Bank Math

PrepBank · পাতা ১৪৯ / ১৬১ · ১৪,৮০১–১৪,৯০০ / ১৬,১২৪

১৪,৮০১.

A watch becomes fast by 5 minutes everyday. By what percent does it become fast?

ক
(25/72)%
খ
(1/5)%
গ
(1/2)%
ঘ
(5/72)%
ঙ
(1/3)%

ব্যাখ্যা

Question: A watch becomes fast by 5 minutes everyday. By what percent does it become fast ?

Solution:
Number of minutes in a day = (24 × 60) = 1440

∴ Required percentage =(5/1440) × 100%
= (50/144)%
= (25/72)%

১৪,৮০২.

If C occupies the 1st chair, who could occupy the fourth chair?

ক
ক) A
খ
খ) B
গ
গ) D
ঘ
ঘ) Y

ব্যাখ্যা

Question: If C occupies the 1st chair, who could occupy the fourth chair?

সমাধান:
- যদি C প্রথম অবস্থানে বসে তাহলে B অবশ্যই দ্বিতীয় অবস্থানে বসবে।
- তাছাড়া শর্তানুযায়ী Y পঞ্চম, ষষ্ঠ অথবা সপ্তম অবস্থানে বসবে।
- তাহলে D চতুর্থ অবস্থানে বসতে পারে।
- তাই সঠিক উত্তর D

১৪,৮০৩.

A, B, and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

ক
12 days
খ
15 days
গ
16 days
ঘ
18 days

ব্যাখ্যা

A's 2 day's work = (1/20) × 2
= 1/10

(A + B + C)'s 1 day's work = (1/20) + (1/30) + (1/60)
= 6/60
= 1/10

(A + B + C) work in 3 days = (1/10) + (1/10)
= 1/5.

Now, 1/5 work is done in 3 days.

∴ The whole work is done in (3 × 5)
= 15 days.

১৪,৮০৪.

The population of bacteria in an experiment was only two in the first day. If each day the population increases by 3, what will be the number of bacteria in 100th day?

ক
ক) 199
খ
খ) 299
গ
গ) 302
ঘ
ঘ) 399
ঙ
ঙ) None

ব্যাখ্যা

The series is = 2 + 5 + 8 + .......
Here, a = 2
d = 3
n = 100
So, n^th number in the series is = a + (n - 2)d
= 2 + (100 - 1)3
= 2 + 99×3
= 299
The number of bacteria on 100th day will be 299

১৪,৮০৫.

A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:

ক
0.8 km/h
খ
0.4 km/h
গ
0.6 km/h
ঘ
0.2 km/h

ব্যাখ্যা

Question: A swimmer swims from a point P against the current for 6 min and then swims back along the current for next 6 min and reaches at a point Q. If the distance between P and Q is 120 m then the speed of the current (in km/h) is:

Solution:
Given that,
Swimmer swims 6 min against current and 6 min along current
Distance between P and Q = 120 m

Let,
Speed of swimmer in still water = u m/min
Speed of current = v m/min

Now,
Distance travelled upstream (against current), d₁ = (u - v) × 6
And distance travelled downstream (along current), d₂ = (u + v) × 6

Net displacement from starting point = 120 m
d₂ - d₁ = 120
⇒ 6(u + v) - 6(u - v) = 120
⇒ 6u + 6v - 6u + 6v = 120
⇒ 12v = 120
⇒ v = 120/12
⇒ v = 10 m/min
⇒ v = (10 × 60)/1000
⇒ v = 600/1000
∴ v = 0.6 km/h

So the speed of the current is 0.6 km/h.

১৪,৮০৬.

What is the probability of getting a number greater than 6 on dice?

ক
1
খ
1/3
গ
1/2
ঘ
0

ব্যাখ্যা

Question: What is the probability of getting a number greater than 6 on dice?

Solution:
Since number greater than 6 cannot appear on dice so probability of getting a number greater than 6 is zero.

১৪,৮০৭.

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

ক
ক) 5600
খ
খ) 6000
গ
গ) 6400
ঘ
ঘ) 7200

ব্যাখ্যা

Number of bricks =Volume of the wall/ Volume of 1 brick
=800 x 600 x 22.5/25 x 11.25 x 6
= 6400.

১৪,৮০৮.

For all numbers x and y, x # y = xy + x. What is the value of 7 # 6?

ক
ক) 50
খ
খ) 49
গ
গ) 48
ঘ
ঘ) 51

ব্যাখ্যা

Question: For all numbers x and y, x # y = xy + x. What is the value of 7 # 6?

Solution:
Given,
x # y = xy + x.
∴ 7 # 6 = (7 × 6) + 7= 49

১৪,৮০৯.

If simple interest on a certain sum of money is Tk. 225 and the rate of interest per annum equals the number of years, then the rate of interest is-

ক
5%
খ
10%
গ
15%
ঘ
20%

ব্যাখ্যা

Question: If simple interest on a certain sum of money is Tk. 225 and the rate of interest per annum equals the number of years, then the rate of interest is-

Solution:
Let,
The rate of interest is x%
∴ Number of years is x

The interest of 1 year of 100 taka is x
∴ The interest of x years of 100 Taka is x × x = x²

ATQ,
x² = 225
∴ x = 15

∴ The rate of interest is 15%

১৪,৮১০.

Mobin deposited Tk 8000 at 10% interest rate in a bank. What would be the compound interest after one year if the interest is calculated on half yearly basis?

ক
410 Tk
খ
820 Tk
গ
520 Tk
ঘ
1040 Tk

ব্যাখ্যা

Question: Mobin deposited Tk 8000 at 10% interest rate in a bank. What would be the compound interest after one year if the interest is calculated on half yearly basis?

Solution:
Compound Principal = P(1 + r)ⁿ
= 8000 × {1 + 10/(2 × 100)}^{2 × 1}
= 8000 × (21/20)²
= 8000 × {(21 × 21)/(20 × 20)}
= 8820

Compound interest = 8820 - 8000 = 820 Tk

১৪,৮১১.

If the ratio of the area of a sector to the area of a circle is 3:5, what is the ratio of the length of the arc of the sector to the circumference of the circle?

ক
ক) 3/5
খ
খ) 2/7
গ
গ) 1/2
ঘ
ঘ) 1/3

ব্যাখ্যা

The ratio of the length of an arc of a circle to its circumference is always the same as the ratio of a sector to its area.
(r × θ) / (2π × r) = θ / 2π

ATQ,
sector area : total area = (θ/2π)×πr² : πr² = 3 : 5
(θ/2π)×πr² / πr² = 3 / 5
θ/2π = 3 / 5
(θ/2π) × 2π = 3/5 × 2π
∴ θ = 6π / 5
Arc length = 6π/5 × r
Circumference = 2πr

∴ Arc length/Circumference = (6π/5 × r) / 2πr = 3/5

১৪,৮১২.

If 2log(x+1)−log(x²−1)=log2, then x equals

ক
ক) 1
খ
খ) 0
গ
গ) 2
ঘ
ঘ) 3

ব্যাখ্যা

By definition x ≠ 1, =1
Given equation can be written as
log(x+1)²/ x²−1=log2
=>x+1 / x−1=2
=>x=3

১৪,৮১৩.

X is west of Y and Y is North of Z. M is south of X. Which direction is M to Z?

ক
ক) West
খ
খ) South
গ
গ) North
ঘ
ঘ) East
ঙ
ঙ) Southeast

ব্যাখ্যা

X is west of Y and Y is North of Z. M is south of X. Which direction is M to Z?

Solution:

M is West of Z.

১৪,৮১৪.

The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils is =?

ক
73
খ
97
গ
93
ঘ
91

ব্যাখ্যা

Question: The maximum number of students among whom 1001 pens and 910 pencils can be distributed in such a way that each student gets the same number of pens and the same number of pencils is =?

