200 and earns a commission of 20% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1000?

Solution:
দৈনিক মোট আয় করতে হবে = 1000 টাকা
দৈনিক মজুরি =200 টাকা
অবশিষ্ট= (1000 - 200) টাকা
= 800 টাকা

20% সেলস কমিশন = 800 টাকা
1% সেলস কমিশন = 800/20 টাকা
100% সেলস কমিশন = (800 × 100)/20 টাকা
= 4000 টাকা

১,৮২৬.

What is the least number when divided by 4, 5 and 6 leaves in each case a remainder of 3?

ক
ক) 33
খ
খ) 43
গ
গ) 53
ঘ
ঘ) 63
ঙ
ঙ) 72

ব্যাখ্যা

LCM of 4, 5, and 6 is 60.
So the number is = 60 + 3 = 63

১,৮২৭.

If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be -

ক
ক) 8 days
খ
খ) 9 days
গ
গ) 10 days
ঘ
ঘ) 12 days

ব্যাখ্যা

Question: If 10 men can do a piece of work in 12 days, the time taken by 12 men to do the same piece of work will be -

Solution:
from 10 men can do a piece of work in 12 days, we get -
M1 = 10
D1 = 12

the time taken by 12 men to do the same piece of work will be
M2 =12
D2 =?

we know that,
M1 × D1 = M2 × D2
D2 = (10 × 12)/12
= 10 days

১,৮২৮.

What is 25% of 30% of 1/3?

ক
ক) 1/40
খ
খ) 1/30
গ
গ) 1/27
ঘ
ঘ) 1/45

ব্যাখ্যা

Question: What is 25% of 30% of 1/3?

Solution:
30% of 1/3 = 3/10 of 1/3 = 1/10

25% of 1/10 = 1/4 of 1/10 = 1/40

১,৮২৯.

What is the median of the modes in the dataset
(-5, 4, 3, 7, 2, 1, 3, 4, 5, -1, 7, 8, -4, 2, 6)

ক
2.5
খ
3
গ
3.5
ঘ
4

ব্যাখ্যা

প্রশ্ন: What is the median of the modes in the dataset
(-5, 4, 3, 7, 2, 1, 3, 4, 5, -1, 7, 8, -4, 2, 6)

সমাধান:
উপাত্তগুলোর প্রচুরক = 2, 3, 4, 7

∴ প্রচুরকের মধ্যক = (3 + 4)/2
= 3.5

১,৮৩০.

In the equation: 31(m - n) - 32(m - n) + (m - n) = ?

ক
- n
খ
- m
গ
0
ঘ
1
ঙ
None of these

ব্যাখ্যা

Question: In the equation: 31(m - n) - 32(m - n) + (m - n) = ?

Solution:
31(m - n) - 32(m - n) + (m - n)
= (m - n)(31 - 32 + 1)
= (m - n)(32 - 32)
= (m - n) × 0
= 0

১,৮৩১.

What decimal of an hour is a second (approximate)?

ক
0.0025
খ
0.0060
গ
0.00028
ঘ
0.000126
ঙ
None

ব্যাখ্যা

Question: What decimal of an hour is a second (approximate)?

Solution:
1 hour = 60 minute
and 1 minute = 60 second

Thus, required decimal = 1/(60 × 60)
= 1/3600
≈ 0.00028

১,৮৩২.

A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have Paint on exactly two sides.

ক
ক) 13
খ
খ) 27
গ
গ) 30
ঘ
ঘ) 12

ব্যাখ্যা

Question: A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have Paint on exactly two sides.

Solution:
A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2.

This means, we get a 3 × 3 × 3 cube
To get the the sides with just 2 faces painted, picture the edges of the each of the sides of the cube.
Apart from the corners (which have 3 faces painted), all other small cubes have 2 faces painted.

In total, we have 12 cubes of side 2 with exactly 2 sides painted

১,৮৩৩.

The average age of a group of 15 people is 30 years. If the age of each person in the group is decreased by 5 years, what will the new average age be?

ক
20
খ
25
গ
27.7
ঘ
32.5

ব্যাখ্যা

Question: The average age of a group of 15 people is 30 years. If the age of each person in the group is decreased by 5 years, what will the new average age be?

Solution:
Here,
Sum of the age/Total number of people = 30
⇒ Sum of the age/ 15 = 30
∴ Sum of the age = 450

Decrease each age by 5 years, the total decrease = 5 × 15 = 75
New sum = 450 - 75 = 375
Therefore, the new average age = 375/15 = 25 years

১,৮৩৪.

For what value of 'K' will the pair of equations 3x + 4y = 12 and kx + 12y = 30 does not have a unique solution?

ক
ক) 3
খ
খ) 7.5
গ
গ) 9
ঘ
ঘ) 12

ব্যাখ্যা

দেয়া আছে, 3x + 4y = 12 এবং kx + 12y = 30
যদি, 3/k = 4/12 হয় তাহলে সমীকরণ জোটটির অসংখ্য সমাধান থাকবে।
এখন, 3/k = 4/12
⇒ 4k = 12 × 3
⇒ k = 36/4
⇒ k = 9

১,৮৩৫.

When 128 guests take seat in auditorium, only 4/5 of the seats occupied. What is the total number of seats in the auditorium?

ক
150
খ
160
গ
168
ঘ
172

ব্যাখ্যা

Question: When 128 guests take seat in auditorium, only 4/5 of the seats occupied. What is the total number of seats in the auditorium?

Solution:
ধরি,
মোট আসন সংখ্যা x টি

প্রশ্নমতে,
x × (4/5) = 128
⇒ x = 128 × (5/4)
∴ x = 160

মোট আসন সংখ্যা ১৬০ টি

১,৮৩৬.

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

ক
ক) 3
খ
খ) 5
গ
গ) 11
ঘ
ঘ) 17

ব্যাখ্যা

এখানে
(2⁴)² - 1 = (2⁴)² - 1²
= (2⁴ + 1)(2⁴ - 1)
  = (16 + 1)(16 - 1)
  = 17 × 15
  = 17 × 3 × 5

সুতরাং, বৃহত্তম মৌলিক উৎপাদক হলো 17

১,৮৩৭.

The area of a square-shaped garden is 3600 square meters. What is the total length of the fence around it?

ক
140 m
খ
240 m
গ
280 m
ঘ
360 m

ব্যাখ্যা

Question: The area of a square-shaped garden is 3600 square meters. What is the total length of the fence around it?
(একটি বর্গাকার বাগানের ক্ষেত্রফল ৩৬০০ বর্গমিটার। বাগানের চারদিকে বেড়া দেওয়া আছে। বেড়ার মোট দৈর্ঘ্য কত?)

