Bank Math

PrepBank · পাতা ৪৮ / ১৬১ · ৪,৭০১–৪,৮০০ / ১৬,১২৪

৪,৭০১.

If m and n are whole numbers such that, mⁿ = 121, then the value of (m - 1)^{n + 1} is-

ক
1
খ
10
গ
121
ঘ
1000
ঙ
None of these

ব্যাখ্যা

Question: If m and n are whole numbers such that, mⁿ = 121, then the value of (m - 1)^{n + 1} is-

Solution:
If mⁿ = 121
∴ mⁿ = 11²

∴ n = 2; m = 11;
then
(m -1) ^{n + 1} = (11 - 1)^{2 +1} = 10³ = 1000

৪,৭০২.

What is the discount rate percentage on a gift whose selling price is Tk. 420 after a reduction of Tk. 60 on its marked price?

ক
ক) 7.2%
খ
খ) 10%
গ
গ) 8.9%
ঘ
ঘ) 12.5%

ব্যাখ্যা

Question: What is the discount rate percentage on a gift whose selling price is Tk. 420 after a reduction of Tk. 60 on its marked price?

Solution:

SP of the gift = Tk. 420
Discount = Tk. 60

MP of the gift = Tk. 420 + Tk. 60 = Tk. 480
Discount percentage = (60/480) × 100 = 12.5%

৪,৭০৩.

In how many ways can 3 guests from a group of 6 guests be seated around a circular table?

ক
20
খ
25
গ
30
ঘ
35
ঙ
40

ব্যাখ্যা

Question: In how many ways can 3 guests from a group of 6 guests be seated around a circular table?

Solution:
Ways of selecting 3 guests from 6 guests:
⁶C₃ = 6!/(3! × 3!)
= (6 × 5 × 4)/(3 × 2 × 1)
= 120/6
= 20

Ways of arranging 3 persons around a circular table = (3 - 1)!
= 2!
= 2

∴ Total ways = 20 × 2 = 40

৪,৭০৪.

If the ratio of syrup and water in a mixture is 7 : 3, then the percentage of water in mixture is-

ক
15%
খ
20%
গ
30%
ঘ
25%

ব্যাখ্যা

Question: If the ratio of syrup and water in a mixture is 7 : 3, then the percentage of water in mixture is-

Solution:
The ratio of syrup and water in a mixture is 7 : 3
Total = 10
∴ percentage of water = (3 × 100)/10 %
= 30%

৪,৭০৫.

A can complete a certain job in 12 days. B is 60% more efficient than A. In how many days can B complete the same job?

ক
ক) 6
খ
খ) 6.25
গ
গ) 7
ঘ
ঘ) 7.5
ঙ
ঙ) 4.8

ব্যাখ্যা

B is 60% more efficient than A, which means that the rate of B is 1.6 times as greater as that of A.
So, if A can complete the job in 12 days,
then B completes the same job in 12/1.6 = 12/(8/5)
= 15/2
= 7.5 days.

Alternative method:
Ratio of times taken by
A and B = 160 : 100 = 8 : 5
Suppose B alone takes x days to do the job.
Then, 8 : 5 :: 12 : x
or, 8x = 5 × 12
or, x = 7.5 days

৪,৭০৬.

The population of a city 3 years ago was 1,28,000. If it decreased by 5% every year, then the present population of the city is -

ক
89750
খ
119035
গ
99744
ঘ
109744

ব্যাখ্যা

Population of the city 3 years ago = P = 128000 and n = 3
And,
The decreasing percentage = R = 5%
The present population = P × (1 - R/100)ⁿ [Population after n years = P × (1 - R/100)ⁿ]
128000 x (1 - 5/100)³
= 128000 × (19/20) × (19/20) × (19/20)
= 16 × 6859 = 109744.
Hence the answer is 109744.

৪,৭০৭.

If m, n, o, p, and q are integers, then m(n + o)(p - q) must be even when which of the following is even-

ক
p
খ
n + p
গ
m
ঘ
m + n

ব্যাখ্যা

Question: If m, n, o, p and q are integers, then m(n + o)(p - q) must be even when which of the following is even-

Solution:
m জোড় সংখ্যা হলে গুণফল জোড় সংখ্যা হবে। কারণ জোড় সংখ্যার সাথে জোড় বা বিজোড় গুণ করলে সবসময় জোড় সংখ্যাই পাওয়া যায়।

৪,৭০৮.

How many ways the letters of the word 'BANKS' can be arranged?

ক
24
খ
120
গ
90
ঘ
30

ব্যাখ্যা

Question: How many ways the letters of the word 'BANKS' can be arranged?

Solution:
the given words contain 5 diffrerent letters.

∴ they can be arranged in = 5! ways
= 120 ways

৪,৭০৯.

Two whole numbers whose sum is 64, cannot be in the ratio:

ক
ক) 5 : 3
খ
খ) 7 : 1
গ
গ) 3 : 4
ঘ
ঘ) 9 : 7

ব্যাখ্যা

Question: Two whole numbers whose sum is 64, cannot be in the ratio:

Solution:
5 : 3 হলে, সংখ্যা দুটি 5x ও 3x
5x + 3x = 64
⇒ 8x = 64
∴ x = 8
সংখ্যা দুটি 40, 24

7 : 1 হলে, সংখ্যা দুটি 7x ও x
7x + x = 64
⇒ 8x = 64
∴ x = 8
সংখ্যা দুটি 56, 8

3 : 4 হলে, সংখ্যা দুটি 3x ও 4x
3x + 4x = 64
⇒ 7x = 64
∴ x = 64/7
যেহেতু ৬৪, ৭ দ্বারা নিঃশেষে বিভাজ্য নয়, এক্ষেত্রে সংখ্যা দুটি পূর্ণসংখ্যা হবে না।

9 : 7 হলে, সংখ্যা দুটি 9x ও 7x
9x + 7x = 64
⇒ 16x = 64
∴ x = 4
সংখ্যা দুটি 36, 28

৪,৭১০.

If in a certain language, PLAYER Is coded as QNDCJX, then how SINGER will be coded in the same language?

ক
TKQKJX
খ
TKJKQX
গ
TXQKXJ
ঘ
TKQXJK

ব্যাখ্যা

Question: If in a certain language, PLAYER Is coded as QNDCJX, then how SINGER will be coded in the same language?

Solution:

PLAYER
P + 1 = Q
L + 2 = N
A + 3 = D
Y + 4 = C
E + 5 = J
R + 6 = X
PLAYER = QNDCJX

SINGER
S + 1 = T
I + 2 = K
N + 3 = Q
G + 4 = K
E + 5 = J
R + 6 = X
SINGER = TKQKJX

৪,৭১১.

If 5x + 1/3x = 4, then what is the value of 9x² + 1/25x² = ?

ক
ক) 118/22
খ
খ) 114/25
গ
গ) 117/27
ঘ
ঘ) 117/24

ব্যাখ্যা

প্রশ্ন : If 5x + 1/3x = 4, then what is the value of 9x² + 1/25x² = ?

সমাধান :

5x + 1/3x = 4

Multiply by 3/5
⇒ 3x + 1/5x = 12/5

Squaring on both sides
⇒ (3x + 1/5x)² = (12/5)²
⇒ 9x² + 1/25x² + 2 × 3x × (1/5x) = 144/25
⇒ 9x² + 1/25x² = 144/25 – 6/5
⇒ 9x² + 1/25x² = (144 – 30)/25

∴ The value is 114/25

৪,৭১২.

A truck can carry 24 motorcycles or 36 bicycles at a time. If there are 10 motorcycles on the truck, how many bicycles can be loaded along with them?

ক
20
খ
11
গ
21
ঘ
15
ঙ
None

ব্যাখ্যা

Question: A truck can carry 24 motorcycles or 36 bicycles at a time. If there are 10 motorcycles on the truck, how many bicycles can be loaded along with them?

Solution:
Here,
24 motorcycles = 36 bicycles
∴ 1 motorcycle = 36/24 bicycles = 3/2 bicycles

∴ 10 motorcycles = 10 × 3/2 = 15 bicycles

Total bicycle capacity = 36
∴ Remaining bicycles that can be loaded = 36 - 15 = 21 bicycles

∴ Required number of bicycles = 21

৪,৭১৩.

cos²11° + cos²79° = ?

ক
0
খ
1
গ
- 2
ঘ
2

ব্যাখ্যা

Question: cos²11° + cos²79° = ?