Solution:
Required number of students
= HCF of 1001 and 910
= 91
........................................................
........................................................
HCF of 1001 and 910:

We can find the HCF of 1001 and 910 using prime factorization.
First, let's find the prime factorization of both numbers:

1001 = 7 × 11 × 13
910 = 2 × 5 × 7 × 13

Now, to find the HCF, we take the product of the common prime factors with the lowest exponent:
The common prime factors are 7 and 13.

So, the product of the common prime factors is 7 × 13 = 91

Therefore, the HCF of 1001 and 910 is 91.

১৪,৮১৫.

If 2x + 5y = 7 and xy = 5, then 5/x + 2/y = ?

ক
5/7
খ
7/5
গ
4
ঘ
1

ব্যাখ্যা

(1/xy)(2x + 5y) = 1/5 × 7
⇒ (1/xy × 2x) + (1/xy × 5y) = 7/5
⇒ 2/y + 5/x = 7/5
⇒ 5/x + 2/y = 7/5

১৪,৮১৬.

If the sum of 5, 8, 12, and 15 is equal to the sum of 3, 4, x, and x + 3, what is the value of x?

ক
14
খ
15
গ
16
ঘ
17

ব্যাখ্যা

Question: If the sum of 5, 8, 12, and 15 is equal to the sum of 3, 4, x, and x + 3, what is the value of x?

Solution:
5+8+12+15 = 40

Now,
40 = 3 + 4 + x + x + 3
⇒ 40 = 10 + 2x
⇒ 30 = 2x
⇒ 30/2 = x
∴ 15 = x

১৪,৮১৭.

A Hotpot is quoted for Tk. 1500. Monir pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

ক
6%
খ
8%
গ
10%
ঘ
12%

ব্যাখ্যা

Question: A Hotpot is quoted for Tk. 1500. Monir pays Tk. 1173 for it. If he gets a series of two discounts and the rate of the first discount is 15%, then the rate of the second discount is?

Solution:
After first discount = 1500 - 1500 × 15%
= 1500 - 1500 × 15/100
= 1500 -225
= 1275 taka

Let second discount is x%

1275 - 1275 × x/100 = 1173
⇒ 1275x/100 = 1275 - 1173 = 102
⇒ x = 102 × 100/1275
∴ x = 8

১৪,৮১৮.

What least digit should come in place of # in the 9 digit number 15549#325, for which the number is divisible by 3?

ক
1
খ
5
গ
2
ঘ
4
ঙ
Both B & C

ব্যাখ্যা

Question: What least digit should come in place of # in the 9 digit number 15549#325, for which the number is divisible by 3?

Solution:
A number if divisible by 3 if sum of digits is multiple of 3. In 15549#325,
Sum of the digits= 1 + 5 + 5 + 4 + 9 + # + 3 + 2 + 5 = 34 + # = 34

Now,
34 + 1 = 35 which is not divisible by 3.
34 + 2 = 36 which is divisible by 3.

১৪,৮১৯.

A bag and a book costs BDT 1100. If the bag costs 1000 more than the book, how much does the book cost?

ক
ক) 100
খ
খ) 150
গ
গ) 50
ঘ
ঘ) 200

ব্যাখ্যা

Let, Book costs x
and Bag costs x + 1000
ATQ,
x + 1000 + x = 1100
Or, x = 50

১৪,৮২০.

Courier charges for packages to a certain destination are Tk. 65 for the first 250 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 155?

ক
1155 gms
খ
1145gms
গ
1040 gms
ঘ
1150 gms

ব্যাখ্যা

Question: Courier charges for packages to a certain destination are Tk. 65 for the first 250 grams and Tk 10 for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is Tk. 155?

Solution:
Let the additional is 100x grams
Additional 100 grams requires Tk.10
∴ Additional 100x grams requires Tk. (10 × 100x)/100 = Tk. 10x

ATQ,
65 + 10x = 155
⇒ 10x = 90
∴ x = 9

∴ The additional weight 100 × 9 = 100 × 9 = 900 grams
∴ Total weight will be 900 + 250 = 1150 gms

১৪,৮২১.

8, 6, 9, 23, 87, … what number should come next?

ক
110
খ
247
গ
332
ঘ
429

ব্যাখ্যা

Question: 8, 6, 9, 23, 87, … what number should come next?

Solution:
(8 x 1) - 2 = 6
(6 x 2) - 3 = 9
(9 x 3) - 4 = 23
(23 x 4) - 5 = 87
(87 x 5) - 6 = 429

১৪,৮২২.

The difference between the length and breadth of a rectangle is 23 m. if its perimeter is 206 m, then its area is:

ক
ক) 2230 m²
খ
খ) 2450 m²
গ
গ) 2350 m²
ঘ
ঘ) 2520 m²

ব্যাখ্যা

Question: The difference between the length and breadth of a rectangle is 23 m. if its perimeter is 206 m, then its area is:

Solution:
According to the question,
The difference between the length and breadth of a rectangle is 23 m
⇒ l - b = 23..............(1)
Its perimeter is 206 m
⇒ 2(l + b) = 206 m
⇒ l + b = 103 m.................(2)

Adding both equation (1) and (2)
⇒ 2l = 126
⇒ l = 63 m

Putting l = 63 in Equation (2)
⇒ b = 103 - 63
⇒ b = 40 m
Area of rectangle = Length(l) × Breadth(B)
⇒ 63 × 40
⇒ 2520 m²
∴ Its area is 2520 m².

১৪,৮২৩.

A can lay a railway track between two given stations in 16 days and B can do the same job in 12 days, With the help of C, they did the job in 4 days only. Then C alone can do the job in:

ক
42/5 days
খ
48/5 days
গ
43/5 days
ঘ
45 days

ব্যাখ্যা

Question: A can lay a railway track between two given stations in 16 days and B can do the same job in 12 days, With the help of C, they did the job in 4 days only. Then C alone can do the job in:

Solution:
A একদিনে করে ১/১৬ অংশ
B একদিনে করে ১/১২ অংশ

C একদিনে করে (১/৪) - {(১/১২) + (১/১৬)}
= (১/৪) - (৭/৪৮)
= ৫/৪৮

C এর কাজটি করতে সময় লাগবে = ৪৮/৫ দিন

১৪,৮২৪.

The speed of a boat in still water is 15 km/hr. If it can travel 40 km downstream and 20 km upstream at the same time, the speed of the stream is-

ক
2 km/hr
খ
3 km/hr
গ
4 km/hr
ঘ
5 km/hr

ব্যাখ্যা

Question: The speed of a boat in still water is 15 km/hr. If it can travel 40 km downstream and 20 km upstream at the same time, the speed of the stream is-

Solution:
Let the speed of the stream be = x km/hr.
Then speed downstream = (15 + x) km/hr.
Speed upstream = (15 - x)km/hr.

ATQ,
40/(15 + x) = 20/(15 - x)
⇒ 600 - 40x = 300 + 20x
⇒ - 40x - 20x = 300 - 600
⇒ - 60x = - 300
⇒ 60x = 300
∴ x = 5 km/hr

১৪,৮২৫.

When 4 fair coins are tossed together what is the probability of getting at least 3 heads?

ক
ক) 1/4
খ
খ) 3/4
গ
গ) 5/16
ঘ
ঘ) 3/8

ব্যাখ্যা

When 4 fair coins are tossed simultaneously, the total number of outcomes is 2⁴ = 16
At least 3 heads imply that one can get either 3 heads or 4 heads.
One can get 3 heads in ⁴C₃ = 4 ways and can get 4 heads in ⁴C₄

∴ Total number of favorable outcomes = 4 + 1 = 5
∴ The required probability = 1/4.

[To get 3 heads, means that one gets only one tail. This tail can be either the 1st coin, the 2nd coin, the 3rd, or the 4th coin. Thus there are only 4 outcomes which have three heads. The probability is 4/16 = 1/4.]

১৪,৮২৬.