Solution:
আমরা জানি,
বর্গক্ষেত্রের বাহু = √ক্ষেত্রফল
∴ বাহু = (√৩৬০০)
= ৬০ মিটার

আবার,
বর্গক্ষেত্রের পরিসীমা = ৪ × বাহু
= (৪ × ৬০) মিটার
= ২৪০ মিটার

∴ বেড়ার মোট দৈর্ঘ্য = ২৪০ মিটার।

১,৮৩৮.

A train 125 m long passes a man, running in the same direction in which the train is going, in 10 seconds. The speed of the train is 50 km/hr, What is the speed of the man?

ক
ক) 4 km/hr
খ
খ) 5 km/hr
গ
গ) 6 km/hr
ঘ
ঘ) 7 km/hr

ব্যাখ্যা

Question: A train 125 m long passes a man, running in the same direction in which the train is going, in 10 seconds. The speed of the train is 50 km/hr, What is the speed of the man?

Solution:
ট্রেনের গতিবেগ 50 km/hr
ধরি, ব্যক্তিটির গতিবেগ x km/hr

যেহেতু ট্রেন ও ব্যক্তিটির গতিবেগ একই দিকে। অতএব, ট্রেন ১২৫ মিটার বা ০.১২৫ কিমি অতিক্রম করে ৫০ - x km/hr বেগে

প্রশ্নমতে,
০.১২৫/৫০ - x = ১০/৩৬০০
⇒ ৫০ - x = (১২৫ × ৩৬০০)/(১০ × ১০০০)
⇒ ৫০ - x = ৪৫
∴ x = ৫০ - ৪৫
= ৫ km/hr

ব্যক্তিটির গতিবেগ ৫ km/hr

১,৮৩৯.

If 6 men can build a wall in 8 days, how many days will 12 men take to build the same wall?

ক
4 days
খ
6 days
গ
8 days
ঘ
10 days

ব্যাখ্যা

Question: If 6 men can build a wall in 8 days, how many days will 12 men take to build the same wall?

Solution:
6 জন লোক একটি দেয়াল 8 দিনে তৈরি করতে পারে।
1 জন লোক সেই দেয়াল তৈরি করতে লাগবে = (8 × 6) দিন
12 জন লোক সেই দেয়াল তৈরি করতে লাগবে = (8 × 6)/12 দিন
= 4 দিন

১,৮৪০.

If (64)² - (36)² = 20x, then what is the value of x?

ক
120
খ
140
গ
112
ঘ
118

ব্যাখ্যা

Question: If (64)² - (36)² = 20x, then what is the value of x?

Solution:
Here, we can apply the formula of a² - b² = (a + b) (a - b)

So, after applying the formula, we will get
(64)² - (36)² = 20x
⇒ (64 + 36) (64 - 36) = 20x
⇒ 100 × 28 = 20x
⇒ x = (100 × 28)/20
∴ x = 140

১,৮৪১.

If Tk. 5,000 is invested at 12% annual rate of interest, how much will the investment be worth after 2 years?

ক
ক) 5785
খ
খ) 6272
গ
গ) 7190
ঘ
ঘ) 8225

ব্যাখ্যা

প্রশ্ন: If Tk. 5,000 is invested at 12% annual rate of interest, how much will the investment be worth after 2 years?

সমাধান:
দেওয়া আছে,
আসল, P = 5000 টাকা
মুনাফার হার, r = 12%
সময়, n = 2 বছর

প্রথম বছর,
মুনাফা I = Pnr = 5000 × 1 × 12%
= 5000 × (12/100)
= 50 × 12
= 600 টাকা
∴ প্রথম বছর পর মোট টাকা = 5000 + 600 = 5600 টাকা

দ্বিতীয় বছর,
মুনাফা I = Pnr = 5600 × 1 × 12%
= 5600 × (12/100)
= 672 টাকা
∴ দ্বিতীয় বছর পর মোট টাকা = 5600 + 672 = 6272 টাকা

∴ দুই বছর পর মোট টাকা = 6272 টাকা।

১,৮৪২.

A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house?

ক
20 km
খ
16 km
গ
14 km
ঘ
10 km
ঙ
12 km

ব্যাখ্যা

Question: A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house?

Solution:
Let distance = x km.
Time taken at 3 kmph : dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30 - (- 20) = 50 mins = 50/60 hours.
Here,
x/3 - x/4 = 50/60
⇒ x/12 = 5/6
∴ x = 10 km.

১,৮৪৩.

If a 44 meter ladder is placed against a 22 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is-

ক
60º
খ
90º
গ
30º
ঘ
45º

ব্যাখ্যা

Question: If a 44 meter ladder is placed against a 22 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is-

Solution:
Given that,
Ladder's length = 44 m
Wall's height = 22 m

Perpendicular = Wall's height = 22 m
Hypotenuse = Ladder's length = 44 m

We know,
Sinθ = Perpendicular/Hypotenuse
⇒ Sinθ = 22/44
⇒ Sinθ = 1/2
⇒ Sinθ = sin30º
∴ θ = 30º

১,৮৪৪.

What is the largest number of mangoes not exceeding 440 that can be distributed among three persons in the proportions 5 : 6 : 7?

ক
ক) 420
খ
খ) 432
গ
গ) 436
ঘ
ঘ) 440

ব্যাখ্যা

Question: What is the largest number of mangoes not exceeding 440 that can be distributed among three persons in the proportions 5 : 6 : 7?

Solution:
ধরি,
তিনজন যথাক্রমে আম পেয়েছে 5x, 6x, 7x

প্রশ্নমতে,
5x + 6x + 7x ≤ 440
⇒ 18x ≤ 440
⇒ x ≤ 440/18
∴ x ≤ 24.44

যেহেতু, আমের সংখ্যা পূর্ণ সংখ্যা হয়, x এর সর্বোচ্চ মান = 24সর্বোচ্চ আমের সংখ্যা = 5x + 6x + 7x
= 18x
= 18 × 24
= 432 টি

১,৮৪৫.

Find the area of a triangle whose sides are 15 cm, 8 cm, and 17 cm.

ক
40 cm²
খ
30 cm²
গ
20 cm²
ঘ
60 cm²

ব্যাখ্যা

Question: Find the area of a triangle whose sides are 15 cm, 8 cm, and 17 cm.