Solution:
Given that,
cos²11° + cos²79°
= cos²11° + cos²(90° - 11°)
= cos²11° + sin²11°
= 1

৪,৭১৪.

If 9^√x + 9^√x= 162 then, what is the value of x?

ক
5
খ
6
গ
9
ঘ
√5
ঙ
4

ব্যাখ্যা

Question: If 9^√x + 9^√x= 162 then, what is the value of x?

Solution:
Given that,
9^√x + 9^√x = 162
⇒ 9^√x(1 + 1) = 162
⇒ 9^√x × 2 = 162
⇒ 9^√x = 162/2
⇒ 9^√x = 81
⇒ 9^√x = 9²
⇒ √x = 2
⇒ (√x)² = 2²
∴ x = 4

৪,৭১৫.

The present age of Mr. Salman is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Salman?

ক
54 years
খ
60 years
গ
48 years
ঘ
63 years

ব্যাখ্যা

Question: The present age of Mr. Salman is three times the age of his son. Six years hence , the ratio of their ages will be 5 : 2. What is the present age of Mr. Salman?

Solution:
Let the son's age be x years ,
Then Mr. Salman's age = 3x years
Then,
∴ (3x + 6)/(x + 6) = 5/2
⇒2(3x + 6) = 5(x + 6)
⇒ 6x + 12 = 5x + 30
⇒ 6x - 5x = 30 - 12
⇒ x = 18

∴ Present age of Mr. Salman = 3x years
= (3 × 18) years
= 54 years

৪,৭১৬.

Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

ক
44
খ
28
গ
32
ঘ
36

ব্যাখ্যা

Question: Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm are to be cut into parts of equal length. Each part must be as long as possible. What is the maximum number of pieces that can be cut?

Solution:
Four metal rods of lengths 78 cm, 104 cm, 117 cm and 169 cm
78 = 2 × 3 × 13
104 = 2 × 2 × 2 × 13
117 = 3 × 3 × 13
169 = 13 × 13

HCF of 78, 104, 117 and 169 = 13

Maximum length of each part = HCF of 78 cm, 104 cm, 117 cm, 169 cm = 13 cm

The maximum number of pieces,
78/13 = 6
104/13 = 8
117/13 = 9
169/13 = 13

The maximum number of pieces = 6 + 8 + 9 + 13 = 36

∴ The maximum number of pieces is 36.

৪,৭১৭.

Kabir 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 Kabir to the number of shares bought by Tom?

ক
12 : 5
খ
12 : 1
গ
11 : 5
ঘ
12 : 7

ব্যাখ্যা

Question: Kabir 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 Kabir to the number of shares bought by Tom?

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

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

৪,৭১৮.

Hasan can dig 18 holes in 12 minutes. Faruk can dig the same number of holes in only 6 minutes. Hasan digs the first 9 holes, then Faruk digs for 2 minutes, and finally Hasan finishes the remaining holes. How long will it take them to dig 27 holes in total?

ক
10 minutes
খ
16 minutes
গ
18 minutes
ঘ
21 minutes

ব্যাখ্যা

Question: Hasan can dig 18 holes in 12 minutes. Faruk can dig the same number of holes in only 6 minutes. Hasan digs the first 9 holes, then Faruk digs for 2 minutes, and finally Hasan finishes the remaining holes. How long will it take them to dig 27 holes in total?

Solution:
Faruk can dig 18 holes in 6 minutes.
∴ In 2 minutes, he can dig = (18 × 2)/6 holes
= 6 holes

Hasan first digs 9 holes.

∴ Total completed = 9 (Hasan) + 6 (Faruk) = 15 holes
Remaining = 27 - 15 = 12 holes

Hasan can dig 18 holes in 12 minutes.
∴ To dig 12 holes, Hasan will take = (12 × 12) / 18 = 8 minutes

Time Hasan spent digging first 9 holes = (12 × 9)/18 = 6 minutes

∴ Total time = 6 (Hasan) + 2 (Faruk) + 8 (Hasan) = 16 minutes

৪,৭১৯.

How much is 80% of 40 greater than 4/5 of 25?

ক
ক) 4
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 12

ব্যাখ্যা

Question: How much is 80% of 40 greater than 4/5 of 25?

Solution:
80% of 40 = 0.8 × 40
= 32

4/5 of 25 = 20

∴ difference = 32 - 20
= 12

৪,৭২০.

If a man was to sell his table for Tk. 600, he would lose 20%. To gain 20% he should sell it for:

ক
Tk. 900
খ
Tk. 1000
গ
Tk. 1040
ঘ
Tk. 1200

ব্যাখ্যা

Question: If a man was to sell his table for Tk. 600, he would lose 20%. To gain 20% he should sell it for:

Solution:
Let the Cost price of the table be = x.

∴ Selling price = x - 20% of x
⇒ 600 = x - (20x/100)
⇒ 600 = 80x/100
⇒ 80x = 60000
⇒ x = 60000/80
∴ x = 750

Now, To gain 20% = 750 + 20% of 750
= 750 + 150
= Tk. 900

৪,৭২১.

What must be added to each term of the ratio 2 : 5, So as to make it equal to 5 : 6?

ক
ক) 3
খ
খ) 9
গ
গ) 12
ঘ
ঘ) 13

ব্যাখ্যা

Question: What must be added to each term of the ratio 2 : 5, So as to make it equal to 5 : 6?

Solution:
Let x be added to each term.

According to the question,
(2 + x) / (5 + x) = 5/6
⇒ 12 + 6x = 25 + 5x
⇒ x = 13

৪,৭২২.

The total age of A and B is 15 years more than the total age of B and C . C is how many years younger than A?

ক
30 years
খ
8 years
গ
15 years
ঘ
None of these

ব্যাখ্যা

Question: The total age of A and B is 15 years more than the total age of B and C . C is how many years younger than A?

Solution:
The given condition is,
⇒ A + B = (B + C) + 15
⇒ A + B = B + C + 15
⇒ A + B - B - C = 15
⇒ A - C = 15
⇒ C = A − 15

∴ C is 15 years younger than A.

৪,৭২৩.

In a town, 64 percent of the population is employed, and 48 percent of the population is employed males. What percentage of the employed people in that town is female?

ক
ক) 16%
খ
খ) 25%
গ
গ) 32%
ঘ
ঘ) 40%

ব্যাখ্যা

Given that, Total employed people are 64% of the population, out of that population 48% are employed males, hence 16% are employed females.

So, (employed females)/(total employed people)
= 16/64
= (1/4)
= 25%

৪,৭২৪.

In sin(A - B) = 1/2 and cos(A + B) = 1/2 where A > B > 0 and (A + B) is an acute angle, then the value of B is?

ক
π/10 radian
খ
π/12 radian
গ
π/8 radian
ঘ
π/3 radian

ব্যাখ্যা

Question: In sin(A - B) = 1/2 and cos(A + B) = 1/2 where A > B > 0 and (A + B) is an acute angle, then the value of B is?

Solution:
Given,
sin(A - B) = 1/2 (A - B) = 30^∘
and cos(A + B) = 1/2 (A + B) = 60^∘

Adding both side
(A - B) + (A + B) = 30^∘ + 60^∘
⇒ 2A = 90^∘⇒ A = 45^∘

∵ A - B = 30^∘B = A - 30^∘⇒ B = 45^∘- 30^∘⇒ B = 15^∘⇒ B = 15 × (π/180)
∴ B = π/12 radian

৪,৭২৫.

The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by

ক
ক) 25%
খ
খ) 20%
গ
গ) 80%
ঘ
ঘ) 75%

ব্যাখ্যা

Let the initial expenses on Sugar was Tk. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Tk. 125.
But, They want to keep expenses on Sugar, so they have to cut Tk. 25 in the expenses to keep it to Tk. 100.
Now, % decrease in Consumption,
(25/125)×100=20%

৪,৭২৬.

40% of 200 is what percent of 160?

ক
50
খ
55
গ
35
ঘ
60
ঙ
65

ব্যাখ্যা

160 × x/100 = 200 × 40%
=> 8x/5 = 80
=> 8x = 400
=> x = 50

৪,৭২৭.

If one-third of one-fourth of a number is 15, then five-ninths of that number is-

ক
86
খ
90
গ
100
ঘ
106

ব্যাখ্যা

Question: If one-third of one-fourth of a number is 15, then five-ninths of that number is-

Solution:
Let, the number be = a

Now
(1/3) × (1/4) × a = 15
⇒ a/12 = 15
⇒ a= 12 × 15
∴ a = 180

So, five-ninths of that number will be = (5a/9)
= (5 × 180)/9
= 5 × 20
= 100

৪,৭২৮.