If y/x = 3/7and x+2y = 13 then y is -

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 7

ব্যাখ্যা

দেয়া আছে,
y/x = 3/7 .........(i)
এবং x + 2y = 13 ............(ii)
(ii) নং সমীকরণ হতে পাই
x + 2y = 13
⇒ x = 13 - 2y .........(iii)
x এর মান (i) নং এ বসাই
y/x = 3/7
⇒ 7y = 3x
⇒ 7y = 3(13 - 2y)
⇒ 7y = 39 - 6y
⇒ 13 y = 39
⇒ y = 3
Answer: 3.

১৪,৮২৭.

Time is taken by two trains running in opposite directions to cross a man standing on the platform in 28 seconds and 18 seconds respectively. It took 26 seconds for the trains to cross each other. What is the ratio of their speeds?

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

ব্যাখ্যা

Let the speed one train be x and the speed of the second train be y
Length of the first train = Speed × Time = 28x
Length of second train = Speed × Time = 18y

So, {(28x + 18y)/(x + y)} = 26
⇒ 28x + 18y = 26x + 26y
⇒ 2x = 8y

Therefore,
x : y = 4 : 1.

১৪,৮২৮.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a prime number or a multiple of 5?

ক
8/20
খ
3/5
গ
11/20
ঘ
4/5

ব্যাখ্যা

Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drwn has a number which is a prime number or a multiple of 5?

Solution:
Given. Total number = 20
Prime number between 1 to 20 = {2, 3, 5, 7, 11, 13, 17, 19}
A multiple of 5 between 1 to 20 = {5,10, 15, 20}

∴ Prime number or a multiple of 5 between 1 to 20 = {2, 3, 5, 7, 10, 11, 13, 15, 17, 19, 20} = 11 numbers

So, Probability = 11/20

১৪,৮২৯.

Kathy bought 4 times as many shares in Company X as Carl and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the number of shares bought by Kathy to the number of shares bought by Tom?

ক
3 : 4
খ
3 : 1
গ
4 : 1
ঘ
12 : 1

ব্যাখ্যা

Question: Kathy bought 4 times as many shares in Company X as Carl and Carl bought 3 times as many shares in the same company as Tom. Which of the following is the ratio of the number of shares bought by Kathy to the number of shares bought by Tom?

Solution:
Let,
Tom bought = a shares
Carl bought = 3a shares
Kathy bought = 4 × 3a = 12a shares

We're asked for the ratio of Kathy's shares to Tom's shares
Kathy : Tom = 12a : a = 12 : 1

১৪,৮৩০.

Butter : Milk : : Oil : ?

ক
ক) Cow
খ
খ) Seeds
গ
গ) Curd
ঘ
ঘ) Grains

ব্যাখ্যা

Butter is obtained from Milk and Oil is obtained from Seeds.

১৪,৮৩১.

A number is double and 9 is added. If the resultant is trebled, it becomes 75. What is that number?

ক
ক) 3.5
খ
খ) 6
গ
গ) 8
ঘ
ঘ) None of these

ব্যাখ্যা

let the number is x
according to the given question-
it is doubled = 2x
then added 9 = 2x+9
resultant is tripled. so, = 3(2x+9)
given, 75
3(2x+9) = 75
6x + 27 = 75
6x = 75 - 27
6x = 48
x = 48/6
x = 8
hence, the number is 8.

১৪,৮৩২.

A monkey climbs a 60m high pole. In first minute he climbs 6m and slips down 3m in the next minute. How much time is required by it to reach the top?

ক
ক) 35 minutes
খ
খ) 33 minutes
গ
গ) 37 minutes
ঘ
ঘ) 40 minutes

ব্যাখ্যা

শেষের মিনিটে সে slip করবে না, অর্থাৎ 54 মিটার উঠার পর 6 মিটার উঠে গেলে সে আর নিচে নামবে না।
তাই এখন দেখি এই 54 মিটার সে কত মিনিটে উঠে।
প্রতি 2 মিনিটে বানরটি উঠে = 6 - 3 = 3 মিটার।
অর্থাৎ 3 মিটার উঠে = 2 মিনিটে
∴ 54 মিটার উঠে = (2 × 54)/3
= 36 মিনিটে
∴ খুঁটি বেয়ে উঠতে সময় লাগবে = 36 + 1 = 37 মিনিট

১৪,৮৩৩.

If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80. What is the value of (z - x)?

ক
70
খ
40
গ
20
ঘ
None

ব্যাখ্যা

Question: If the average (arithmetic mean) of x and y is 60 and the average (arithmetic mean) of y and z is 80. What is the value of (z - x)?

Solution:
(x + y)/2 = 60
∴ x + y = 120 ...............(1)

(y + z)/2 = 80
∴ y + z = 160 .................(2)

From (2) - (1) we get,
y + z - x - y = 160 - 120
∴ z - x = 40

১৪,৮৩৪.

If 2^{x - 1} + 2^{x + 1} = 320, then 2^{x - 6} is equal to

ক
2
খ
1/2
গ
3
ঘ
1/3
ঙ
4

ব্যাখ্যা

Question: If 2^{x - 1} + 2^{x + 1} = 320, then 2^{x - 6} is equal to

Solution:

১৪,৮৩৫.

At what rate percent per annum of compound interest will TK 1600 amount to Tk 1852.20 in 3 years?

ক
7%
খ
5%
গ
9%
ঘ
8%
ঙ
3%

ব্যাখ্যা

1852.20 = 1600(1 + r/100)3
Or, 1852.2/1600 = (1 + r/100)3
Or, 18522/16000 = (1 + r/100)3
Or, (21/20)3 = (1 + r/100)3
Or, (1 + r/100) = 21/20
Or, r/100 = 1/20
So, r = 5

১৪,৮৩৬.

If two values are 25% and 75% of a third value, what percentage is the first value of the second value?

ক
33.33%
খ
50%
গ
66.67%
ঘ
45.67%

ব্যাখ্যা

Question: If two values are 25% and 75% of a third value, what percentage is the first value of the second value?

Solution:
Let
The third value x
∴ First value = (25x)/100 = x/4
∴ Second value = (75x)/100 = 3x/4

Now,
(First Value/Second value) × 100
= (x/4) × (4/3x) × 100
= 33.33%

১৪,৮৩৭.

On selling 13 pens at Tk. 540, there is a loss equal to the cost price of 3 pens. The cost price of a pen is-

ক
Tk. 80
খ
Tk. 72
গ
Tk. 54
ঘ
Tk. 48

ব্যাখ্যা

Question: On selling 13 pens at Tk. 540, there is a loss equal to the cost price of 3 pens. The cost price of a pen is-

Solution:
Let,
cost price of 1 pen is = Tk. x
∴ cost price of 13 pens is = Tk. 13x
∴ cost price of 3 pens is = Tk. 3x

We know,
Loss = Cost price - Selling price
3x = 13x - 540
⇒ 10x = 540
⇒ x = 540/10
∴ x = 54

∴ Cost price of 1 pen is Tk. 54

১৪,৮৩৮.

Mr. Anis marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

ক
2% profit
খ
1% loss
গ
2.33% loss
ঘ
3.50% profit

ব্যাখ্যা

Question: Mr. Anis marks his goods 10% above his cost price. If he allows his customers 10% discount on the marked price. What is his profit or loss percent?

Solution:
Let the cost price of goods = Tk. 100
The market price of goods = 110% of 100
= (110/100)×100
= Tk. 110

After the discount, the selling price of the goods
= 90% of 110
= (90/100) × 110
= Tk. 99

Loss = 100 - 99 = Tk. 1

∴ Loss % = (1/100) × 100 = 1%

১৪,৮৩৯.

(88% of 370) + (24% of 210) - ? = 118

ক
196
খ
225
গ
258
ঘ
300

ব্যাখ্যা

Question: 88% of 370 + 24% of 210 - ? = 118

Solution:
88% of 370 + 24% of 210 - x = 118
⇒ 88 × 370/100 + 24 × 210/100 - x = 118
⇒ 325.6 + 50.4 - x = 118
⇒ x = 325.6 + 50.4 - 118 = 258

১৪,৮৪০.