Solution:
ত্রিভুজের তিন বাহু যথাক্রমে,
a = 15 cm, b = 8 cm, c = 17 cm

অর্ধপরিধি, S = (a + b + c)/2
= (15 + 8 + 17)/2
= 40/2 = 20 cm

আমরা জানি,
ত্রিভুজের ক্ষেত্রফল = √{S(S - a)(S - b)(S - c)}
= √{20(20 - 15)(20 - 8)(20 - 17)}
= √{20 × 5 × 12 × 3}
= √3600
= 60 cm²

অতএব, ত্রিভুজের ক্ষেত্রফল = 60 cm²

১,৮৪৬.

A water tank contains 24 liters of water. Rahim uses 1/4 of the total water. Then Karim uses 1/2 of the remaining water. How many liters of water are left in the tank?

ক
9 liters
খ
12 liters
গ
10 liters
ঘ
15 liters

ব্যাখ্যা

Question: A water tank contains 24 liters of water. Rahim uses 1/4 of the total water. Then Karim uses 1/2 of the remaining water. How many liters of water are left in the tank?

Solution:
Total water = 24 liters
Water used by Rahim = (1/4) × 24 = 6 liters

∴ Remaining water = 24 - 6 = 18 liters

Water used by Karim = (1/2) × 18 = 9 liters

∴ Water left in the tank = 18 - 9 = 9 liters

১,৮৪৭.

There are three prizes to be distributed among five students. If no students gets more than one prize, then this can be done in:

ক
ক) 10
খ
খ) 12
গ
গ) 16
ঘ
ঘ) 24

ব্যাখ্যা

3 prize among 5 students can be distributed in ⁵C₃ ways = 10 ways.

১,৮৪৮.

What is the probability of getting a sum 9 from two throws of a dice?

ক
ক) 1/12
খ
খ) 1/8
গ
গ) 1/6
ঘ
ঘ) 1/9

ব্যাখ্যা

Question: What is the probability of getting a sum 9 from two throws of a dice?

Solution:
Total events = 6 × 6 = 36
Set of expected events = {(3, 6), (4, 5), (5, 4), (6, 3)}

∴ Probability = 4/36 = 1/9

১,৮৪৯.

If f(x) = 2x - 1 and g(x) = x², what is the value of f{g(- 3)}?

ক
ক) - 7
খ
খ) 2
গ
গ) 9
ঘ
ঘ) 17

ব্যাখ্যা

দেয়া আছে,
g(x) = x²
g(- 3) = (- 3)²
= 9

আবার,
f(x) = 2x - 1
f{g(- 3)} = 2 × 9 - 1
= 18 - 1
= 17

১,৮৫০.

600 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 75% sugar in the solution?

ক
1000 grams
খ
1400 grams
গ
1200 grams
ঘ
1080 grams

ব্যাখ্যা

Question: 600 grams of sugar solution has 30% sugar in it. How much sugar should be added to make 75% in the solution?

Solution:
Amount of sugar =600 × 30/100
=180 grams
Let,
x gram sugar to be added

ATQ,
(180 + X)/(600 + X) = 75%
⇒ (180 + X)/(600 + X) = 75/100
⇒ (180 + X)/(600 + X) = 3/4
⇒ 4(180 + X) = 3(600 + X)
⇒ 4X + 720 = 3X + 1800
⇒ 4X - 3X= 1800 - 720
∴ X = 1080 grams

১,৮৫১.

If shoes are bought at prices ranging from Tk. 500 to Tk. 700 and sold at prices ranging from Tk. 650 to Tk. 900, what is the greatest possible profit from selling 8 pairs?

ক
Tk. 3200
খ
Tk. 3400
গ
Tk. 3550
ঘ
Tk. 3600

ব্যাখ্যা

Question: If shoes are bought at prices ranging from Tk. 500 to Tk. 700 and sold at prices ranging from Tk. 650 to Tk. 900, what is the greatest possible profit from selling 8 pairs?

Solution:
Lowest total cost price = 8 × 500 = Tk. 4000
Highest total selling price = 8 × 900 = Tk. 7200
Greatest profit = 7200 − 4000 = Tk. 3200

১,৮৫২.

A passenger paid 50% customs duty on accompanied baggage items. He paid another 20% sales tax on the total value of the items plus the custom duty paid. The total custom duty and sales tax is Tk. 350. What is the value of the baggage items?

ক
Tk. 400
খ
Tk. 450.75
গ
Tk. 437.5
ঘ
Tk. 435.5

ব্যাখ্যা

Question: A passenger paid 50% customs duty on accompanied baggage items. He paid another 20% sales tax on the total value of the items plus the custom duty paid. The total custom duty and sales tax is Tk. 350. What is the value of the baggage items?

Solution:
ধরি,
Item গুলোর মূল্য = 100x টাকা
∴ Customs duty = 100x এর 50%
= 100x এর (50/100)
= 50x টাকা

Total value of the items plus the custom duty = 100x + 50x = 150x টাকা

∴ Sales tax = 150x এর 20%
= 30x টাকা

Total custom duty and sales tax = 50x + 30x = 80x

প্রশ্নমতে,
⇒ 80x = 350
⇒ x = 350/80
⇒ 100x = (350 × 100)/80 = 437.5

∴ Item গুলোর মূল্য = 437.50 টাকা

১,৮৫৩.

In a right triangle, the length of one of the legs is 4 and the length of the hypotenuse is 5. What is the length of the other leg?

ক
3
খ
6
গ
4
ঘ
3.5

ব্যাখ্যা

Question: In a right triangle, the length of one of the legs is 4 and the length of the hypotenuse is 5. What is the length of the other leg?

Solution:
সমকোণী ত্রিভুজের অতিভুজ = 5
সমকোণ সংলগ্ন এক বাহু = 4
সমকোণ সংলগ্ন অপর বাহু = a

পিথাগোরাসের উপপাদ্য অনুসারে,
a² + 4² = 5²
⇒ a² + 16 = 25
⇒ a² = 25 - 16
⇒ a² = 9
⇒ a² = 3²
∴ a = 3

১,৮৫৪.

A can complete 1/5 of a task in 4 days, while B can complete 1/10 of the same task in 5 days. If they work together and receive a total payment of Tk 900, what amount should A receive?

ক
400 Tk
খ
643 Tk
গ
700 Tk
ঘ
500 Tk

ব্যাখ্যা

Question: A can complete 1/5 of a task in 4 days, while B can complete 1/10 of the same task in 5 days. If they work together and receive a total payment of Tk 900, what amount should A receive?

