Bank Math

PrepBank · পাতা ৯৮ / ১৬১ · ৯,৭০১–৯,৮০০ / ১৬,১২৪

৯,৭০১.

What is the average (arithmetic mean) of the values 39, 40, 39, 45, 42, 35, 47?

ক
ক) 39
খ
খ) 41
গ
গ) 45
ঘ
ঘ) 47

ব্যাখ্যা

Question: What is the average (arithmetic mean) of the values 39, 40, 39, 45, 42, 35, 47?

Solution:
সংখ্যাগুলোর গড় = (39 + 40 + 39 + 45 + 42 + 35 + 47)/7
= 287/7
= 41

৯,৭০২.

One-third of a number's quarter is 15. Find the value of three-tenths of the same number.

ক
24
খ
37
গ
54
ঘ
68

ব্যাখ্যা

Question: One-third of a number's quarter is 15. Find the value of three-tenths of the same number.

Solution:
Let,
The number be x
Then,
1/3 of 1/4 of x = 15
⇒ x = 15 × 12 = 180

So, required number = (3/10) × 180 = 54

৯,৭০৩.

The sum of the ages of 5 children born at the intervals of 3 year each is 50 year. What is the age of the youngest child?

ক
ক) 8 years
খ
খ) 16 years
গ
গ) 6 years
ঘ
ঘ) 4 years

ব্যাখ্যা

Let the age of the youngest child is 'X' year.
Then the child elder than the yongest is 'X + 3' years
Since each have 3years difference upto 5 children
And given that
=> X + X+3 + X+6 + X+9 + X+12 = 50
=> 5X + 30 = 50
=> X = 4 years.

৯,৭০৪.

One of three numbers, the first is twice the second and the second is twice the third. The average of the reciprocal of the numbers is 7/72. The numbers are:

ক
ক) 16, 8, 4
খ
খ) 24, 12, 6
গ
গ) 20, 10, 5
ঘ
ঘ) 28, 14, 7

ব্যাখ্যা

Let
the third number be x
Then Second number =2x and first number =4x

(1/x) + (1/2x) + 1/4x = (7/72) × 3
(4 + 2 + 1)/4x = 7/24
7/4x = 7/24
4x = 24
x = 6

Therefore, the three numbers are 4 × 6 = 24 , 2 × 6 = 12 , 6

৯,৭০৫.

The average monthly income of P and Q is Tk. 6,000; that of Q and R is 5,250; and, that P and R are Tk. 5,500. What is P’s monthly income?

ক
ক) Tk. 3,500
খ
খ) Tk. 4,500
গ
গ) Tk. 6,250
ঘ
ঘ) Tk. 4,800

ব্যাখ্যা

Question: The average monthly income of P and Q is Tk. 6,000; that of Q and R is 5,250; and, that P and R are Tk. 5,500. What is P’s monthly income?

Solution:
Average monthly income of P and Q = Tk. 6000
Average monthly income of Q and R = Tk. 5250
Average monthly income of P and R = Tk. 5500

Total income of P + Q = Tk. 2 × 6000 = Tk. 12000 .........(i)
Total income of Q + R = Tk. 2 × 5250 = Tk. 10500 .........(ii)
Total income of P + R = Tk. 2 × 5500 = Tk. 11000 ...........(iii)

On adding equation (i) + (ii) + (iii), we get
2 (P +Q + R) = 12000 + 10500 + 11000
P + Q + R = 33500/2
P + Q + R = Tk 16750 ........(iv)
by equation (iv) - (ii)
P's income = (16750 - 10500) = Tk. 6250.

৯,৭০৬.

ক
1
খ
1/2
গ
3
ঘ
abc

ব্যাখ্যা

Question:

Solution:

৯,৭০৭.

If A = A and B = D then what will be equivalent to C?

ক
I
খ
J
গ
K
ঘ
L

ব্যাখ্যা

Question: If A = A and B = D then what will be equivalent to C?

Solution:
A = A(1 = 1)
B = D(2 = 4)
from the above relation, we get,
1² = 1
2² = 4

As C values 3 in the alphabet rank,
3² = 9
so, C = I

৯,৭০৮.