A number exceeds 20% of itself by 40. The number is:

ক
ক) 50
খ
খ) 60
গ
গ) 80
ঘ
ঘ) 320
ঙ
ঙ) None of the above

ব্যাখ্যা

Hints: x-20/100 x=40,
so x = 50

১৪,৮৪১.

Tk 1200 is given as a loan with a 5% annual simple interest rate for 3 years. What will the final amount be?

ক
Tk. 1380
খ
Tk. 1110
গ
Tk. 1220
ঘ
Tk. 1580

ব্যাখ্যা

Question: Tk 1200 is given as a loan with a 5% annual simple interest rate for 3 years. What will the final amount be?

Solution:
Here,
p = Tk. 1200
r% = 5%
n = 3 years

Now,
A = p[1 + (nr/100)]
= 1200[1 + (3 × 5)/100]
= 12000 × (115/100)
= 1380

Hence, the amount after 3 years is Tk. 1380

১৪,৮৪২.

A shopkeeper marks up his goods by 40% above the cost price. He then offers a discount of 15% on the marked price. What is the overall percentage profit?

ক
19%
খ
25%
গ
20%
ঘ
23%

ব্যাখ্যা

Question: A shopkeeper marks up his goods by 40% above the cost price. He then offers a discount of 15% on the marked price. What is the overall percentage profit?

Solution:
Let,
the cost price (CP) be Tk. 100

Marked Price = 40% more than cost price
= 100 + 40
= Tk. 140

Discount = 15% of 140
= (15/100) × 140
= Tk. 21

Selling Price (SP)= 140 - 21 = Tk. 119

∴ Profit = SP - CP = 119 - 100 = Tk. 19

∴ overall percentage profit = (profit/cost price) × 100%
= (19/100) × 100%
= 19%

১৪,৮৪৩.

A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected?

ক
11/32
খ
17/42
গ
15/29
ঘ
8/19

ব্যাখ্যা

Question: A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected?

Solution:
3 letters can be choosen out of 9 letters in ⁹C₃ ways.
More than one vowels ( 2 vowels + 1 consonant or 3 vowels ) can be choosen in (⁴C₂ × ⁵C₁) + ⁴C₃ ways

Hence,required probability = {(⁴C₂ × ⁵C₁) + ⁴C₃}/⁹C₃
= 17/42

১৪,৮৪৪.

What is the value of expression (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 - x)?

ক
ক) x¹⁶ - 1
খ
খ) 1 - x¹⁶
গ
গ) 1 + x¹⁶
ঘ
ঘ) 1 - x⁸

ব্যাখ্যা

Question: What is the value of expression (1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 - x)?

Solution:
Given expression
(1 + x) (1 + x²) (1 + x⁴) (1 + x⁸) (1 - x)
= (1 + x) (1 - x) (1 + x²) (1 + x⁴) (1 + x⁸)
= (1 - x²) (1 + x²) (1 + x⁴) (1 + x⁸)
= (1 - x⁴) (1 + x⁴) (1 + x⁸)
= (1 - x⁸) (1 + x⁸)
= (1 - x¹⁶)

১৪,৮৪৫.

A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of hens will be:

ক
ক) 32
খ
খ) 27
গ
গ) 34
ঘ
ঘ) 26

ব্যাখ্যা

Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140
x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 26.

১৪,৮৪৬.

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
ক) 22 hours
খ
খ) 26 hours
গ
গ) 35 hours
ঘ
ঘ) Cannot be determined

ব্যাখ্যা

Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
∴ 1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
⇒ x = 35 hours

১৪,৮৪৭.

In how many ways can 8 examination papers be arranged so that the best and the worst papers never come together?

ক
19,580
খ
23,830
গ
25,650
ঘ
30,240
ঙ
None of the above

ব্যাখ্যা

Question: In how many ways can 8 examination papers be arranged so that the best and the worst papers never come together?

Solution:
No. of ways in which 8 papers can be arranged = 8! ways.
When the best and the worst papers come together, regarding the two as one paper, we have only 7 papers.
These 7 papers can be arranged in 7! ways.
And two papers can be arranged themselves in 2! ways.

No. of arrangements when best and worst papers do not come together
= 8! - 7! × 2!
= 7!(8 - 2)
= 6 × 7!
= 30,240

১৪,৮৪৮.

What is the length of a train that takes 15 seconds to pass a pole when it runs at a speed of 54 km/h?

ক
200 m
খ
225 m
গ
250 m
ঘ
300 m

ব্যাখ্যা

Question: What is the length of a train that takes 15 seconds to pass a pole when it runs at a speed of 54 km/h?

Solution:
আমরা জানি, ট্রেন যখন কোনো খুঁটি বা ব্যক্তিকে অতিক্রম করে, তখন ট্রেনটি তার নিজের দৈর্ঘ্য অতিক্রম করে।

ট্রেনের দৈর্ঘ্য = গতিবেগ × সময়

এখানে, ট্রেনের গতিবেগ = 54 km/h
= 54 × (1000/3600) m/s
= 15 m/s

সময় = 15 সেকেন্ড

∴ ট্রেনের দৈর্ঘ্য = গতিবেগ × সময়
= 15 × 15 মিটার
= 225 মিটার

অতএব, ট্রেনটির দৈর্ঘ্য হলো 225 মিটার।

১৪,৮৪৯.

Two cans have the same height equal to 21 cm. One can is cylindrical, the distance of whose base is 10 cm. The other can has square base of side 10 cm. What is the difference in their capacities?

ক
ক) 300 cm³
খ
খ) 350 cm³
গ
গ) 400 cm³
ঘ
ঘ) 450 cm³

ব্যাখ্যা

Question: Two cans have the same height equal to 21 cm. One can is cylindrical, the distance of whose base is 10 cm. The other can has square base of side 10 cm. What is the difference in their capacities?

Solution:
Difference in capacities = Volume of cubodial can - Volume of cylindrical can
= [ (10 × 10 × 21) - ((22/7) × 5 × 5 × 21))] cm³
= (2100 - 1650) cm³
= 450 cm³

১৪,৮৫০.

ক
1/8
খ
- 1/8
গ
8/3
ঘ
- 8/3

ব্যাখ্যা

Question:

Solution:

১৪,৮৫১.

Solve: 16y² = 32y³ + 2y

ক
1/4
খ
1
গ
4
ঘ
14

ব্যাখ্যা

Question: Solve: 16y² = 32y³ + 2y

Solution:
16y² = 32y³ + 2y
⇒ 16y = 32y² + 2
⇒ 32y² - 16y + 2 = 0
⇒ 16y² - 8y + 1 = 0
⇒ (4y)² - 2.4y.1 + 1² = 0
⇒ (4y - 1)² = 0
⇒ 4y - 1 = 0
∴ y = 1/4

১৪,৮৫২.

Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 12 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is:

ক
7 : 3
খ
4 : 5
গ
4 : 1
ঘ
7 : 1
ঙ
5 : 2

ব্যাখ্যা

Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 12 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is:

Solution:
Let,
the speeds of the two trains be x m/sec and y m/sec respectively.

Then,
length of the first train = 27x metres,
and length of the second train = 12y metres.

ATQ,
(27x + 12y)/(x + y) = 24
⇒ 27x + 12y = 24x + 24y
⇒ 27x - 24x = 24y - 12y
⇒ 3x = 12y
⇒ x/y = 12/3
∴ x : y = 4 : 1

১৪,৮৫৩.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 8/3 hours to fill the tank. The leak can drain all the water of the tank in-

ক
9 hours
খ
8 hours
গ
10 hours
ঘ
6 hours

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 8/3 hours to fill the tank. The leak can drain all the water of the tank in-

Solution:
ধরি,
ফুটো দিয়ে ক ঘণ্টায় ট্যাংক খালি হবে
ফুটো দিয়ে ১ ঘণ্টায় খালি হয় ১/ক অংশ
ফুটো দিয়ে ৮/৩ ঘণ্টায় খালি হয় ৮/৩ক অংশ

পাম্প দ্বারা ১ ঘণ্টায় পূর্ণ হয় ১/২ অংশ
পাম্প দ্বারা ৮/৩ ঘণ্টায় পূর্ণ হয় ৮/৬ অংশ = ৪/৩ অংশ

∴ ৪/৩ - ৮/৩ক = ১
বা, ৮/৩ক = ৪/৩ - ১
বা, ৮/৩ক = ১/৩
বা, ৩ক/৮ = ৩
বা, ৩ক = ২৪
∴ ক = ৮

১৪,৮৫৪.