Solution:

Whole work is done by A in (5 × 4) = 20 days
∴ A's 1-day work = (1/5) ÷ 4 = 1/20

Whole work is done by B in (5 × 10) = 50 days
∴ B's 1-day work = (1/10) ÷ 5 = 1/50

Ratio of A's and B's 1-day work = 1/20 : 1/50
= 50 : 20 = 5 : 2

∴ A's share of payment = (5/(5+2)) × 900
= (5/7) × 900
= 643 Tk

১,৮৫৫.

If today is Monday, what will be the day 350 days from now?

ক
ক) Monday
খ
খ) Tuesday
গ
গ) Wednesday
ঘ
ঘ) Thursday

ব্যাখ্যা

350 days, 350/7 = 50, no odd days, so it will be a Monday.

১,৮৫৬.

The average speed of a train is 20% less on the return journey than on the onward journey. The train halts for half an hour at the destination before starting the return trip. If the total time taken for the entire round trip (including the halt) is 23 hours, covering a distance of 1000km, the speed of the train on the return journey is-

ক
40 km/h
খ
45 km/h
গ
50 km/h
ঘ
60 km/h

ব্যাখ্যা

Question: The average speed of a train is 20% less on the return journey than on the onward journey. The train halts for half an hour at the destination before starting the return trip. If the total time taken for the entire round trip (including the halt) is 23 hours, covering a distance of 1000km, the speed of the train on the return journey is-

Solution:
Let,
the average speed on the onward journey be x km/h

Then,
the average speed on return journey = (80% of x) = 4x/5 km/h

ATQ,
500/x + 500/(4x/5) = 23 - (1/2)
⇒ 500/x + 625/x = 45/2
⇒ (500+ 625)/x = 45/2
⇒ 1125/x = 45/2
⇒ 45x = 1125 × 2
⇒ x = (1125 × 2)/45
∴ x = 50

∴ speed of return journey = (4× 50)/5 = 40 km/h

১,৮৫৭.

If a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is-

ক
22
খ
12
গ
18
ঘ
10

ব্যাখ্যা

Question: If a : b : c = 2 : 3 : 4 and 2a - 3b + 4c = 33, then the value of c is-

Solution:
Let,
a = 2x, b = 3x and c = 4x ; (since a : b : c = 2 : 3 : 4)

Now substitute into the equation,
2a - 3b + 4c = 33
⇒ 2(2x) - 3(3x) + 4(4x) = 33
⇒ 4x - 9x + 16x = 33
⇒ 11x = 33
∴ x = 3

Since c = 4x = 4 × 3 = 12

১,৮৫৮.

The sum of two numbers is 40 and their difference is 4. The ratio of the number is

ক
ক) 12 : 13
খ
খ) 11 : 9
গ
গ) 11 : 10
ঘ
ঘ) 10 : 11

ব্যাখ্যা

Given:
The sum of two numbers is 40.
The difference of two number is 4.
Let
the larger number be x.
the smaller number be y.
According to the question,
(x + y)/(x - y) = 40/4
(x + y)/(x - y) =10/1
10(x - y) = x + y
10x - 10y = x + y
10x - x = 10y + y
9x = 11y
x/y = 11/9
x : y = 11 : 9

∴ The ratio of the number is 11 : 9

১,৮৫৯.

The difference between two numbers is 16. If one-third of the smaller number is greater than one-seventh of the larger number by 4, then the two numbers are:

ক
9, 25
খ
12, 28
গ
33, 49
ঘ
None of the above

ব্যাখ্যা

Question: The difference between two numbers is 16. If one-third of the smaller number is greater than one-seventh of the larger number by 4, then the two numbers are:

Solution:
Let the numbers be p and (p + 16)
ATQ,
(p/3) - {(p + 16)/7} = 4
⇒ (7p - 3p - 48)/21 = 4
⇒ 4p = 81 + 48
⇒ p = 132/4
∴ p = 33

So, the numbers are 33 and (33 + 16) = 49

১,৮৬০.

What is the value of x in the equation 3x - 15 - 6 = 0?

ক
ক) 7
খ
খ) 8
গ
গ) 9
ঘ
ঘ) - 9

ব্যাখ্যা

3x - 15 - 6 = 0
3x - 21 = 0
3x = 21
x = 7

১,৮৬১.

From a point C on a level ground, the angle of elevation of the top of a tower is 30 degree. If the tower is 100 meter high, find the distance from point C to the foot of the tower.

ক
ক) 170 meter
খ
খ) 172 meter
গ
গ) 173 meter
ঘ
ঘ) 167 meter

ব্যাখ্যা

Let AB be the tower
then∠ACB=30º
AB=100 meter
AB/AC= tan30º
=>100/AC= 1/√3
=>AC= √3/100
=>AC= 1.73×100
=>AC= 173meter

১,৮৬২.

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

ক
66π m²
খ
60π m²
গ
50π m²
ঘ
48π m²

ব্যাখ্যা

Question: The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

Solution:
Here, l = 10m
h = 8m

So, r = √(l² - h²)
= √(10² - 8²)
=√(100 - 64)
= √36
= 6

∴Curved surface area = πrl
= (π × 6 × 10) m² = 60π m²

১,৮৬৩.

The price of 357 apples is Tk. 1517.25. Find the approximate price of 49 dozens of such apples?

ক
2288 Tk.
খ
2499 Tk.
গ
2377 Tk.
ঘ
2522 Tk.

ব্যাখ্যা

Question: The price of 357 apples is Tk. 1517.25. Find the approximate price of 49 dozens of such apples?

Solution:
1 dozen = 12 pcs
49 dozens = 49 × 12 = 588 apples

Now,
357 apples = 1517.25 Tk.
∴ 1 apple = 1517.25/357 Tk.
∴ 588 apples = (1517.25 × 588)/357 Tk.
= 2499 Tk.

১,৮৬৪.

Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is-

ক
4 : 3
খ
1 : 5
গ
4 : 9
ঘ
4 : 5

ব্যাখ্যা

Question: Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is-

Solution:
Let the third number be x

Then, first number = 120% of x = 120x/100 = 6x/5
Second number = 150% of x = 150x/100 = 3x/2

∴ Ratio of first two numbers = 6x/5 : 3x/2
= 12x : 15x
= 4 : 5

১,৮৬৫.

Tk. 500 is deposited in a savings account which pays 7% annual interest compounded semi-annually. To the nearest Taka, how much is in the account at the end of the year?

ক
ক) 542
খ
খ) 536
গ
গ) 512
ঘ
ঘ) 524

ব্যাখ্যা

I = P(1+r)²
= 500{1 + 7/(2 × 100)}²
= 500 × (1 + 0.035)²
= 500 × (1.035)²
= 535.6125 ≅ 536

১,৮৬৬.