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

ক
4 mats
খ
8 mats
গ
12 mats
ঘ
16 mats

ব্যাখ্যা

Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

Solution:
4 mat-weavers in 4 days weave = 4 mats
∴ 1 mat-weavers in 1 days weave = 4/(4 × 4) mats
∴ 8 mat-weavers in 8 days weave = (4 × 8 × 8)/(4 × 4) mats
= 16 mats

৪,৭২৯.

Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

ক
9 : 20
খ
11 : 9
গ
11 : 20
ঘ
None of these

ব্যাখ্যা

Question: Two trains starting at the same time from two stations 200 km apart and going in opposite directions cross each other at a distance of 110 km from one of the stations. What is the ratio of their speeds?

Solution:
In the same time, they cover 110 km and 90 km respectively.
Therefore, Ratio of their speeds = 110 : 90 = 11 : 9

৪,৭৩০.

If x and y are two positive integers and x + y = 4 then, what is the probability of x and y are same?

ক
ক) 1/2
খ
খ) 1/3
গ
গ) 3/4
ঘ
ঘ) none of these

ব্যাখ্যা

Question: If x and y are two positive integers and x + y = 4 then, what is the probability of x and y are same?

Solution:
total possible ways = (1, 3), (2, 2), (3, 1) = 3
favorable event = (2, 2) = 1

∴ probability = 1/3

৪,৭৩১.

The first number is 25% greater than a third number, and the second number is 40% greater than the same third number. What is the ratio of the first number to the second number?

ক
25 : 30
খ
36 : 25
গ
5 : 8
ঘ
25 : 28
ঙ
None

ব্যাখ্যা

Question: The first number is 25% greater than a third number, and the second number is 40% greater than the same third number. What is the ratio of the first number to the second number?

Solution:
Let the third number be x

Then,
First number = 125% of x
= 125x/100
= 5x/4

Second number = 140% of x
= 140x/100
= 7x/5

∴ Ratio of first two numbers
= 5x/4 : 7x/5
= 25x : 28x
= 25 : 28

৪,৭৩২.

The average of 55 numbers is 35. If two numbers, 32 and 38, are discarded, then the average of the remaining numbers is-

ক
35
খ
39
গ
31
ঘ
29

ব্যাখ্যা

Question: The average of 55 numbers is 35. If two numbers, 32 and 38, are discarded, then the average of the remaining numbers is-

Solution:
The average of 55 numbers is 35
Sum of all the numbers = (35 × 55) = 1925

Sum of 53 numbers =1925 - (32 + 38)
= 1855

The average of the remaining numbers =1855/53 = 35

৪,৭৩৩.

The perimeter of a rectangular garden is 54 yards and the width is 36 feet. What is the length of the garden?

ক
12 yards
খ
15 yards
গ
15 feet
ঘ
27 feet

ব্যাখ্যা

Question: The perimeter of a rectangular garden is 54 yards and the width is 36 feet. What is the length of the garden?

Solution:
Given that,
Perimeter of rectangle = 54 yards
54 × 3 = 162 feet ; [1 yard = 3 feet]
And Width = 36 feet

We know,
Perimeter = 2(length + width)
⇒ 162 = 2(L + 36)
⇒ 81 = L + 36
∴ L = 81 - 36 = 45 feet

∴ The length of the garden is 45 feet = 45/3 = 15 yards.

৪,৭৩৪.

A sum of Tk. 312 was divided among 100 boys and girls in such a way that each boys gets Tk. 3.6 and each girl Tk. 2.4. The number of girls is :

ক
ক) 35
খ
খ) 40
গ
গ) 55
ঘ
ঘ) 50

ব্যাখ্যা

ধরি,
বালিকার সংখ্যা =x জন
বালকের সংখ্যা = (100 - x) জন

1 জন বালক পায় 3.60 টাকা
(100-x) জন বালক পায় =3.60 (100 - x) টাকা

1 জন বালিকা পায় = 2.40 টাকা
x জন বালিকা পায় = 2.40x টাকা

প্রশ্নমতে,
3.60(100 - x) + 2.40x=312
360 - 3.60x + 2.40x=312
360 - 1.2x = 312
360 - 312 = 1.2x
1.2x = 48
x = 48/1.2
x = 40

৪,৭৩৫.

A runner can complete a 750 m race in two and a half minutes. What is the speed of runner in km/hr?

ক
17.95 km/hr
খ
18 km/hr
গ
5 km/hr
ঘ
16 km/hr

ব্যাখ্যা

Question: A runner can complete a 750 m race in two and a half minutes. What is the speed of runner in km/hr?

Solution:
We are given that the first runner can complete a 750 m race in 2 minutes and 30 seconds or 150 seconds.
∴ Speed of the first runner = 750/150 = 5m/sec

We convert this speed to km/hr by multiplying it by 18/5.
Speed of the first runner = (5 × 18)/5 = 18 km/hr

৪,৭৩৬.

The annual salary of A, B, C is in the proportion of 3 : 4 : 5. If C's annual salary is Tk 80000 more than that of A, then B's monthly salary is-

ক
ক) Tk 13666.67
খ
খ) Tk 13333.33
গ
গ) Tk 14373.67
ঘ
ঘ) Tk 16666.67
ঙ
ঙ) None of the above

ব্যাখ্যা

Let the annual salary of A, B, C respectively be 3x, 4x and 5x.
Then 5x - 3x = 80000
x = 40000
So, B's annual salary = 4x = Tk. 160000
Hence, B's monthly salary
= Tk (160000)/12
= Tk. 13333.33

৪,৭৩৭.

The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue.

ক
Increases by 2%
খ
Decreases by 1%
গ
Increases by 1%
ঘ
Decreases by 2%

ব্যাখ্যা

Question: The tax on a commodity is diminished by 10% and its consumption increases by 10%. Find the effects on revenue.

Solution:
Revenue is directly proportional to consumption (C) and tax (T).
Initial revenue = C × T

When tax decrease by 10% and consumption increases by 10%
New revenue =(C + 10C/100) × (T - 10T/100)
New revenue = (110C/100) × (90T/100)
New revenue = 0.99 × C × T
Thus, % decrease in revenue = [{(C × T) − (0.90 × C × T)}/(C × T)] ×100 = 1%

৪,৭৩৮.

In an AP, the ratio of the 2nd term to the 7th term is 1/3. If the 5th term is 11, what is the 15th term?

ক
ক) 33
খ
খ) 28
গ
গ) 31
ঘ
ঘ) 36

ব্যাখ্যা

Question: In an AP, the ratio of the 2nd term to the 7th term is 1/3. If the 5th term is 11, what is the 15th term?

Solution:
The 2nd term is a + d.
The 7th term is a + 6d

ATQ,
(a + d)/(a + 6d) = 1/3
⇒ 3a + 3d = a + 6d
∴ 2a = 3d
∴ a = (3d)/2

The 5th term is a + 4d = 11
⇒ (3d)/2 + 4d = 11
⇒ 3d + 8d = 22
⇒ 11d = 22
∴ d = 2

∴ a = (3 × 2)/2 = 3
∴ The 15th term is: a + 14d
= 3 + 14 × 2
= 3 + 28
= 31

৪,৭৩৯.

A sum of Tk. 24,000 is invested at 5% per annum simple interest. Find the interest earned in 4 years 6 months.

ক
Tk. 4,800
খ
Tk. 5,000
গ
Tk. 5,200
ঘ
Tk. 5,400

ব্যাখ্যা

Question: A sum of Tk. 24,000 is invested at 5% per annum simple interest. Find the interest earned in 4 years 6 months.

Solution:
Given that,
Principal, P = Tk. 24,000
Rate of interest, r = 5%
Time, n = 4 years 6 months
= 9/2 years

We know,
I = Pnr
⇒ I = 24,000 × 9/2 × 5/100
= 24,000 × 9 × 5/(2 × 100)
= 24,000 × 45/200
= 24,000 × 9/40
= 600 × 9
= Tk. 5,400

৪,৭৪০.