If x is a whole number greater than 1. Then x²(x² - 1) is always divisible by?

ক
10
খ
6
গ
8
ঘ
5

ব্যাখ্যা

Question: If x is a whole number greater than 1. Then x²(x² - 1) is always divisible by?

Solution:
Here, x = 2, 3, 4...
When x = 2,
then = x²(x²- 1)
= 2²(2²- 1)
= 4 (4 - 1)
= 4 × 3
= 12

When, x = 3,
then = x²(x² - 1)
= 3² (3²- 1)
= 9 × 8
= 72
............

Now, the given options are 10, 6, 8 and 5.
∴ 12 and 72 is not divisible by 10, 8 and 5.
But, 12 and 72 is divisible by 6.

So, x²(x² - 1) is always divisible by 6.

১৪,৮৫৫.

In triangle ABC, AB = AC and ∠C = 30°. Find the measure of ∠A.

ক
30°
খ
95°
গ
90°
ঘ
120°

ব্যাখ্যা

Question: In triangle ABC, AB = AC and ∠C = 30°. Find the measure of ∠A.

Solution:

AB = AC
∴ ∠B = ∠C = 30°

∴ ∠A = 180° - ∠B - ∠C
= 180° - 30° - 30°
= 180° - 60°
= 120°

১৪,৮৫৬.

What will come at the place of question mark?
3, 7, 23, 95, ?

ক
65
খ
479
গ
132
ঘ
575

ব্যাখ্যা

Question: What will come at the place of question mark?
3, 7, 23, 95, ?

Solution:
1st number = 3
2nd number = 3 × 2 + 1 = 7
3rd number = 7 × 3 + 2 = 23
4th number = 23 × 4 + 3 = 95
5th number = 95 × 5 + 4 = 479

So the next number is 479.

১৪,৮৫৭.

A train 240m long passes a pole in 24 seconds. How long will it take to pass a platform 650m long?

ক
ক) 80 sec
খ
খ) 89 sec
গ
গ) 90 sec
ঘ
ঘ) 95 sec

ব্যাখ্যা

Question: A train 240m long passes a pole in 24 seconds. How long will it take to pass a platform 650m long?

Solutiona:
সমাধান:
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (240 + 650) মিটার = 890 মিটার

ট্রেনটি 240 মিটার অতিক্রম করতে সময় নেয় = 24 সেকেন্ড
ট্রেনটি1 মিটার অতিক্রম করতে সময় নেয় = 24/240 সেকেন্ড
ট্রেনটি 890 মিটার অতিক্রম করতে সময় নেয় = (24 × 890)/240 সেকেন্ড
= 89 সেকেন্ড

১৪,৮৫৮.

A boat takes 19 hours to travel downstream from point A to point B and coming back to a point C midway between A and B. If the speed of the stream is 4 km/hr and the speed of the boat in still water is 14 km/her, what is the distance between A and B?

ক
ক) 160 km
খ
খ) 200 km
গ
গ) 180 km
ঘ
ঘ) 220 km

ব্যাখ্যা

Question: A boat takes 19 hours to travel downstream from point A to point B and coming back to a point C midway between A and B. If the speed of the stream is 4 km/hr and the speed of the boat in still water is 14 km/her, what is the distance between A and B?

Solution:
ধরি
A থেকে B এর দূরত্ব = x কি.মি.
B থেকে C এর দূরত্ব = x/2 কি.মি.

নৌকাটির স্রোতের অনুকূলে বেগ = 14 + 4 = 18 কি.মি./ঘণ্টা
নৌকাটির স্রোতের প্রতিকূলে বেগ = 14 - 4 = 10 কি.মি./ঘণ্টা

প্রশ্নমতে
(x/18) + (x/2)/10 = 19
(x/18) + (x/20) = 19
(10x + 9x)/180 = 19
19x/180 = 19
x/180 = 1
x = 180

১৪,৮৫৯.

What is the angle between the hour hand and the minute hand when the clock says 3:15?

ক
7.5 °
খ
8.5 °
গ
6.5 °
ঘ
2.5 °

ব্যাখ্যা

Question: What is the angle between the hour hand and the minute hand when the clock says 3:15?

Solution:
আমরা জানি,
মধ্যবর্তী কোণ = | (11M - 60H)/2 |°
= | {(11 × 15) - (60 × 3)} /2 |°
= | (165 - 180) /2 |°
= 7.5 °

১৪,৮৬০.

Two pipes, A and B can fill a tank in 30 and 20 minutes respectively. If both pipes are used together, then how long will it take to fill the tank?

ক
2 minutes
খ
7 minutes
গ
10 minutes
ঘ
12 minutes

ব্যাখ্যা

Question: Two pipes, A and B can fill a tank in 30 and 20 minutes respectively. If both pipes are used together, then how long will it take to fill the tank?

Solution:
Pipe A fill a tank in 30 minutes
So, it fills in one minute (1/30)

Pipe B fills a tank in 20 minutes
So, it fills in one minute (1/20)

both pipes fill in one minute = (1/30) + (1/20)
= 1/12

so, it will take 1/(1/12) or 12 minutes to fill the tank.

১৪,৮৬১.

A man buys an article for 25% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

ক
23% gain
খ
33.33% loss
গ
28.25% gain
ঘ
36% loss

ব্যাখ্যা

Question: A man buys an article for 25% more than its value and sells it for 20% less than its value. His gain or loss percentage is –

Solution:
Let the original value of the article = 100
∴ Cost Price (CP) = 100 + 25% of 100
= 100 + 25 = 125

∴ Selling Price (SP) = 100 - 20% of 100
= 100 - 20 = 80

Since SP 80 is less than CP 125, there is a Loss.

∴ Loss = CP - SP = 125 - 80 = 45 টাকা
∴ Loss percentage = (Loss/CP) × 100%
= (45/125) × 100%
= 36% loss

১৪,৮৬২.

A can do a 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) 12 hours
খ
খ) 10 hours
গ
গ) 8 hours
ঘ
ঘ) 6 hours

ব্যাখ্যা

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

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

(A + B + C)'s 1 hour work = 1/4 + 1/3 = 7/12

∴ B's 1 hour work is = {(A + B + C)'s 1 hour work} - {(A + C)'s 1 hour work}
= 7/12 - 1/2
= 1/12

so, B alone can do it in 12 hours.

১৪,৮৬৩.

If 5x - 6 = 3x - 8, then x =?

ক
ক) 1
খ
খ) 2
গ
গ) - 1
ঘ
ঘ) - 2

ব্যাখ্যা

Question: If 5x – 6 = 3x – 8, then x =?

Solution:
Given,
5x – 6 = 3x – 8
⇒ 5x – 6 + 6 = 3x – 8 + 6
⇒ 5x = 3x – 2
⇒ 5x – 3x = – 2
⇒ 2x = -2
⇒ 2x/2 = -2/2
∴ x = -1

১৪,৮৬৪.

A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?

ক
583.33 gallons
খ
1000 gallons
গ
1250 gallons
ঘ
1625 gallons

ব্যাখ্যা

Question: A small pool filled only with water will require an additional 300 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 300 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons?

Solution:
let, the capacity of pool is x gallons

.3 of initial water = 300
⇒ initial water = 300/.3
= 1000 gallons

ATQ,
0.8x =1000 + 300
⇒ x = (1300 × 10)/( 8)
= 1625 gallons

১৪,৮৬৫.