In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Tk. 2.40 per hour for regular work and Tk. 3.20 per hour for overtime. If he earns Tk. 432 in 4 weeks, then how many hours does he work for?

ক
145 hours
খ
160 hours
গ
165 hours
ঘ
175 hours

ব্যাখ্যা

Question: In a regular week, there are 5 working days and for each day, the working hours are 8. A man gets Tk. 2.40 per hour for regular work and Tk. 3.20 per hour for overtime. If he earns Tk. 432 in 4 weeks, then how many hours does he work for?

Solution:
Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 × 8 × 4) = 160

ATQ,
(160 × 2.40) + (x × 3.20) = 432
⇒ 3.20x = 432 - 384
⇒ 3.20x = 48
⇒ x = 15

Hence, total hours of work = (160 + 15) = 175 hours.

১,৮৬৭.

At a certain party attended by 32 people, 24 were students. If 12 of those in attendance were women, and if 6 of the women in attendance were students, then how many of the men who attended the party were not students.

ক
2
খ
4
গ
8
ঘ
12
ঙ
18

ব্যাখ্যা

Question: At a certain party attended by 32 people, 24 were students. If 12 of those in attendance were women, and if 6 of the women in attendance were students, then how many of the men who attended the party were not students.

Solution:
Given,
People who are not students = (32 - 24)
= 8

Women who are not students = (12 - 6)
= 6

∴ Men who are not students = (8 - 6)
= 2

১,৮৬৮.

The area of a square is equal to the area of a parallelogram. If the base of the parallelogram is 45 meters and its height is 5 meters, what is the length of one side of the square?

ক
18 meters
খ
15 meters
গ
7 meters
ঘ
12 meters

ব্যাখ্যা

Question: The area of a square is equal to the area of a parallelogram. If the base of the parallelogram is 45 meters and its height is 5 meters, what is the length of one side of the square?

Solution:
Area of the parallelogram = Base × Height
= 45 × 5
= 225 square meters

Let,
Side of the square = k meters
∴ Area of the square = k² square meters

ATQ,
k² = 225
⇒ k = √225
∴ k = 15
Therefore, the length of one side of the square = 15 meters

১,৮৬৯.

In how many years will Tk. 2000 amounts to Tk. 2420 at 10% per annum compound interest?

ক
2 years
খ
3 years
গ
4 years
ঘ
2.5 years

ব্যাখ্যা

Question: In how many years will Tk. 2000 amounts to Tk. 2420 at 10% per annum compound interest?

Solution:
Principal = Tk. 2000
Amount = Tk. 2420
Rate = 10%

We Know
C = P(1 + r)ⁿ
2420 = 2000(1 + 10/100)ⁿ
2420/2000 = (11/10)ⁿ
121/100 = (11/10)ⁿ
(11/10)² = (11/10)ⁿ
n = 2

১,৮৭০.

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
35 hours
খ
32 hours
গ
25 hours
ঘ
40 hours
ঙ
None of the above

ব্যাখ্যা

Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

Solution:
Suppose,
Pipe A alone takes x hours to fill the tank.
So, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

Now,
1/x + 2/x + 4/x = 1/5
⇒ (1 + 2 + 4)/x = 1/5
⇒ 7/x = 1/5
∴ x = 35

∴ Pipe A alone takes 35 hours to fill the tank.

১,৮৭১.

Five years ago, Rahul was half as old as Maya. If Rahul is 15 years old now, how old is Maya now?

ক
20 years
খ
25 years
গ
27 years
ঘ
23 years

ব্যাখ্যা

Question: Five years ago, Rahul was half as old as Maya. If Rahul is 15 years old now, how old is Maya now?

Solution:
Let,
Age of Maya now = x years
ATQ,
(15 - 5)/2 = (x - 5)
⇒ 5 = (x - 5)
⇒ x = 10

∴ The age of Maya now is 25 years

১,৮৭২.

Ratio of the income of A and B is 6 : 5 and the ratio of the savings of A and B is 3 : 1. If the expenditure of A and B is Tk. 12000 and Tk.16000 respectively, then find the difference between the income of A and B?

ক
Tk. 4000
খ
Tk. 3550
গ
Tk. 5200
ঘ
Tk. 2500

ব্যাখ্যা

Question: Ratio of the income of A and B is 6 : 5 and the ratio of the savings of A and B is 3 : 1. If the expenditure of A and B is Tk. 12000 and Tk.16000 respectively, then find the difference between the income of A and B?

Solution:
Let,
Income of A = 6x and Income of B = 5x
And
Savings of A = 3y and Savings of B = y

We know,
Income = Savings + Expenditure

ATQ,
6x = 3y + 12000 ......(1) (for A)
5x = y + 16000 (for B)
⇒ y = 5x - 16000 ...... (2)

Puting this value in (1) then we get,
⇒ 6x = 3y + 12000
⇒ 6x = 3(5x - 16000) + 12000
⇒ 6x = 15x - 48000 + 12000
⇒ 6x = 15x - 36000
⇒ 15x - 6x = 36000
⇒ 9x = 36000
∴ x = 4000
(2) ⇒ y = 5x - 16000 = 20000 - 16000 = 4000

∴ Income of A = 24000
∴ Income of B = 20000

∴ Difference = 24000 - 20000 = Tk. 4000

১,৮৭৩.

The height of a cone is 12 cm and the radius of its base is 5 cm. What is the approximate volume of the cone in cubic centimeters?

ক
70π cm³
খ
50π cm³
গ
100π cm³
ঘ
None of the above

ব্যাখ্যা

Question: The height of a cone is 12 cm and the radius of its base is 5 cm. What is the approximate volume of the cone in cubic centimeters?
(একটি সমবৃত্তভূমিক কোণকের উচ্চতা ১২ সে.মি. এবং ভূমির ব্যাসার্ধ ৫ সে.মি. হলে, কোণকটির আয়তন প্রায় কত ঘন সে.মি.?)

Solution:
ধরি,
কোণকের ব্যাসার্ধ, r = ৫ সে.মি.
কোণকের উচ্চতা, h = ১২ সে.মি.

আমরা জানি,
কোণকের আয়তন = (1/3)πr²h.
= (১/৩) × π × ৫^২ × ১২
= ১০০π ঘন সে.মি.

১,৮৭৪.

The smallest value of natural number n for which 2n + 1 is not prime number?