Simplify

ক
8
খ
10
গ
12
ঘ
14

ব্যাখ্যা

Question: Simplify

Solution:

= 22 - [9 - {6 - (10 - 1)}]
= 22 - [ 9 - { 6 - 9}]
= 22 - [9 - {-3}]
= 22 - [9 + 3]
= 22 - [12]
= 22 - 12
= 10

৯,৭০৯.

In a school there are 286 students where boys and girls are in the ratio 8:5. If 22 new girls are admitted, then new ratio of boys and girls:

ক
4 : 3
খ
12 : 7
গ
10 : 7
ঘ
8 : 7

ব্যাখ্যা

Question: In a school there are 286 students where boys and girls are in the ratio 8:5. If 22 new girls are admitted, then new ratio of boys and girls:

Solution:
দেওয়া আছে,
একটি বিদ্যালয়ে মোট ছাত্র-ছাত্রীর সংখ্যা 286 জন
বিদ্যালয়ে বালক ও বালিকার সংখ্যার অনুপাত 8:5

মনে করি,
বিদ্যালয়ে বালকের সংখ্যা 8x জন
বিদ্যালয়ে বালিকার সংখ্যা 5x জন

প্রশ্নমতে,
8x + 5x = 286
⇒ 13x = 286
⇒ x = 286/13
∴ x = 22

∴ বিদ্যালয়ে বালকের সংখ্যা (8 × 22) = 176 জন
∴ বিদ্যালয়ে বালিকার সংখ্যা (5 × 22) = 110 জন

∴ যদি 22 জন বালিকা নতুন করে ভর্তি হয় তাহলে বালিকার সংখ্যা হবে = (110 + 22) = 132 জন

∴ বিদ্যালয়ে বালক ও বালিকার সংখ্যার নতুন অনুপাত = 176 : 132
= 4 : 3 [44 দ্বারা ভাগ করে]

৯,৭১০.

The average of A and B is 30, and the average of B and C is 20. What is the value of (A - C)/2?

ক
24
খ
20
গ
12
ঘ
10
ঙ
None

ব্যাখ্যা

Question: The average of A and B is 30, and the average of B and C is 20. What is the value of (A - C)/2?

Solution:
Given,
(A + B)/2 = 30
⇒ A + B = 60 ...... (1)

and,
(B + C)/2 = 20
⇒ B + C = 40 ...... (2)

from (1) - (2) we get,
A + B - B - C = 60 - 40
⇒ A - C = 20
⇒ (A - C)/2 = 20/2
∴ (A - C)/2 = 10

৯,৭১১.

35% of Rifat's income is equal to 25% of Reaz's income. The ratio of their income is-

ক
ক) 7 : 5
খ
খ) 4 : 3
গ
গ) 4 : 7
ঘ
ঘ) 5 : 7
ঙ
ঙ) 3 : 4

ব্যাখ্যা

Question: 35% of Rifat's income is equal to 25% of Reaz's income. The ratio of their income is-

Solution:
Let,
The income of Rifat = x
The income of Reza = y

ATQ,
x × 35% = y × 25%
⇒ x/y = 25/35 = 5/7

∴ x : y = 5 : 7

৯,৭১২.

If 25% of a number is subtracted from a second number, the second number reduces to the five-sixth. The ratio of the first number to the second number is

ক
ক) 1 : 3
খ
খ) 3 : 2
গ
গ) 2 : 3
ঘ
ঘ) None

ব্যাখ্যা

Question: If 25% of a number is subtracted from a second number, the second number reduces to the five-sixth. The ratio of the first number to the second number is

Solution:
Let,
A = First Number
B = Second Number

ATQ,
B - 25A/100 = 5B/6
⇒ B - A/4 = 5B/6
⇒ B = A/4 + 5B/6
⇒ B - 5B/6 = A/4
⇒ B/6 = A/4
⇒ 4B = 6A
⇒ 2B = 3A
∴ A : B = 2 : 3

৯,৭১৩.

The son was born when the father was 25 years old. At what age will the father's age be twice the son's age?

ক
40 years
খ
50 years
গ
60 years
ঘ
70 years

ব্যাখ্যা

প্রশ্ন: The son was born when the father was 25 years old. At what age will the father's age be twice the son's age?