What will be the ratio of the numbers which have a difference of 56 and the first number is 2/9 of the second?

ক
ক) 14 ∶ 56
খ
খ) 15 ∶ 56
গ
গ) 2 : 9
ঘ
ঘ) 16 ∶ 81

ব্যাখ্যা

Given that,

The difference between numbers = 56

first digit is = 2/9 of second number

let second number = x

then first number = (2/9) x

the ratio of number = (2/9)x : x

∴ ratio is = 2: 9

১৪,৮৬৬.

Find the area of the rhombus having each side equal to 17 cm and one of its diagonals equal to 16 cm.

ক
180
খ
200
গ
220
ঘ
240

ব্যাখ্যা

ABCD is a rhombus in which AB = BC = CD = DA = 17 cm

Diagonal AC = 16 cm (with O being the diagonal intersection point)

Therefore, AO = 8 cm

In ∆ AOD,

AD² = AO² + OD²⇒ 17² = 8² + OD²⇒ 289 = 64 + OD²⇒ 225 = OD²⇒ OD = 15

Therefore, BD = 2 × OD
= 2 × 15
= 30 cm

Now, area of rhombus

= 1/2 × d₁ × d₂= 1/2 × 16 × 30
= 240 cm²

১৪,৮৬৭.

Which of the following is the lowest positive integer that is divisible by 8, 9, 10, 11 and 12?

ক
ক) 7920
খ
খ) 5940
গ
গ) 3960
ঘ
ঘ) 2970

ব্যাখ্যা

Question: Which of the following is the lowest positive integer that is divisible by 8, 9, 10, 11 and 12?

Solution:
ক্ষুদ্রতম সংখ্যাটি হবে 8, 9, 10, 11 এবং 12 এর ল.সা.গু
8 = 2 × 2 × 2
9 = 3 × 3
10 = 2 × 5
11 = 1 × 11
12 = 2 × 2 × 3

8, 9, 10, 11 এবং 12 এর ল.সা.গু = 2 × 2 × 2 × 3 × 3 × 5 × 11 = 3960

১৪,৮৬৮.

If 3^{(n + 4)} - 3^{(n + 2)} = 8. What is the value of n?

ক
ক) -1
খ
খ) 1
গ
গ) 2
ঘ
ঘ) -2

ব্যাখ্যা

3^{(n + 4)} - 3^{(n + 2)} = 8
⇒ 3ⁿ.3⁴ - 3ⁿ.3² = 8
⇒ 3ⁿ.3².3² - 3ⁿ.3² = 8
⇒ 3ⁿ.3²(3² - 1) = 8
⇒ 3ⁿ.9.8 = 8
⇒ 3ⁿ = 1/9
⇒ 3ⁿ = 1/3² = 3^{- 2}
∴ n = - 2

১৪,৮৬৯.

If the numbers from 1 to 24, Which are divisible by 2 are arranged in descending order, which will be at the 7^thplace from the bottom?

ক
ক) 12
খ
খ) 14
গ
গ) 16
ঘ
ঘ) 18

ব্যাখ্যা

The descending order of the number from 1 to 24 which are divisible by 2 is:
24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2
Now count the 7th place number from the right.

The number will be at the 8th place from the bottom is 14.

১৪,৮৭০.

A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk. 4,000 more than B and B Tk. 5,000 more than C. Out of a total profit of Tk. 35,000 A receives

ক
Tk. 14700
খ
Tk. 1900
গ
Tk. 13600
ঘ
Tk. 8400

ব্যাখ্যা

Let C subscribes Tk. y.
Therefore, B subscribes Tk. (y + 5000)
and A subscribes Tk. (y + 5000 + 4000) or Tk. (y + 9000)
y + y + 5000 + y + 9000 = 50,000
3y + 14,000 = 50,000
3y = 36,000
y = 12,000
The ratio of investment of A, B and C = (12,000 + 9,000) : (12,000 + 5000) : 12,000 = 21,000 : 17,000 : 12,000 = 21: 17 : 12
Therefore, A receives 21 × 35,000/(21 + 17 + 12) = Tk. 14,700

১৪,৮৭১.

In a proportion the product of 1st and 4th terms is 40 and that of 2nd and 3rd terms is 2.5x. Then the value of x is.

ক
ক) 16
খ
খ) 26
গ
গ) 75
ঘ
ঘ) 90

ব্যাখ্যা

Product of 1st and 4th terms (extremes) = product of 2nd and 3rd terms (means)
⇒ 2.5x = 40
⇒ x = 40/2.5 = 16

১৪,৮৭২.

A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

ক
83 sec
খ
89 sec
গ
92 sec
ঘ
98 sec

ব্যাখ্যা

Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?

Solution:
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (240 + 650) মিটার = 890 মিটার

ট্রেনটি 240 মিটার অতিক্রম করতে সময় নেয় = 24 সেকেন্ড
ট্রেনটি1 মিটার অতিক্রম করতে সময় নেয় = 24/240 সেকেন্ড
ট্রেনটি 890 মিটার অতিক্রম করতে সময় নেয় = (24 × 890)/240 সেকেন্ড
= 89 সেকেন্ড

১৪,৮৭৩.

The difference between a two-digit number and the number obtained by reversing its digits is 54. If the ratio of the tens digit to the units digit of the number is 3 : 1, what is the difference between the sum and the difference of its digits?

ক
2
খ
3
গ
6
ঘ
8

ব্যাখ্যা

Question: he difference between a two-digit number and the number obtained by reversing its digits is 54. If the ratio of the tens digit to the units digit of the number is 3 : 1, what is the difference between the sum and the difference of its digits?

Solution:
Let the digits of the number be:

Tens digit = x
Units digit = y
So, the number = 10x + y
The reversed number = 10y + x

Given condition: The difference between the number and its reverse number is 54:
(10x + y) - (10y + x) = 54
9x - 9y = 54
⇒ x - y = 6 ............... (1)

Given ratio of digits: Tens : Units = 3 : 1
x/y = 3/1
⇒ x = 3y.................(2)

Solve the two equations:

Substitute x = 3y into x - y = 6:
3y - y = 6
⇒ 2y = 6
⇒ y = 3
Then x = 3y = 9

Digits found: Tens = 9, Units = 3
Sum and difference of digits:

Sum = x + y = 9 + 3 = 12
Difference = x - y = 9 - 3 = 6

Difference between sum and difference of digits = 12 - 6 = 6

১৪,৮৭৪.

If one-half of one-sixth of three-fourths of a number is 9, what is one-third of the number?

ক
24
খ
32
গ
60
ঘ
48

ব্যাখ্যা

Question: If one-half of one-sixth of three-fourths of a number is 9, what is one-third of the number?

Solution:
let the number is P

ATQ,
⇒ P × (1/2) × (1/6) × (3/4) = 9
⇒ 3P/48 = 9
⇒ P = (9 × 16)
∴ P = 144

∴ one-third of the number is = 144/3 = 48

১৪,৮৭৫.

A rower travels at 10 km/hr downstream and 6 km/hr upstream. What are the rower’s speed in still water and the speed of the current?

ক
5 km/hr and 3 km/hr
খ
4 km/hr and 2 km/hr
গ
6 km/hr and 4 km/hr
ঘ
8 km/hr and 2 km/hr
ঙ
None of these

ব্যাখ্যা

Question: A rower travels at 10 km/hr downstream and 6 km/hr upstream. What are the rower’s speed in still water and the speed of the current?

Solution:
Given that,
Downstream speed = 10 km/h
Upstream speed = 6 km/h

We know that,
Still water speed = (Downstream + Upstream)/2
= (10 + 6)/2 = 8 km/h
And,
Current speed = (Downstream − Upstream)/2
= (10 - 6)/2
= 2 km/h

∴ Speed of still water is 8 km/hr and Speed of the current is 2 km/hr

১৪,৮৭৬.

A man wanted to sell an article with 20% profit: but he actually sold at 20% loss for Tk. 480, at what price he wanted to sell it to earn the profit = ?