ক
ক) 1
খ
খ) 2
গ
গ) 3
ঘ
ঘ) 4

ব্যাখ্যা

Given:
n is the natural number
Substitute values n = 1, 2, 3,4 ... in the expression 2n + 1

If n = 1, 2n + 1 = 2 × 1 + 1 ⇒ 3
If n = 2, 2n + 1 = 2 × 2 + 1 ⇒ 5
If n = 3, 2n + 1 = 2 × 3 + 1 ⇒ 7
If n = 4, 2n + 1 = 2 × 4 + 1 ⇒ 9

9 is not a prime number

∴ Smallest natural number is 4

১,৮৭৫.

In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C invests the rest of the capital for the whole time. Out of a profit of Tk 3680, C's share is -

ক
ক) Tk 2480
খ
খ) Tk 2880
গ
গ) Tk 3000
ঘ
ঘ) Tk 3260

ব্যাখ্যা

Question: In a partnership, A invests 1/6 of the capital for 1/6 of the time, B invests 1/3 of the capital for 1/3 of the time and C invests the rest of the capital for the whole time. Out of a profit of Tk 3680, C's share is -

Solution:
Let A invests Tk x/6 for y/6
A invests Tk x/3 for y/3
C invests= x - (x/6 + x/3) = x/2 for y months

Ratio of their investments = (6/x × 6/y) : (3/x × 3 /y) : (2/x × y)
= 1/36 : 1/9 : 1/2
= 1 : 4 : 18

∴B′s Share = Tk (3680 × 18/23) = Tk 2880

১,৮৭৬.

When an article is sold for Tk. 116, the profit percent is thrice as much as when it is sold for Tk. 92. The cost price of the article is-

ক
ক) Tk. 90
খ
খ) Tk. 70
গ
গ) Tk. 80
ঘ
ঘ) Tk. 100

ব্যাখ্যা

Let the cost price of an article be Tk. x
⇒ Selling price of an article is Tk.116

Profit percentage = {(Selling Price – Cost Price) /Cost Price} × 100
= {(116 - x) /x} × 100

Selling price = Tk. 92
⇒ Profit percentage = {(92 - x) /x} × 100

According to question,
⇒ {(116 - x) /x} × 100 = 3 × [{(92 - x) /x} × 100]
⇒ 116 - x = 276 - 3x
⇒ 3x - x = 276 - 116
⇒ 2x = 160
⇒ x = 80

∴ Cost price of an article is Tk. 80

১,৮৭৭.

Fresh grapes contain 80% water by weight, while dry grapes contain only 20% water. If a person has 100 kg of fresh grapes, how many kilograms of dry grapes can be obtained from them after drying?

ক
25 kg
খ
20 kg
গ
30 kg
ঘ
40 kg

ব্যাখ্যা

Question: Fresh grapes contain 80% water by weight, while dry grapes contain only 20% water. If a person has 100 kg of fresh grapes, how many kilograms of dry grapes can be obtained from them after drying?

Solution:
Fresh grapes: 80% water → 20% solid
So, in 100 kg fresh grapes:
Water = 80 kg
Solid = 20 kg
When grapes dry, water evaporates, but the solid remains unchanged.

Dry grapes: 20% water → 80% solid
That means the 20 kg solid must now be 80% of the dry grape weight
So, let total weight of dry grapes = x

Then:
0.8x=20
⇒x=200/0.8 =25 kg

১,৮৭৮.

Which of the following numbers is divisible by 11?

ক
44212
খ
59403
গ
30217
ঘ
60411

ব্যাখ্যা

Question: Which of the following numbers is divisible by 11?

Solution:
Here,
30217, (3 + 2 +7) - (0 + 1) = 11, which is divisible by 11.
44212, (4 + 2 + 2) - (4 + 1) = 3, which is not divisible by 11.
59403, (5 + 4 + 3) - (9 + 0) = 3, which is not divisible by 11.
60411, (6 + 4 + 1) - (0 + 1) = 10, which is not divisible by 11.

১,৮৭৯.

The sum of squares of two numbers is 80 and the square of difference between the two numbers is 36. Find the product of two numbers.

ক
ক) 11
খ
খ) 22
গ
গ) 33
ঘ
ঘ) 26

ব্যাখ্যা

Let,
Two numbers x & y
ATQ,
x² + y² = 80
And,
(x – y)² = 36
Or, x² + y² – 2xy = 36
Or, 80 – 2xy = 36
Or, 2xy = 44
Or, xy = 22

∴ The product of two numbers is: 22

১,৮৮০.

A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

ক
50%
খ
40%
গ
42%
ঘ
60%
ঙ
55%

ব্যাখ্যা

Question: A merchant sells an item at a 20% discount, but still makes a gross profit of 20 percent of the cost. What percent of the cost would the gross profit on the item have been if it had been sold without the discount?

Solution:
Let the Market Price of the product be MP.
Let the Original Cost Price of the product be CP.

Selling Price (Discounted Price) = 100%of MP - 20%MP = 80% of MP ....... (1)
Profit made by selling at discounted price = 20% of CP ....... (2)

Now, Profit = Selling Price - Original Cost Price
⇒ 20% of CP = 80% of MP - 100% CP
⇒ MP = 120CP/80 = 3/2 (CP)

Now if Product is sold without any discount, then,

Profit = Selling Price (without discount) - Original Cost Price
= Market Price - Original Cost Price
= MP - CP
= (3/2)CP - CP
= 1/2 CP
= 50% of CP

১,৮৮১.

A train that is 300 meters long takes 30 seconds to pass a stationary pole. At the same constant speed, how much time will the train take to completely pass a platform that is 500 meters long?

ক
50 seconds
খ
80 seconds
গ
70 seconds
ঘ
90 seconds

ব্যাখ্যা

Question: A train that is 300 meters long takes 30 seconds to pass a stationary pole. At the same constant speed, how much time will the train take to completely pass a platform that is 500 meters long?

Solution:
Length of the train = 300 m
Time taken to pass a pole = 30 seconds

So, speed of the train
= 300/30
= 10 m/s

Length to be covered while passing the platform
= Length of train + Length of platform
= 300 + 500
= 800 m

Time taken to pass the platform
= Total distance/Speed
= 800/10
= 80 seconds

Therefore, the train will take 80 seconds to pass the platform.

১,৮৮২.

If a : b : c = 3 : 4 : 7, then the ratio (a + b + c) : 5c is equal to

ক
ক) 1 : 3
খ
খ) 2 : 1
গ
গ) 4 : 1
ঘ
ঘ) 2 : 5

ব্যাখ্যা

(a + b + c) : 5c = (3 + 4 + 7) : 5 × 7 = 14 : 35 = 2 : 5

১,৮৮৩.

A fair coin is flipped three times. What is the probability that coin lands head each time?