A, B, C enter into a partnership investing Tk. 35,000 and Tk. 45,000 and Tk. 55,000 respectively. Total profit of A, B, C, at Tk. 44,550. So B's profit is-

ক
Tk. 18,150
খ
Tk. 14,850
গ
Tk. 11,550
ঘ
Tk. 14,750

ব্যাখ্যা

Question: A, B, C enter into a partnership investing Tk. 35,000 and Tk. 45,000 and Tk. 55,000 respectively. Total profit of A, B, C, at Tk. 44,550. So B's profit is-

Solution:
A : B : C = 35000 : 45000 : 55000
A : B : C = 35 : 45 : 55

∴ Sum of the ratio = 35 + 45 + 55 = 135

∴ B's profit is = 44550 × (45/135)
= 14850

∴ B's profit is Tk. 14,850.

৪,৭৪১.

How many ways can the letters in "TRIANGLE" be arranged if vowels must occupy odd positions?

ক
720
খ
1440
গ
2880
ঘ
5760

ব্যাখ্যা

Question: How many ways can the letters in "TRIANGLE" be arranged if vowels must occupy odd positions?

Solution:

Letters in "TRIANGLE" = 8 (T, R, I, A, N, G, L, E)

Vowels = I, A, E = total 3 vowels

Consonants = 8 − 3 = 5 consonants
Total odd positions: 1, 3, 5, 7 = 4

Number of ways to place 3 vowels in 4 odd positions = ⁴C₃ = 4
Arrange 3 vowels in chosen positions = 3! = 6
Arrange 5 consonants in the remaining 5 positions = 5! = 120

Total arrangements = 4 × 6 × 120 = 2880

৪,৭৪২.

The average of the first seven prime numbers is-

ক
ক) 5.286
খ
খ) 6.286
গ
গ) 8.286
ঘ
ঘ) 7.286

ব্যাখ্যা

The first seven prime numbers :2, 3, 5, 7, 11, 13, 17

The average = (2 + 3 + 5 + 7 + 11 + 13 + 17)/7
= 58/7
= 8.2857
= 8.286

৪,৭৪৩.

A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?

ক
ক) 15%
খ
খ) 10%
গ
গ) 5%
ঘ
ঘ) 25%

ব্যাখ্যা

প্রশ্ন: A trader marks his goods at 40% above the cost price and allows a discount of 25%. What is his gain percent?

সমাধান:
ধরি,
দ্রব্যটির আসল মূল্য ক টাকা

৪০% দাম বাড়িয়ে ধরলে দাম হয় = ক + (ক × ৪০)/১০০ টাকা
= ১.৪ক টাকা

২৫% কমিশন দিলে দাম হয় = ১.৪ক - (১.৪ক × ২৫)/১০০ টাকা
= ১.৪ক - ০.৩৫ক টাকা
= ১.০৫ক টাকা

লাভ = ১.০৫ক - ক টাকা
= ০.০৫ক টাকা

ক টাকায় লাভ হয় = ০.০৫ক টাকা
∴ ১ টাকায় লাভ হয় = ০.০৫ক/ক = ০.০৫ টাকা
∴ ১০০ টাকায় লাভ হয় = (০.০৫ × ১০০) টাকা
= ৫ টাকা

৪,৭৪৪.

The true discount on a bill of Tk. 540 is Tk. 90. The banker's discount is:

ক
ক) 60
খ
খ) 108
গ
গ) 110
ঘ
ঘ) 112

ব্যাখ্যা

P.W. = Tk.(540−90) = Tk.450
∴S.I. on Tk.450
= Tk. 90
S.I.on Tk. 540
= Tk.(90/450×540)
= Tk.108
∴B.D.= Tk.108

৪,৭৪৫.

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
ক) Tk. 14,700
খ
খ) Tk. 1,900
গ
গ) Tk. 13,600
ঘ
ঘ) Tk. 8,400

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

৪,৭৪৬.

A car travels at a speed of 80 km/hr and reaches its destination in 6 hours. A bus travels at a speed of 50 km/hr and reaches its destination in 10 hours. What is the ratio of the distance covered by the car to the distance covered by the bus?

ক
7 : 8
খ
12 : 13
গ
4 : 5
ঘ
24 : 25
ঙ
None of these

ব্যাখ্যা

Question: A car travels at a speed of 80 km/hr and reaches its destination in 6 hours. A bus travels at a speed of 50 km/hr and reaches its destination in 10 hours. What is the ratio of the distance covered by the car to the distance covered by the bus?

Solution:
Car,
Speed = 80 km/hr
Time = 6 hours
∴ Distance = 80 × 6 = 480 km

And Bus,
Speed = 50 km/hr
Time = 10 hours
∴ Distance = 50 × 10 = 500 km

∴ Ratio of distances (Car : Bus) = 480 : 500 = 24 : 25

৪,৭৪৭.

84 Maths books, 90 Physics books, and 120 Chemistry books have to be stacked topicwise. How many books will be there in each stack so that each stack will have the same height too?

ক
6
খ
12
গ
4
ঘ
None of these

ব্যাখ্যা

Question: 84 Maths books, 90 Physics books, and 120 Chemistry books have to be stacked topicwise. How many books will be there in each stack so that each stack will have the same height too?

Solution:
As the height of each stack is the same, the required number of books in each stack
= HCF of 84, 90 and 120

84 = 2 × 2 × 3 × 7
90 = 2 × 3 × 3 × 5
120 = 2 × 2 × 2 × 3 × 5

∴ HCF = 2 × 3 = 6

Hence, The required number of books in each stack is 6.

৪,৭৪৮.

What would be the measure of the perimeter of a square whose area is equal to 256 square cm?

ক
16 cm
খ
36 cm
গ
64 cm
ঘ
128 cm

ব্যাখ্যা

Question: What would be the measure of the perimeter of a square whose area is equal to 256 square cm?

Solution:
দেওয়া আছে
বর্গক্ষেত্রের ক্ষেত্রফল = 256
বর্গের এক বাহুর দৈর্ঘ্য = a

প্রশ্নমতে
a² = 256
a² = (16)²
a = 16

বর্গক্ষেত্রের পরিসীমা = 4a
= 4 × 16
= 64

৪,৭৪৯.

Find the difference between 5/8 of Tk. 4 and 4/5 of Tk. 2?

ক
ক) Tk. 0.90
খ
খ) Tk. 1.60
গ
গ) Tk. 0.09
ঘ
ঘ) Tk. 1

ব্যাখ্যা

Question: Find the difference between 5/8 of Tk. 4 and 4/5 of Tk. 2?

Solution:
5/8 of Tk. 4 = (4 × 5)/8 = 2.5 Tk.
4/5 of Tk. 2 = (2 × 4)/5 = 1.6 Tk.

∴ Difference = (2.5 - 1.6) = Tk. 0.90

৪,৭৫০.

The milk and water in a mixture are in the ratio 5 : 4. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 5 : 7. The total quantity of water in the new mixture is:

ক
24 litres
খ
35 litres
গ
42 litres
ঘ
50 litres

ব্যাখ্যা

Question: The milk and water in a mixture are in the ratio 5 : 4. When 15 litres of water are added to it, the ratio of milk and water in the new mixture becomes 5 : 7. The total quantity of water in the new mixture is:

Solution:
Let the initial quantity of milk = 5x litres
and initial quantity of water = 4x litres

According to the question,15 litres of water is added.

New amount of water = (4x + 15)
The amount of milk remains the same = 5x

As per the new ratio,
5x/(4x + 15) = 5/7
⇒ 7(5x) = 5(4x + 15)
⇒ 35x = 20x + 75
⇒ 35x − 20x = 75
⇒ 15x = 75
⇒ x = 5

The total quantity of water in the new mixture,
= (4x + 15)
= (4 × 5) + 15
= 20 + 15
= 35 litres

∴ Total quantity of water in new mixture 35 litres.

৪,৭৫১.

The ratio of boys and girls in a class is 4:5. If 10% of the boys and 20%of the girls failed In an examination, what percentage of students passed in the exam?

ক
ক) 80%
খ
খ) 82%
গ
গ) 85%
ঘ
ঘ) None

ব্যাখ্যা

The percentage of boys = {4/(4+5)}×100 = (4/9)×100 = 400/9%
and The percentage = {5/(4 + 5)}×100 = (5/9)×100 = 500/9% .
So, The percentage of students passed in the exam = (400/9 - 10)% + (500/9 - 20)% = 310/9 + 320/9 = 630/9 = 70%.

৪,৭৫২.

Which of the following fractions is the largest?