ক
ক) Tk 720
খ
খ) Tk. 840
গ
গ) Tk. 600
ঘ
ঘ) Tk. 750

ব্যাখ্যা

According to the question,
Loss 20%
Selling price
=100%−20=80%
80%=480
1=480/80
∴(Profit 20%) = 480/ 80 ×120
=Tk. 720

১৪,৮৭৭.

A swimming pool is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?

ক
30 hours
খ
18 hours
গ
15 hours
ঘ
10 hours

ব্যাখ্যা

Question: A swimming pool is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the pool in the same time during which the pool is filled by the third pipe alone. The second pipe fills the pool 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is?

Solution:
Suppose, the first pipe alone takes x hours to fill the tank.
Then, the second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.

ATQ,
1/x + 1/(x - 5) = 1/(x - 9)
⇒ (x - 5 + x)/x(x - 5) = 1/(x - 9)
⇒ (2x - 5)/(x² - 5x) = 1/(x - 9)
⇒ 2x² - 18x - 5x + 45 = x² - 5x
⇒ 2x² - 23x + 45 - x² + 5x = 0
⇒ x² - 18x + 45 = 0
⇒ x² - 15x - 3x + 45 = 0
⇒ x(x - 15) - 3(x - 15) = 0
⇒ (x - 15)(x - 3) = 0
∴ x = 15 [neglecting x = 3]

So, first pipe alone takes 15 hours to fill the tank.

১৪,৮৭৮.

A mixture of 20kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?

ক
ক) 2 kg
খ
খ) 4 kg
গ
গ) 3 kg
ঘ
ঘ) 1 kg

ব্যাখ্যা

20 কেজি মিশ্রনে পানি আছে = 20 এর 10%
= 20 এর 10/100
= 2 কেজি

স্পিরিট আছে = 20 - 2 = 18 কেজি

ধরি, মিশ্রনে পানি মেশাতে হবে x কেজি

প্রশ্নমতে,
⇒ 18/(2 + x) = 75/25
⇒18/(2 + x) = 3/1
⇒3(2 + x) = 18
⇒6 + 3x =18
⇒3x = 18 - 6
⇒3x =12
⇒ x = 4

১৪,৮৭৯.

The fourth proportional to 5, 8, and 15 is -

ক
20
খ
22
গ
24
ঘ
25

ব্যাখ্যা

Question: The fourth proportional to 5, 8, and 15 is-

Solution:
Let, The fourth proportional is x.

So, 5/8 = 15/x
⇒ 5x = 120
∴ x = 24

১৪,৮৮০.

A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is:

ক
50 km/h
খ
70 km/h
গ
80 km/h
ঘ
90 km/h

ব্যাখ্যা

Question: A train 250 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 20 seconds. The speed of the train is:

Solution:
Let the speed of the train is x km/h

As the man was running in the same direction,
the resultant speed is = train - man
= x - 5 km/h
= (x - 5)/3.6 m/s

ATQ,
time = distance/speed
20 = 250/((x-5)/3.6)
20x - 100 = 900
x = 50 km/h

১৪,৮৮১.

If an investment of m dollars is made today and the value of the investment doubles every 6 years, what will be the value of the investment, in dollars 24 years from today?

ক
m⁴
খ
2m²
গ
4m
ঘ
16m
ঙ
8m⁴

ব্যাখ্যা

Question: If an investment of m dollars is made today and the value of the investment doubles every 6 years, what will be the value of the investment, in dollars 24 years from today?

Solution:
Present investment = m

The investment doubles every 6 years.
∴ After 6 years, it will be 2m
∴ After (6 + 6) = 12 years, it will be (2²)m = 4m
∴ After (6 + 6 + 6 + 6) = 24 years, it will be (2⁴)m = 16m

১৪,৮৮২.

Out of two numbers, 4 times the smaller one is less than 3 times the larger one by 5. If the sum of the numbers is larger than 6 times their differences by 6, find the two numbers.

ক
ক) 55 and 58
খ
খ) 23 and 28
গ
গ) 59 and 43
ঘ
ঘ) 65 and 67

ব্যাখ্যা

Let the smaller number be x and greater number be y
ATQ,
4x = 3y – 5
Or, 3y – 4x = 5 ......(1)
Again,
x + y = 6(y – x) + 6
Or, x + y = 6y – 6x + 6
Or, 7x – 5y = 6 ..... (2)

Multiply equation (1) by 5 and equation (2) by 3 and add them,
15y – 20x = 25
21x – 15y = 18
_____________
∴ x = 43

From equation (1),
3y – 4 × 43 = 5
Or, 3y – 172 = 5
Or, 3y = 177
Or, y = 177/3
∴ y = 59

১৪,৮৮৩.

A train left Dhaka for Chittagong at 59 km per hour and at the same time another train left Chittagong for Dhaka at 43 km per hour on the same route. How far apart were the two trains one hour before they met?

ক
ক) 105 km.
খ
খ) 102 km.
গ
গ) 110 km
ঘ
ঘ) 108 km.

ব্যাখ্যা

ঢাকা থেকে চট্টগ্রামগামী ট্রেনটি 1 ঘন্টায় 59 km. যায়।
চট্টগ্রাম থেকে ঢাকাগামী ট্রেনটি 1 ঘন্টায় 43 km. যায়।
∴ 1 ঘন্টায় দুটি বিপরীতমুখী ট্রেন মোট যায় (59 + 43)
= 102 km. দূরত্ব অতিক্রম করে।
অর্থাৎ মুখোমুখি হওয়ার 1 ঘন্টা আগে তাদের দুরত্ব = 102 km.

১৪,৮৮৪.

When heated an iron bar expands 0.2%. If the increased length is 1 cm. What is the original length of the bar?

ক
ক) 5 cm
খ
খ) 0.98 cm
গ
গ) 500 cm
ঘ
ঘ) 50 cm

ব্যাখ্যা

Question: When heated an iron bar expands 0.2%. If the increased length is 1 cm. What is the original length of the bar?

Solution:
দেওয়া আছে,
প্রসারিত দৈর্ঘ্য = 1 সে.মি.

প্রশ্নমতে,
0.2% প্রসারণ = 1 সে.মি.
∴ 100% প্রসারণ = (100 × 10)/2 সে.মি.
= 500 সে.মি.

১৪,৮৮৫.

Find the volume of a cone with radius 9 cm and height 10 cm.

ক
392π cubic cm
খ
270π cubic cm
গ
553.33 cubic cm
ঘ
None of these

ব্যাখ্যা

Question: Find the volume of a cone with radius 9 cm and height 10 cm.

Solution:
Volume = (1/3) × π × r² × h
Volume = (1/3) × π × 9² × 10
= 270π cubic cm

১৪,৮৮৬.

If what is the value of x?

ক
ক) - 1
খ
খ) 0
গ
গ) 5
ঘ
ঘ) - 5

ব্যাখ্যা

Question: If what is the value of x?

Solution:
3/(x - 1) = 2/(x + 1)
⇒ 3x + 3 = 2x - 2
⇒ 3x - 2x = - 2 - 3
∴ x = - 5

১৪,৮৮৭.

A tank is 1/3 parts full with water. If 9 liters of water is added, the tank becomes 5/6 parts full. What is the capacity of the tank?

ক
12 liters
খ
16 liters
গ
24 liters
ঘ
18 liters

ব্যাখ্যা

Question: A tank is 1/3 parts full with water. If 9 liters of water is added, the tank becomes 5/6 parts full. What is the capacity of the tank?

Solution:
Let the capacity of the tank = x liters

According to the question,
(x/3) + 9 = 5x/6
⇒ (5x/6) - (x/3) = 9
⇒ (5x - 2x)/6 = 9
⇒ 3x = 54
⇒ x = 54/3
⇒ x = 18

Therefore, the capacity of the tank = 18 liters.

১৪,৮৮৮.

Find the compound interest on TK. 30000 at 7% interest compounded annually for two years.