ক
ক) 1/2
খ
খ) 1/4
গ
গ) 1/6
ঘ
ঘ) 1/8

ব্যাখ্যা

Question: A fair coin is flipped three times. What is the probability that coin lands head each time?

Solution:
একটি মুদ্রাকে তিনবার নিক্ষেপ করলে নমুনা বিন্দু হবে = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
= 8 টি
নমুনা ক্ষেত্র থেকে দেখা যাচ্ছে, প্রতিবারে H অর্থাৎ তিনটিই H আসার অনুকূল ফলাফল 1টি

নির্ণেয় সম্ভাবনা = 1/8

১,৮৮৪.

Which largest 4-digit number is divisible by 16, 24, 30 and 36?

ক
ক) 9356
খ
খ) 9465
গ
গ) 9360
ঘ
ঘ) 9670

ব্যাখ্যা

Question: Which largest 4-digit number is divisible by 16, 24, 30 and 36?
Solution:
৪ অংকের বৃহত্তম সংখ্যা = ৯৯৯৯
আবার,
১৬, ২৪, ৩০, ৩৬ এর ল.সা.গু = ৭২০
৯৯৯৯ কে ৭২০ দ্বারা ভাগ করলে ৬৩৯ অবশিষ্ট থাকে।
∴ বৃহত্তম সংখ্যাটি = ৯৯৯৯ - ৬৩৯ = ৯৩৬০।

১,৮৮৫.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk.1400 after 3 years at the same rate?

ক
463.4 Tk.
খ
350.5 Tk.
গ
223.2 Tk.
ঘ
145.4 Tk.

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of Tk.1400 after 3 years at the same rate?

Solution:
Let P = Tk. 100.
Then, S.I. Tk. = 60 and n = 6 years

Rate =(100 × 60)/(100 × 6) = 10%

Now, P = Tk.. 1400.
n = 3 years and R = 10% p.a.

C.I. = 1400(1 + 10/100)³ - 1400
= 1400(1.1)³ - 1400
= 1863.4 - 1400
= 463.4

১,৮৮৬.

Two train running in parallel line in the same direction at 40km/h and 22km/h respectively completely pass one another in 75 seconds. If the length of the first train is 255 meters, how long will it take the second train to pass a platform that is 100 meters long?

ক
18 seconds
খ
20 seconds
গ
30 seconds
ঘ
36 seconds

ব্যাখ্যা

We know, Time = distance/speed
Time, t = 75 seconds
Let the length of second train be y meter
For 75 seconds, distance, s = (255 + y) meters
and speed, v = (40 - 22) km/h = (40 - 22) × 1000 m/3600s = (18 × 5/18) m/s = 5 m/s
75 = (255 + y)/5
or, 255 + y = 375
or, y = 120
The length of second train is 120m
Therefore, required time taken = (120 + 100)/(22 × 5/18) = 36 seconds

১,৮৮৭.

Which number should be placed in the question-marked position?

ক
480
খ
600
গ
720
ঘ
850

ব্যাখ্যা

Question: Which number should be placed in the question-marked position?

Solution:
By going in clockwise direction we find the following pattern,
5 × 1 = 5
5 × 2 = 10
10 × 3 = 30
30 × 4 = 120
120 × 5 = 600
600 × 6 = 3600
3600 × 7 = 25200

১,৮৮৮.

54 toymakers can prepare 36 toys per day. Ajay wants 416 toys. How many toymakers should he employ to get the job done in 16 days?

ক
39
খ
41
গ
27
ঘ
43
ঙ
None

ব্যাখ্যা

Question: 54 toymakers can prepare 36 toys per day. Ajay wants 416 toys. How many toymakers should he employ to get the job done in 16 days?

Solution:
Let, the required number of toymakers x

54 toymakers make 36 toys per day
So, 1 toymaker makes 36/54 = 2/3 toys per day
Each toymaker in 16 days makes = 2/3 × 16 = 32/3 toys
So, x toymakers will make = 32x/3 toys

ATQ,
32x/3 = 416
⇒ x = 416 × (3/32)
∴ x = 39

১,৮৮৯.

A man's investment doubles in every 5 years. If he invested Tk. 5,000 in each of the years 2010, 2015, 2020 then what will be the amount received by him in 2025?

ক
Tk. 50000
খ
Tk. 70000
গ
Tk. 110000
ঘ
Tk. 120000

ব্যাখ্যা

Question: A man's investment doubles in every 5 years. If he invested Tk. 5,000 in each of the years 2010, 2015, 2020 then what will be the amount received by him in 2025?

Solution:
২০১০ এ বিনিয়োগ করা ৫০০০ টাকার ক্ষেত্রে,
২০২৫ সালে পাওয়া যাবে = ৫০০০ × ২^৩
= ৪০০০০ টাকা

২০১৫ এ বিনিয়োগ করা ৫০০০ টাকার ক্ষেত্রে,
২০২৫ সালে পাওয়া যাবে = ৫০০০ × ২^২
= ২০০০০ টাকা

২০২০ এ বিনিয়োগ করা ৫০০০ টাকার ক্ষেত্রে,
২০২৫ সালে পাওয়া যাবে = ৫০০০ × ২^১
= ১০০০০ টাকা

মোট = ৪০০০০ + ২০০০০ + ১০০০০
= ৭০০০০ টাকা

১,৮৯০.

A square lawn with side 50 m long has a circular flower bed in the center. If the area of the lawn, excluding the flower bed, is 1884 m²what is the radius of the circular flower bed?

ক
ক) 12 meters
খ
খ) 14 meters
গ
গ) 15 meters
ঘ
ঘ) 16 meters

ব্যাখ্যা

Question: A square lawn with side 50 m long has a circular flower bed in the center. If the area of the lawn, excluding the flower bed, is 1884 m²what is the radius of the circular flower bed?

Solution:
Area of the flower bed = Area of square lawn - Area of lawn excluding circular bed
= [(50)² - 1884] m²= 616 m²

Let the radius of the circular flower bed is r meters.
Area of the circular flower bed is πr²

ATQ,
πr² = 616
⇒ r² = (7/22) × 616
⇒ r² = 196
∴ r = 14

১,৮৯১.

Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. If there is no current how much time will the boat take to travel 22km ?

ক
3 hour
খ
4 hour
গ
2 hour
ঘ
1.5 hour

ব্যাখ্যা

Question: Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. If there is no current how much time will the boat take to travel 22km ?