ক
ক) 63/80
খ
খ) 13/16
গ
গ) 31/40
ঘ
ঘ) 7/8

ব্যাখ্যা

63/80 =
13/16 = 65/80
31/40 = 62/80
7/8 = 70/80

সবগুলো হরকে 80 তে রূপান্তর করার পর দেখা যাচ্ছে সবচেয়ে বড় লব হচ্ছে 7/8 এর, তাই এটিই সবচেয়ে বড় সংখ্যা

৪,৭৫৩.

A train takes 12 seconds to cross a telegraph pole. It takes 42 seconds to cross a tunnel. What is the ratio of the length of the tunnel to that of the train?

ক
3 : 2
খ
3 : 5
গ
4 : 7
ঘ
5 : 2

ব্যাখ্যা

Question: A train takes 12 seconds to cross a telegraph pole. It takes 42 seconds to cross a tunnel. What is the ratio of the length of the tunnel to that of the train?

Solution:
Let the speed of the train be x m/s

While crossing the telegraph pole,
The train travels 12 × x meters = 12x meters, which is the length of the train.

While crossing the tunnel,
The train travels 42 × x meters = 42x meters

∴ Length of the tunnel = 42x - 12x = 30x meters

∴ Length of the tunnel : Length of the train = 30x : 12x
= 30 : 12
= 5 : 2

৪,৭৫৪.

Romel bought a television set with a 20% discount on the labelled price. He made a profit of Tk. 800 by selling it for Tk. 16800. The labelled price of the set was -

ক
Tk. 10,000
খ
Tk. 20,000
গ
Tk. 20,800
ঘ
Tk. 24,000

ব্যাখ্যা

Let the labeled price of TV = Tk. R
∴ SP of the TV = [R x (100 - 20)] / 100
= Tk. 4R/5
But 16,800 - 800 = 4R/5
∴ x = (16,000 x 5)/4
= Tk. 20,000

৪,৭৫৫.

A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

ক
75 m
খ
25 m
গ
50 m
ঘ
100 m
ঙ
125 m

ব্যাখ্যা

Question: A 100 m long 3 m high and 30 cm wide wall is built by 30 men, 20 women and 50 children working 9 hours a day in 20 days. How long a wall 1.5 m high 30 cm wide can be built by 15 men, 25 women and 35 children working 2 hour a day in 15 days (given men, women and children are equally efficient)?

Solution:
Earlier dimensions of the wall = 100 × 3 × 0.30.
Volume of the wall = 90
New dimensions = L × 1.5 × 0.3.
Volume of the wall = 0.45L
∴ As men, women and children are given to be equally efficient, so in the first case, the total number of persons is (30 + 20 + 50) = 100 and the same in the second case is (15 + 25 + 35) = 75

working 9 hours a day in 20 days 100 persons make 90 m³ wall
∴ working 1 hours a day in 1 days 1 persons make 90/(100 × 20 × 9) m³ wall
∴ working 2 hours a day in 15 days 75 persons make (90 × 75 × 15 × 2)/(100 × 20 × 9) m3 wall
= 11.25

∴ Length of the wall = L = 11.25/0.45 = 25 m

৪,৭৫৬.

What is the maximum side length of a square slab that can be used to tile the floor of a room with dimensions 5 meters 44 cm by 3 meters 74 cm?

ক
26 cm
খ
30 cm
গ
32 cm
ঘ
34 cm

ব্যাখ্যা

Question: What is the maximum side length of a square slab that can be used to tile the floor of a room with dimensions 5 meters 44 cm by 3 meters 74 cm?

Solution:
length = 5 meters 44 cm
= 500 + 44 cm
= 544 cm

breadth = 3 meters 74 cm
= 300 + 74
= 374 cm

∴ The side of the square slab is the H.C.F. of 544 and 374 cm i.e. 34.

৪,৭৫৭.

Tk. 3000 becomes Tk. 3600 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of same principal in 5 years will be -

ক
Tk. 4000
খ
Tk. 4500
গ
Tk. 4625
ঘ
Tk. 4125

ব্যাখ্যা

Question: Tk. 3000 becomes Tk. 3600 in 4 years at a certain rate of simple interest. If the rate becomes 1.5 times of itself, the amount of same principal in 5 years will be -

Solution:
৩০০০ টাকা ৪ বছরে ৩৬০০ টাকা হয়।
∴ ৪ বছরের সুদ = ৩৬০০ - ৩০০০ টাকা
= ৬০০ টাকা
১ বছরে সুদ = ৬০০/৪ = ১৫০ টাকা

১.৫ গুণ বৃদ্ধিতে ১ বছরে সুদ হবে = ১৫০ × ১.৫ টাকা
= ২২৫ টাকা

৫ বছরে সুদ হবে = ২২৫ × ৫ টাকা
= ১১২৫ টাকা

∴ ৫ বছর পর সুদাসলে হবে = ৩০০০ + ১১২৫ টাকা
= ৪১২৫ টাকা

৪,৭৫৮.

How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

ক
6! × 2!
খ
6! - 2!
গ
5!
ঘ
4!

ব্যাখ্যা

Question: How many words can be formed by re-arranging the letters of the word ASCENT such that A and T occupy the first and last position respectively?

Solution:
As S and N should occupy the first and last position, the first and last position can be filled in only one following way.
S _ _ _ _ N.
The remaining 4 positions can be filled in 4! Ways by the remaining words (A, C, E, T).
Hence by rearranging the letters of the word ASCENT we can form,
1 × 4! = 4!

৪,৭৫৯.

A number is divided into two parts in such a way that 60% of 1st part is 2 more than the 40% of 2nd part and 60% of the 2nd part is 1 more than the 40% of 1st part. Find the number.

ক
12
খ
15
গ
16
ঘ
18

ব্যাখ্যা

Question: A number is divided into two parts in such a way that 60% of 1st part is 2 more than the 40% of 2nd part and 60% of the 2nd part is 1 more than the 40% of 1st part. Find the number.

Solution:
Let,
Two part of the number be a, b respectively
∴ The number = a + b

ATQ,
60% of a - 40% of b = 2
⇒ (60/100)a - (40/100)b = 2
∴ 6a - 4b = 20…………(1)

and
60% of b - 40% of a = 1
⇒ (60/100)b - (40/100)a = 1
∴ 6b - 4a = 10………….(2)

From (1) × 2 + (2) × 3 we get,
12a - 8b + 18b - 12a = 40 + 30
⇒ 10b = 70
∴ b = 7

Put b in 1, we get
6a - 28 = 20
⇒ 6a = 48
∴ a = 8

Hence, the number is (7 + 8) = 15

৪,৭৬০.

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

ক
ক) 48 km/hr
খ
খ) 54 km/hr
গ
গ) 82 km/hr
ঘ
ঘ) 66 km/hr

ব্যাখ্যা

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

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

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

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

৪,৭৬১.

If x + (1/x) = 3, then the value of (3x² - 4x + 3)/(x² - x + 1) is?

ক
3/4
খ
1/2
গ
5/2
ঘ
7/5

ব্যাখ্যা

Question: If x + (1/x) = 3, then the value of (3x² - 4x + 3)/(x² - x + 1) is?

Solution:
Given that,
x + (1/x) = 3
⇒ (x² + 1)/x = 3
∴ x² + 1 = 3x

Now,
(3x² - 4x + 3)/(x² - x + 1)
= (3x² + 3 - 4x)/(x² + 1 - x)
= {3(x² + 1) - 4x}/(x² + 1 - x)
= {(3 × 3x) - 4x}/(3x - x) [মান বসিয়ে]
= (9x - 4x)/2x
= 5x/2x
= 5/2

৪,৭৬২.

if - 1 < x < 0 then which of the following is biggest?

ক
x/2
খ
x²
গ
1/x²
ঘ
x + 1

ব্যাখ্যা

Question: if - 1 < x < 0 then which of the following is biggest?

Solution:
let,
x = - 1/2

a) x/2 = (- 1/2)/2
= - 1/4

b) x² = (- 1/2)²
= 1/4

c) 1/(x²) = 1/(- 1/2)²
= 1/(1/4)
= 4

d) x + 1 = (- 1/2) + 1
= (- 1 + 2)/2
= 1/2

৪,৭৬৩.

Pipes A, B can fill a tank in 15 minutes and 20 minutes respectively. But pipe C can empty the full tank in 12 minutes. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

ক
ক) 30 minutes
খ
খ) 35 minutes
গ
গ) 38 minutes
ঘ
ঘ) 29 minutes

ব্যাখ্যা

Question: Pipes A, B can fill a tank in 15 minutes and 20 minutes respectively. But pipe C can empty the full tank in 12 minutes. If all these pipes are opened simultaneously, how much time will be taken to fill the tank?