ক
4237
খ
4465
গ
4550
ঘ
4347

ব্যাখ্যা

Question: Find the compound interest on TK. 30000 at 7% interest compounded annually for two years.

Solution:
Principal, P = Rs 30000
Rate, R = 7%
Time, T = 2 year

By formula:
A = P(1 + R/100)^T
= 30000 (1 + 7/100)²
= 30000 (107/100)²
= 30000 × (11449/10000)
= 34347

Compound Interest = A - P = 34347 - 30000
= 4347

১৪,৮৮৯.

ক
10
খ
18
গ
12
ঘ
15

ব্যাখ্যা

Question:

Solution:
কোনো বর্গ ম্যাট্রিক্সের ট্রেস (Trace) হলো তার প্রধান কর্ণ বরাবর উপাদানগুলির যোগফল।
এখানে ম্যাট্রিক্স A এর প্রধান কর্ণ বরাবর উপাদানগুলি হলো 2, 5, এবং 8.
∴ Trace(A) = 2 + 5 + 8 = 15

১৪,৮৯০.

A lent Tk. 5,000 to B for 2 years and Tk. 3,000 to C for 4 years on simple interest at the same rate of interest and received Tk. 2,200 in all from both of them as interest. The rate of interest per annum is:

ক
ক) 5%
খ
খ) 7%
গ
গ) 15/2%
ঘ
ঘ) 10%

ব্যাখ্যা

Let the rate be R%p.a.
Then,
5000 × R × 2/100 + 3000 × R × 4/100 = 2200.
⇒ 100R + 120R = 2200
⇒ R = 2200/220 =10
∴Rate = 10%

১৪,৮৯১.

A jar contains white, red and green marbles in the ratios 2 : 3 : 5. Six more green marbles are added to the jars, and then the ratio becomes 2 : 3 : 7. How many white marbles are three in the jar?

ক
ক) 5
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 10

ব্যাখ্যা

Question: A jar contains white, red and green marbles in the ratios 2 : 3 : 5. Six more green marbles are added to the jars, and then the ratio becomes 2 : 3 : 7. How many white marbles are three in the jar?

Solution:
let the amount of white, red and green marbels is 2x, 3x, 5x
after adding 6 more marbels it become 2x, 3x, 7x

so,
(2x + 3x + 7x) - (2x + 3x + 5x) = 6
12x - 10x = 6
2x = 6
x = 3

so, white marbels = 2 × 3 = 6

১৪,৮৯২.

If the annual rate of simple interest increases from 6% to 8%, a man's yearly income increased by Tk.650. What is his principal?

ক
ক) Tk. 73000
খ
খ) Tk. 71500
গ
গ) Tk. 32500
ঘ
ঘ) Tk. 36500

ব্যাখ্যা

Question: If the annual rate of simple interest increases from 6% to 8%, a man's yearly income increased by Tk.650. What is his principal?

Solution:
Let the principal is Tk. x

Then,
(x × 8 × 1/100) - (x × 6 × 1/100) = 650
2x/25 - 3x/50 = 650
x/50 = 650
x = 650 × 50
x = 32500

His principal is Tk.32500

১৪,৮৯৩.

A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

ক
400 kg
খ
560 kg
গ
600 kg
ঘ
640 kg

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

Solution:
Let
The cost price of sugar be tk. x per kg
∴ Total cost price = Tk. 1000x
The sugar sold at 8% gain by y kg
The sugar sold at 18% gain by (1000 - y) kg

Now
{(108xy)/100} + [{118x(1000 - y)}/100] = (114/100) × (1000x)
⇒ (108y)/100 + [{118(1000 - y)}/100] = (114 × 1000)/100
⇒ 108y + {118(1000 - y)} = 114 × 1000
⇒ 108y + 118000 - 118y = 114000
⇒ 118000 - 114000 = 10y
⇒ 4000 = 10y
∴ y = 400

∴ The sugar sold at 18% gain by (1000 - 400) kg
= 600 kg

১৪,৮৯৪.

Half the people on a bus get off at each stop after the first and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

ক
ক) 128
খ
খ) 64
গ
গ) 16
ঘ
ঘ) 32

ব্যাখ্যা

Question: Half the people on a bus get off at each stop after the first and no one gets on after the first stop. If only one person gets off at stop number 7, how many people got on at the first stop?

Solution:
7th stop only one was left and in each preceding stop twice the nos... there were so 6 stops before 7th.
so 2⁶ = 64

১৪,৮৯৫.

Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on a principal of Tk 4000.

ক
5 Tk
খ
10 Tk
গ
15 Tk
ঘ
41 Tk

ব্যাখ্যা

Question: Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on a principal of Tk 4000.

Solution:
We know, Simple Interest, I = Pnr
and Compound Principal, C = p(1 + r)ⁿ

∴ Simple Interest = 4000 × 2 × (5/100) = 400 Tk

Compound Principal = 4000 × {1 + (5/100)}²
= 4000 × (105/100)²
= 4000 × (105/100) × (105/100)
= 4410

So, Compound interest = 4410 - 4000 = 410 Tk
∴ Difference = 410 - 400 = 10 Tk

১৪,৮৯৬.

Find the least number of five digits which when divided by 40, 60 and 75, leave remainders 31, 51 and 66 respectively.

ক
ক) 10,196
খ
খ) 10,199
গ
গ) 10,197
ঘ
ঘ) 10,191

ব্যাখ্যা

Difference, 40 - 31 = 9
60 - 51 = 9
75 - 66 = 9
Difference between numbers and remainder is same in each case.
Then,
The answer = {(LCM of 40, 60, 75) - 9}

40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
LCM = 2 × 2 × 2 × 5 × 5 × 3 = 600

But, the least number of 5 digits = 10000
10000/600, we get remainder as 400
Then, the answer = 10000 + (600 - 400) - 9 = 10,191

১৪,৮৯৭.

The circumcentre of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠AOC is-

ক
20°
খ
30°
গ
40°
ঘ
50°

ব্যাখ্যা

Question: The circumcentre of a triangle ABC is O. If ∠BAC = 85° and ∠BCA = 75°, then the value of ∠AOC is-

Solution:

∠BAC = 85°
∠BCA = 75°
∠ABC = 180° - 85° - 75°
= 20°

∠AOC = 2 ∠ABC
= 2 × 20°
= 40°

১৪,৮৯৮.

Today is Monday. After 45 days, it will be:

ক
Monday
খ
Wednesday
গ
Thursday
ঘ
Saturday

ব্যাখ্যা

Question: Today is Monday. After 45 days, it will be:

Solution:
Each day of the week is repeated after 7 days.

So, after 42 days, it will be Monday.

After 43 days, it will be Tuesday.
After 44 days, it will be Wednesday.
∴ After 45 days, it will be Thursday.

১৪,৮৯৯.

The scale of a local map is 1cm to 5km. An area is represented on the map by a rectangle of dimensions 5cm × 9cm. The actual area in km² is -

ক
1024
খ
1038
গ
1048
ঘ
1125

ব্যাখ্যা

Question: The scale of a local map is 1cm to 5km. An area is represented on the map by a rectangle of dimensions 5cm × 9cm. The actual area in km² is -

Solution:
The actual area = (5 × 5) × (9 × 5) km² [1 cm = 5 km]
= 25 × 45 km²
= 1125 km²

১৪,৯০০.

What would be the measure of the perimeter of a square whose area is equal to 324 square cm?

ক
36 cm
খ
72 cm
গ
64 cm
ঘ
48 cm

ব্যাখ্যা

Question: What would be the measure of the perimeter of a square whose area is equal to 324 square cm?

Solution:
দেওয়া আছে
বর্গক্ষেত্রের ক্ষেত্রফল = 324 square cm
বর্গের এক বাহুর দৈর্ঘ্য = a cm

প্রশ্নমতে
a² = 324
⇒ a² = (18)²
∴ a = 18

বর্গক্ষেত্রের পরিসীমা = 4a
= 4 × 18
= 72 cm