Solution:
Let the speed of the boat is S
the speed of the current is W

S + W = 14 . . . . . . (i)
S - W = 8 . . . . . . . .(ii)
_________________
from equation (i) & (ii)
S = 11 km/hr, W = 3 km/hr

so, time to travel 22km is = 22/11 hour
= 2 hour

১,৮৯২.

The square root of (272² - 128²) is:

ক
144
খ
200
গ
240
ঘ
256

ব্যাখ্যা

Question: The square root of (272² - 128²) is:

Solution:
The square root of (272² - 128²) is = √{(272² - 128²)}
=√{(272 + 128)(272 - 128)}
= √(400 × 144)
= 20 × 12
= 240

১,৮৯৩.

OPH, QRI, STJ, ____, WXL.

ক
TUN
খ
UVK
গ
VWO
ঘ
UJI

ব্যাখ্যা

Question: OPH, QRI, STJ, ____, WXL.

Solution:
There are two alphabetical series here.
The first series is with the first letters only: OP, QR, ST, UV, WX.
The second series: H, I, J, K, L.

∴ Answer will be = UVK

১,৮৯৪.

A certain sum of money triples itself in 8 years at simple interest. What is the rate of interest per annum?

ক
25%
খ
20%
গ
12.5%
ঘ
15%

ব্যাখ্যা

Question: A certain sum of money triples itself in 8 years at simple interest. What is the rate of interest per annum?

Solution:
Let,
Principal = P
Interest, I = 3P - P = 2P
Time, n = 8 years
rate = r

r = I/(Pn)
= (2P)/(P × 8)
= (1/4) × 100%
= 25%

১,৮৯৫.

Tk. 8000 becomes Tk. 9600 in 2 years at a certain rate of simple interest. If the rate becomes double, what will be the total amount in 5 years on the same principal?

ক
Tk. 13200
খ
Tk. 18500
গ
Tk. 12000
ঘ
Tk. 16000

ব্যাখ্যা

Question: Tk. 8000 becomes Tk. 9600 in 2 years at a certain rate of simple interest. If the rate becomes double, what will be the total amount in 5 years on the same principal?

Solution:
Principal = Tk. 8000
Amount after 2 years = Tk. 9600
∴ Interest in 2 years = 9600 - 8000 = Tk. 1600
∴Interest per year = 1600/2 = Tk. 800

Since the interest rate doubles, the yearly interest also doubles,
∴ Interest per year = 800 × 2 = Tk. 1600
⇒ Interest for 5 years = 1600 × 5 = Tk. 8000
⇒ New total amount = 8000 + 8000 = Tk. 16000

১,৮৯৬.

The speed of a boat when travelling downstream is 42 km/hr, whereas when travelling upstream it is 38 km/hr, what is the speed of the stream?

ক
ক) 2 km/hr
খ
খ) 4 km/hr
গ
গ) 3 km/hr
ঘ
ঘ) 6 km/hr

ব্যাখ্যা

Question: The speed of a boat when travelling downstream is 42 km/hr, whereas when travelling upstream it is 38 km/hr, what is the speed of the stream?

Solution:
Here, The speed of a boat in downstream = 42 km/hr.
The speed of a boat in upstream = 38 km/hr,
∴ The speed of stream = (Speed downstream - Speed upstream) / 2
= (42 - 38)km/hr / 2
= (4/2) km/hr
= 2 km/hr

১,৮৯৭.

If a regular square pyramid has a base of size 8 cm and height 30 cm. What is its volume?

ক
ক) 256 cc
খ
খ) 350 cc
গ
গ) 425 cc
ঘ
ঘ) 640 cc

ব্যাখ্যা

Question: If a regular square pyramid has a base of size 8 cm and height 30 cm. What is its volume?

Solution:
Volume of the pyramid = (1/3) × 8² × 30 cm³
= 640 cm³ or 640 cc

১,৮৯৮.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water from the tank in:

ক
16 hours
খ
14 hours
গ
10 hours
ঘ
12 hours

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water from the tank in:

Solution:
ধরি, ছিদ্র দিয়ে ট্যাঙ্ক খালি হয় x ঘণ্টায়
১ ঘণ্টায় খালি হয় ১/x ঘন্টায়

একটি পাম্প ২ ঘন্টায় পূর্ণ হয় ১ অংশ
১ ঘণ্টায় পূর্ণ হয় ১/২ অংশ

প্রশ্নমতে,
(১/২) - (১/x) = ৩/৭
⇒ ১/x = (১/২) - (৩/৭)
= ১/১৪
x = ১৪ ঘণ্টা

১,৮৯৯.

In an election a candidate who gets 84% of the votes is elected by a majority of 476 votes. What is the total number of votes polled?

ক
ক) 672
খ
খ) 749
গ
গ) 700
ঘ
ঘ) 848

ব্যাখ্যা

মনেকরি,
মোট ভোট দেয় x জন

জয়ী প্রার্থী ভোট পায় = x এর 84%
= x এর84/100
= 84x/100
= 21x/25

অপর প্রার্থী ভোট পায় = x এর 16%
= 16x/100
= 4x/25

প্রশ্নমতে,
(21x/25) - (4x/25) = 476
(21x - 4x)/25 = 476
17x/25 = 476
x = (476 × 25)/17
x = 700

১,৯০০.

Three partners, X, Y, and Z, invest Tk. 90000 in a business. X invests Tk. 12000 more than Y, and Y invests Tk. 6000 more than Z. If the total profit is Tk. 45000, how much does X receive?

ক
Tk. 20000
খ
Tk. 18000
গ
Tk. 22000
ঘ
Tk. 24000
ঙ
Tk. 21000

ব্যাখ্যা

Question: Three partners, X, Y, and Z, invest Tk. 90000 in a business. X invests Tk. 12000 more than Y, and Y invests Tk. 6000 more than Z. If the total profit is Tk. 45000, how much does X receive?

Solution:
Let Z's investment be Tk. x.
∴ Y's investment = Tk. (x + 6000)
∴ X's investment = Tk. (x + 6000 + 12000) = Tk. (x + 18000)

Since the total investment is Tk. 90000,
∴ X + Y + Z = 90000
⇒ (x + 18000) + (x + 6000) + x = 90000
⇒ 3x + 24000 = 90000
⇒ 3x = 90000 - 24000
⇒ 3x = 66000
⇒ x = 22000

So, Z's investment = Tk. 22000
Y's investment = Tk. (22000 + 6000) = Tk. 28000
X's investment = Tk. (28000 + 12000) = Tk. 40000

Total profit = Tk. 45000
∴ X's share of profit = (X's investment/Total investment) × Total profit
= (40000/90000) × 45000
= Tk. 20000

∴ X receives Tk. 20000