Solution:
A, 1 মিনিটে পূর্ণ করে (1/15) অংশ
B, 1 মিনিটে পূর্ণ করে (1/20) অংশ
অপরদিকে,
C, 1 মিনিটে খালি করে (1/12) অংশ

সবগুলো পাইপ খুলে দিলে ট্যাংকটি পূর্ণ হবে-
= (1/15) + (1/20) − (1/12)
= (4 + 3 − 5)/60
= 2/60
= 1/30

1/30 অংশ পূর্ণ করে 1 মিনিটে
∴ 1 অংশ পূর্ণ করে 30/1 মিনিটে
= 30 মিনিটে

৪,৭৬৪.

ক
0
খ
1
গ
5
ঘ
60

ব্যাখ্যা

Question:

Solution:

৪,৭৬৫.

If 0 < x ≤ 1, then which one of the following is the maximum value of (x - 1)² + x ?

ক
ক) - 1
খ
খ) - 2
গ
গ) 0
ঘ
ঘ) 1

ব্যাখ্যা

0 < x ≤ 1, হলে x এর মান 0 থেকে বড় কিন্তু 1 এর চেয়ে ছোট বা সমান।

(x - 1)² + x এর সর্বোচ্চ মান বের করার জন্য x = 1 ধরে পাই,
(x - 1)² + x = (1 - 1)² + 1
= 0² + 1
= 0 + 1
= 1

৪,৭৬৬.

A group of men decided to do a job in 6 days. But since 5 men dropped out every day, the job completed at the end of the 8th day. How many men were there at the beginning?

ক
90
খ
85
গ
70
ঘ
65

ব্যাখ্যা

Question: A group of men decided to do a job in 6 days. But since 5 men dropped out every day, the job completed at the end of the 8th day. How many men were there at the beginning?

Solution:
Let
x be the initial number of men then

ATQ,
6x = x + (x - 5) + (x - 10) + (x - 15) + (x - 20) + (x - 25) + (x - 30) + (x - 35)
⇒ 6x = 8x - 140
⇒ 2x = 140
⇒ x = 140/2
∴ x = 70

৪,৭৬৭.

Which one will sit in the blank?
QPO, NML, KJI, _____, EDC

ক
GHI
খ
JKL
গ
CAB
ঘ
HGF

ব্যাখ্যা

Question: Which one will sit in the blank?
QPO, NML, KJI, _____, EDC

Solution:
এই সিরিজটি একটি বিপরীত বর্ণানুক্রমিক অক্ষর নিয়ে গঠিত।
শেষের দিক থেকে C D E, F G H, I J K, L M N, O P Q

∴ শূন্যস্থানে HGF বসবে।

৪,৭৬৮.

A teacher has 3 hours to grade all the papers submitted by the 35 students in her class. She gets through the first 5 papers in 30 minutes. How much faster does she have to work to grade the remaining papers in the allotted time?

ক
ক) 10%
খ
খ) 15%
গ
গ) 20%
ঘ
ঘ) 16.67%

ব্যাখ্যা

প্রথম 5 টি copy এর প্রত্যেকটি দেখতে সময় লাগে = 30/5
= 6 মিনিট
পরের 30 টি copy এর প্রত্যেকটি দেখতে সময় পাবে = 150/30
= 5 মিনিট

বর্তমান রেট - 1/6
কাঙ্ক্ষিত রেট - 1/5
বাড়াতে হবে - 1/30

অতএব, {(1/30) / (1/6)} × 100
= 20% faster হতে হবে ।

৪,৭৬৯.

If 2^x + 2^y = 2²², what is the value of x + y?

ক
39
খ
40
গ
41
ঘ
42
ঙ
None

ব্যাখ্যা

Question: If 2^x + 2^y = 2²², what is the value of x + y?

Solution:
Here,,
2^x + 2^y=2²²
⇒ 2^x(1 + 2^{y - x})=2²²

2^x must be a power of 2 that divides 2²²
(1 + 2y - x) must be a power of 2
Only way (1 + 2y - x) is a power of 2 is if, y - x = 0

So, y - x = 0
⇒ y = x

∴ 2^x + 2^x = 2²²
⇒ 2.2^x = 2²²
⇒ 2^{1 + x}=2²²
⇒ 1 + x = 22
∴ x = 21
∴ x + y = 21 + 21 = 42

৪,৭৭০.

An investment becomes Tk. 12,100 in 2 years at compound interest, the rate being 10% per annum. Find the principal.

ক
10,000 taka
খ
11,000 taka
গ
10,100 taka
ঘ
11,100 taka

ব্যাখ্যা

Question: An investment becomes Tk. 12,100 in 2 years at compound interest, the rate being 10% per annum. Find the principal.

Solution:
Given,
Amount, A = 12,100 Taka
Rate, R = 10%
Time, T = 2 years

Compound Interest Formula:
A = P[1 + 100/R]^T
⇒ 12,100 = P[1.1]²
⇒ 12,100 = 1.21P
⇒ P = 12,100/1.21
P = 10,000

∴ Principle = 10,000 taka

৪,৭৭১.

Fuad, Rubel and Pavel are cousins. Fuad’s age is one-third of Rubel and Pavel is five years elder than Rubel. If the sum of the age of the cousins is 40, find the ages of Fuad.

ক
15 years
খ
35 years
গ
25 years
ঘ
10 years
ঙ
5 years

ব্যাখ্যা

Question: Fuad, Rubel and Pavel are cousins. Fuad’s age is one-third of Rubel and Pavel is five years elder than Rubel. If the sum of the age of the cousins is 40, find the ages of Fuad.

Solution:
Let,
Rubel’s age = x
Fuad’s age = x/3
Pavel’s age = x + 5

ATQ,
Fuad + Rubel + Pavel = 40
(x/3) + x + (x + 5) = 40
⇒ (x/3) + 2x + 5 = 40
⇒ (x + 6x)/3 = 40 - 5
⇒ 7x/3 = 35
⇒ x = (35 × 3)/7 = 15
∴ x = 15 years

∴ Fuad age is = 15 × (1/3) = 5 years.

৪,৭৭২.

It is Tuesday on May 23, 2023. What will be the day of June 1, 2023?

ক
ক) Wednesday
খ
খ) Thursday
গ
গ) Friday
ঘ
ঘ) Saturday

ব্যাখ্যা

Question: It is Tuesday on May 23, 2023. What will be the day of June 1, 2023?

Solution:
মে মাস ৩১ দিনের।
মে মাসের ২৩ তারিখ থেকে ৩১ তারিখের মাঝে =(৩১ - ২৩) দিন
= ৮ দিন
১ জুনসহ মোট দিন ৮ + ১ দিন = ৯ দিন

এখন,
৯ ÷ ৭ = ভাগফল ১, ভাগশেষ ২।

সুতরাং, ৩১ তারিখ হবে মঙ্গলবার + ২ দিন।
= বৃহস্পতিবার

৪,৭৭৩.

At the end of 3 years, the difference between the compound interest and simple interest comes to be Tk. 320. The rate of interest is 25%. Find the principal amount.

ক
ক) Tk. 1525.50
খ
খ) Tk. 1545.78
গ
গ) Tk. 1550
ঘ
ঘ) Tk. 1575.38

ব্যাখ্যা

Principle = P
Compound Interest = Total amount - Principle
P = P(1 + R/100]ⁿ - P

Simple interest = PRT/100
R= 25% per annum; T and n = 3 years
Compound Interest - Simple Interest = Tk. 320

∴ [{P(1 + R/100]ⁿ - P} - (PRT/100)] = 320
⇒ [{P(1 + 25/100]³ - P} - {(P × 25 × 3)/100)}] = 320
⇒ P(5/4)³ - P - 3P/4 = 320
⇒ P(125/64) - (P + 3P/4) = 320
⇒ {(125P/64) - (7P/4)} = 320
∴ P = Tk. 1575.38

৪,৭৭৪.

If one root of x² - (p - 1)x + 10 = 0 is 5, then the value of P is-

ক
6
খ
7
গ
8
ঘ
10

ব্যাখ্যা

Question: If one root of x² - (p - 1)x + 10 = 0 is 5, then the value of P is-

Solution:
x² - (p - 1)x + 10 = 0
Putting x = 5
5²-(p - 1)5 + 10 = 0
⇒ 25 - 5p + 5 + 10 = 0
⇒ 40 - 5p = 0
⇒ 5p = 40
∴ p = 8

৪,৭৭৫.

Karim Traveled 60 miles from Dhaka to Gazipur at a certain speed. If his speed per hour were 2 miles faster, he would need 1 hour less to reach Gazipur. What was his initial speed?

ক
ক) 8 miles per hour
খ
খ) 10 miles per hour
গ
গ) 12 miles per hour
ঘ
ঘ) 15 miles per hour
ঙ
ঙ) None

ব্যাখ্যা

Let, initial speed = x
ATQ,
⇒ 60/x - 60/(x+2) = 1
⇒ {60(x+2) - 60x} / x(x+2) = 1
⇒ 60x + 120 - 60x = x² + 2x
⇒ x² + 2x - 120 = 0
⇒ x² + 12x - 10x - 120 = 0
⇒ x(x + 12) - 10(x + 12) = 0
⇒ (x + 12)(x - 10) = 0
Either, x = -12 [Not acceptable] or, x = 10

৪,৭৭৬.

By what percentage should the cost price of an article be increased, so as to earn a profit of 20% even after allowing a discount of 40% on the price marked on the article?

ক
33.33%
খ
50%
গ
66.67%
ঘ
100%

ব্যাখ্যা

Discount = 40%
S.P. = (100-40)% of M.P. = 60% of M.P.
Profit = 20%

∴ S.P. = (100+20)% of C.P.
∴ 60% x MP = 120% of C.P.
∴ C.P. = (1/2) M.P.
∴ MP = 2CP

Since MP should be twice of C.P. to fit into the criteria, we need to increase C.P. by 100% to make it MP.

৪,৭৭৭.

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

ক
648
খ
1800
গ
2700
ঘ
1080
ঙ
None

ব্যাখ্যা

Question: Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

Solution:
৬টি মেশিন ১ মিনিটে বোতল বানায় ২৭০টি
১টি মেশিন ১ মিনিটে বোতল বানায় ২৭০/৬ = ৪৫টি
১০টি মেশিন ১ মিনিটে বোতল বানায় ৪৫ × ১০ = ৪৫০টি
১০টি মেশিন ৪ মিনিটে বোতল বানায় ৪৫০ × ৪ = ১৮০০টি

৪,৭৭৮.

In an examination, 85% of examinees passed in Mathematics. If total 75 examinees failed in Mathematics, then what is the total number of examinees?

ক
500
খ
450
গ
350
ঘ
400

ব্যাখ্যা

Question: In an examination, 85% of examinees passed in Mathematics. If total 75 examinees failed in Mathematics, then what is the total number of examinees?

Solution:
পরীক্ষায় পাশ করেছে = ৮৫%
ফেল করেছে = ১০০ - ৮৫
= ১৫%

মোট পরীক্ষার্থীর ১৫% = ৭৫
⇒ মোট পরীক্ষার্থী × ০.১৫ = ৭৫
∴ মোট পরীক্ষার্থী = ৭৫/০.১৫
= ৫০০ জন

৪,৭৭৯.

If a + b + c = 12 and a² + b² + c² = 56, then what is the value of ab + bc + ca ?

ক
26
খ
34
গ
42
ঘ
44

ব্যাখ্যা

Question: If a + b + c = 12 and a² + b² + c² = 56, then what is the value of ab + bc + ca ?

Solution:
দেওয়া আছে,
a + b + c = 12
a² + b² + c² = 56
আমরা জানি,
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
⇒ (12)² = 56 + 2(ab + bc + ca)
⇒ 144 = 56 + 2(ab + bc + ca)
⇒ 2(ab + bc + ca) = 144 - 56
⇒ 2(ab + bc + ca) = 88
⇒ ab + bc + ca = 88/2
∴ ab + bc + ca = 44

৪,৭৮০.

A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35,000, A receives-

ক
Tk. 8400
খ
Tk. 11,900
গ
Tk. 13,600
ঘ
Tk. 14,700

ব্যাখ্যা

Question: A, B, C subscribe Tk. 50,000 for a business. A subscribes Tk. 4000 more than B and B Tk. 5000 more than C. Out of a total profit of Tk. 35,000, A receives-

Solution:
Let C = x.
Then, B = x + 5000 and
A = x + 5000 + 4000 = x + 9000.

So,
x + x + 5000 + x + 9000 = 50000
⇒ 3x = 36000
∴ x = 12000

A : B : C = 21000 : 17000 : 12000
= 21 : 17 : 12.

A's share = 35000 × (21/50) = Tk. 14,700.

৪,৭৮১.

In a cyclic quad. ABCD, ∠A = 80°. Then ∠C = ?

ক
80°
খ
100°
গ
120°
ঘ
160°
ঙ
180°

ব্যাখ্যা

Question: In a cyclic quad. ABCD, ∠A = 80°. Then ∠C = ?

Solution:
Opposite angles of a cyclic quadrilateral are supplementary.
∴ ∠A + ∠C = 180°
⇒ 80° + ∠C =180°
⇒ ∠C = 100°.

৪,৭৮২.

The average of a non-zero number and its square is 5 times the number. The number is-

ক
9
খ
17
গ
29
ঘ
none of these

ব্যাখ্যা

Question: The average of a non-zero number and its square is 5 times the number. The number is-

Solution:
Let the number be x (x ≠ 0).

According to the question,
The average of the number and its square is 5 times the number.
⇒ (x + x²)/2 = 5x
⇒ x + x² = 10x
⇒ x² + x - 10x = 0
⇒ x² - 9x = 0
⇒ x(x - 9) = 0
So, x = 0 or x = 9
But the number is non-zero, so we discard x = 0.

Therefore, the number is 9.

৪,৭৮৩.

A man spends 75% of his income, His income increases by 20% & his expenditure increases by 15%. His savings are then increased by -

ক
ক) 5%
খ
খ) 10%
গ
গ) 23%
ঘ
ঘ) 35%

ব্যাখ্যা

ধরি,
লোকটির আয় ১০০ টাকা

লোকটির ব্যয় = ৭৫ টাকা
লোকটির সঞ্চয় = ২৫ টাকা

২০% বৃদ্ধিতে নতুন আয় = (১০০ + ২০) টাকা = ১২০ টাকা
১৫% বৃদ্ধিতে নতুন ব্যয় = ৭৫ + ৭৫ এর ১৫%
= ৭৫ + ৭৫ এর ১৫/১০০
= ৮৬.২৫ টাকা

নতুন সঞ্চয় = (১২০ - ৮৬.২৫) টাকা
= ৩৩.৭৫ টাকা

সঞ্চয় বাড়ে = (৩৩.৭৫ - ২৫) টাকা = ৮.৭৫ টাকা

শতকরা বাড়ে = {(৮.৭৫/২৫) × ১০০}% = ৩৫%

৪,৭৮৪.

If the price of petrol is increased by 10% to keep the expenditure value constant, then how much percentage must be reduced in its consumption?

ক
9.09%
খ
15%
গ
16.67%
ঘ
17.765
ঙ
12%

ব্যাখ্যা

Let before increasing the price of petrol we are purchasing 1-litre petrol in 100 tk. So total quantity 100×1=100.

After increasing the price of petrol by 10% let we are receiving x litre petrol. Then final quantity 110×x=100x

After equating the initial and final quantity we will get the value of x.

100×1=110×x
Then x=10÷11

Initially, we are getting 1 litre and after increment, we are getting 10÷11
Reduction in the amount of petrol = 1-(10÷11) = 1÷11
Reduction in the amount of petrol in percentage = 1÷11×100 = 100÷11 = 9.09%

৪,৭৮৫.

The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the height of a cylindrical pillar.

ক
7 meters
খ
8 meters
গ
6 meters
ঘ
9 meters

ব্যাখ্যা

Question: The curved surface area of a cylindrical pillar is 264 m² and its volume is 924 m³. Find the height of a cylindrical pillar.

Solution:
Let the radius of the cylinder be r meters and the height be h meters.
Curved surface area = 2πrh
∴ 2πrh = 264 .......(1)

And Volume = πr2h
∴ πr²h = 924 ......(2)

Now, (2) ÷ (1),
πr²h/2πrh = 924/264
⇒ r/2 = 924/264
⇒ r = (924/264) × 2
∴ r = 7

From (1) we get,
h = 264/2πr = 264 × (7/22 × 2 × 7) = 6m
∴ h = 6m

So the height of the cylindrical pillar is 6 meters

৪,৭৮৬.

A shopkeeper mixes 3 litres of water with 15 litres of milk costing Tk 60 per litre and sells the whole at cost price. What is the profit percentage?

ক
10%
খ
15%
গ
20%
ঘ
25%

ব্যাখ্যা

Question: A shopkeeper mixes 3 litres of water with 15 litres of milk costing Tk 60 per litre and sells the whole at cost price. What is the profit percentage?

Solution:
→ Total cost = 15 × 60 = Tk 900
→ Total volume = 18 litres, Selling price per litre = 900/18 = Tk 50
→ Profit per litre = 60 – 50 = Tk 10
→ Profit % = (10/50)×100 = 20%

৪,৭৮৭.

If the day before yesterday was Thursday, when will Sunday be?

ক
Today
খ
Tomorrow
গ
Day after tomorrow
ঘ
Two days after today
ঙ
None of these

ব্যাখ্যা

Question: If the day before yesterday was Thursday, when will Sunday be?

Solution:
Day before yesterday was Thursday
⇒ Yesterday was a Friday
⇒ Today is a Saturday
⇒ Tomorrow is a Sunday

৪,৭৮৮.

A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is =?

ক
86 days
খ
92 days
গ
95 days
ঘ
96 days

ব্যাখ্যা

Question: A takes three times as long as B and C together to do a job. B takes four times as long as A and C together to do the work. If all three, working together can complete the job in 24 days, then the number of days, A alone will take to finish the job is =?

Solution:
Let the time taken by B and C = x days
∴ Time taken by A = 3x days
∴ Part of the work done by A, B and C in 1 day = 1/x + 1/3x = (3 + 1)/3x = 4/3x

∴ 4/3x = 1/24
⇒ 3x = 4 × 24
⇒ x = 96/3
∴ x = 32 days

∴ Time taken by A = 32 × 3 = 96 days.

৪,৭৮৯.

Ramesh and Suresh’s mud forts have heights 8cm and 15 cm. They are 24 cm apart. How far are the fort tops from each other?

ক
ক) 22 cm
খ
খ) 23 cm
গ
গ) 25 cm
ঘ
ঘ) 24.5 cm

৪,৭৯০.

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

ক
8
খ
9
গ
10
ঘ
11
ঙ
12

ব্যাখ্যা

Question: 3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

Solution:
Let the required no of working hours per day be x.
More pumps , Less working hours per day (Indirect Proportion)
Less days, More working hours per day (Indirect Proportion)

∴ (4 × 1 × x) = (3 × 2 × 8)
⇒ x = 12

৪,৭৯১.

Two small circular parks of diameters 6 m and 8 m are to be replaced by a bigger circular park. What would be the radius of this new park, in meter, if the new park occupies the same space as the two small parks (in meter)?

ক
5
খ
10
গ
15
ঘ
20
ঙ
25

ব্যাখ্যা

Question: Two small circular parks of diameters 6 m and 8 m are to be replaced by a bigger circular park. What would be the radius of this new park, in meter, if the new park occupies the same space as the two small parks (in meter)?

Solution:
Let,
The radious of the new circular park = R
Area of the new circular park = sum of the areas of the 2 smaller parks
⇒ π (6/2)² + π (8/2)²
= π (3)² + π (4)²
= π 9 + π 16
= π(9 + 16)
= 25π

⇒ 25 π = π R².
∴ R² = 25
⇒ R = 5 m

৪,৭৯২.

A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 78 minutes, will be covered by A in :

ক
ক) 12 minutes
খ
খ) 13 minutes
গ
গ) 14 minutes
ঘ
ঘ) 15 minutes

ব্যাখ্যা

The ratio of the speed of A, B and C = 6 ∶ 3 ∶ 1
The ratio of the time taken = 1/6 ∶ 1/3 ∶ 1 = 1 ∶ 2 ∶ 6

Time taken by C to cover the distance = 78 minutes

If C takes 6 min, then A takes 1 min.
If C takes 78 min, then A takes 78 × (1/6) min.
= 13 minutes.

৪,৭৯৩.

If log₁₀5 = m then log₁₀(1/50) is equal to-

ক
ক) - m + 1
খ
খ) (m + 1)
গ
গ) - (m + 1)
ঘ
ঘ) m - 1

ব্যাখ্যা

Given that
log₁₀5 = m

log₁₀(1/50) = log₁₀1 - log₁₀50
= 0 - log₁₀(5 × 10)
= - (log₁₀5 + log₁₀10)
= - (m + 1)

৪,৭৯৪.

A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is-

ক
1/22
খ
3/22
গ
2/77
ঘ
2/91
ঙ
None of these

ব্যাখ্যা

Question: A bag contains 4 white, 5 red and 6 blue balls. Three balls are drawn at random from the bag. The probability that all of them are red, is-

Solution:
Let S be the sample space.
Then, n(S) = number of ways of drawing 3 balls out of 15 = ¹⁵C₃ = 455

Let E = event of getting all the 3 red balls.
n(E) = ⁵C₃ = 10

∴ P(E) = n(E)/n(S) = 10/455 = 2/91

৪,৭৯৫.

A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

ক
ক) Tk. 25
খ
খ) Tk. 30
গ
গ) Tk. 50
ঘ
ঘ) Tk. 75

ব্যাখ্যা

Question: A shopkeeper sells a pair of sunglasses at a profit of 25%. If he had bought it at 25% less and sold it for Tk. 10 less, he would have gained 40%. Determine the cost price of the pair of sunglasses.

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

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

এখন,
২০ টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = 100 টাকায়
∴ 10 টাকা বিক্রয়মূল্য কম হয় ক্রয়মূল্য = (100 × 10)/20 টাকায়
= 50 টাকা

৪,৭৯৬.

In a class 75% passed in English, 60% in Mathematics and 25% failed in both the subjects. What is the percentage who passed in both subjects?

ক
60%
খ
55%
গ
50%
ঘ
45%

ব্যাখ্যা

Question: In a class 75% passed in English, 60% in Mathematics and 25% failed in both the subjects. What is the percentage who passed in both subjects?

Solution:
75% passed in English then fail 25%
60% passed in Mathematics then fail 40%
Failed in both 25%

Total no. Of fail = (25 + 40 - 25) = 40%

Then passed is 60%

৪,৭৯৭.

What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?

ক
Tk. 1800
খ
Tk. 1600
গ
Tk. 1750
ঘ
Tk. 1850

ব্যাখ্যা

Question: What yearly income can be earned by investing Tk. 14400 in 15% stock at Tk. 120?

Solution:
From Tk. 120 earn 15
From Tk. 1 earn 15/120
From Tk. 14400 earn (15 × 14400)/120
= 1800

৪,৭৯৮.

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 there in the jar?

ক
ক) 5
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 10

ব্যাখ্যা

Ratio of W : R : G = 2 : 3 : 5
If 6 Green marbel is added, Ratio becomes W : R : G = 2 : 3 : 7
Difference of ratio for 6 marbles = 7 – 5 = 2
So, 1 ratio = 3 marbles
∴ White marbles = 2×3 = 6

৪,৭৯৯.

Find the three consecutive odd numbers whose sum of the squares is 2531.

ক
19, 21, 23
খ
23, 25, 27
গ
27, 29, 31
ঘ
31, 33, 35

ব্যাখ্যা

Question: Find the three consecutive odd numbers whose sum of the squares is 2531.

Solution:
Let three consecutive odd numbers be x, x + 2, x + 4.
x² + (x + 2)² + (x + 4)² = 2531
Simplifying we get,
⇒ x² + 4x - 837=0
⇒ x² + 31x - 27x - 837=0 [ 27 × 31 = 837 and also the difference between 27 and 31 is 4 ]
⇒ (x + 31) (x - 27)
⇒ x = 27 or x = - 31
Hence, the value of
x = 27
(x + 2) = 27 + 2 = 29
(x + 4) = 27 + 4 = 31

৪,৮০০.

If ƒ(y) = y³ + ky² - 4y - 8, then for what value of k will ƒ(- 2) = 0?

ক
2
খ
4
গ
0
ঘ
3

ব্যাখ্যা

Question: If ƒ(y) = y³ + ky² - 4y - 8, then for what value of k will ƒ(- 2) = 0?

Solution:
f(y) = y³ + ky² - 4y - 8
∴ f(- 2) = (- 2)³ + k(- 2)² - 4(- 2) - 8
= - 8 + 4k + 8 - 8
= 4k - 8

∴ 4k - 8 = 0
⇒ 4k = 8
∴ k = 2