সমাধান:

পিতার বয়স 2a হলে পুত্রের বয়স হবে a বছর
আবার, পিতা পুত্রের চেয়ে 25 বছরের বড় হলে,
পুত্রের বয়স = 2a - 25 বছর

শর্তমতে,

2a - 25 = a

∴ a = 25

অতএব, পিতার বয়স = 2a বছর

= 2 ×25

= 50 বছর

৯,৭১৪.

Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100kg of fresh fruits?

ক
ক) 20 kg
খ
খ) 30 kg
গ
গ) 35 kg
ঘ
ঘ) 40 kg

ব্যাখ্যা

100kg of fresh fruit is 68kg of water and 32kg of non water.
If you dry it you still have 32kg of non water but now it's 80% non water and 20% water.

80% of dry food = 32
100% of dry food = 32 × 100/80 = 40 kg

৯,৭১৫.

If |x - 5| < 6 , then what is the solution-

ক
- 1 < x < 11
খ
- 2 < x < 9
গ
- 3 < x < 10
ঘ
- 1 < x < 8

ব্যাখ্যা

Question: If |x - 5| < 6 , then what is the solution-

Solution:
Given
|x - 5| < 6
⇒ - 6 < x - 5 < 6
⇒ - 6 + 5 < x - 5 + 5 < 6 + 5
⇒ - 1 < x < 11

৯,৭১৬.

ক
18
খ
16
গ
14
ঘ
12

ব্যাখ্যা

Question:

Solution:

৯,৭১৭.

A sum invested at the rate of interest 5% S.I grows to Tk. 5400 in 4 years. The same amount in 3 years at the rate of 10% per annum S.I will grow to-

ক
Tk. 5750
খ
Tk. 5800
গ
Tk. 5850
ঘ
Tk. 5700

ব্যাখ্যা

Question: A sum invested at the rate of interest 5% S.I grows to Tk. 5400 in 4 years. The same amount in 3 years at the rate of 10% per annum S.I will grow to-

Solution:
In the first case,
The sum be Tk. P
I = 5400 - P
n = 4 years
r = 5%

∴ I = Pnr
⇒ 5400 - P = P × 4 × (5/100)
⇒ 5400 - P = P/5
⇒ 27000 - 5P = P
⇒ 6P = 27000
∴ P = 4500

In the second case,
P = 4500
r = 10%
n = 3 years
I =?

∴ I = Pnr
= 4500 × 3 × (10/100)
= 1350

∴ The same amount in 3 years at the rate of 10% per annum S.I will grow to (4500 + 1350) = 5850

৯,৭১৮.

A man deposits Tk. 5000 in a Bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

ক
ক) Tk. 6055
খ
খ) Tk. 6655
গ
গ) Tk. 6565
ঘ
ঘ) Tk. 6775

ব্যাখ্যা

Question: A man deposits Tk. 5000 in a Bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

Solution:
Given,
Principal, P = 5000 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 3 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 5000 × (1 + 1/10)³
= 5000 × (11/10)³
= 5000 × (11/10) × (11/10) × (11/10)
= 6655

৯,৭১৯.

Two-fifth of one-fourth of three seventh of a number is 15. What is the half of the number?

ক
175
খ
157
গ
75
ঘ
57

ব্যাখ্যা

Question: Two-fifth of one-fourth of three seventh of a number is 15. What is the half of the number?

Solution:
let the number is P

ATQ,
P × (3/7) × (1/4) × (2/5) = 15
3P/70 = 15
P = 350

∴ half of the number is = 350/2 = 175

৯,৭২০.

On a sum of money, the simple interest for 2 years is Tk. 320, while the compound interest is Tk. 340, the rate of interest being the same in both the cases. The rate of interest is -

ক
ক) 12.5%
খ
খ) 14.25%
গ
গ) 15%
ঘ
ঘ) 10.5%

ব্যাখ্যা

Simple interest for 2 years is Tk. 320
⇒ Simple interest for first year = 320/2 = 160
⇒ Similarly, simple interest for the second year is also 160
Compound Interest for first year = 160
Compound Interest for second year = 340-160 = 180
we can see that compound Interest for the second year is more than
simple interest for the second year by 180-160 = 20
i.e., Tk. 20 is the simple interest on Tk. 160 for 1 year
R = 100 × S.I./PT
= (100 × 20)/(160 × 1)
= 12.5%

৯,৭২১.

A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 660 for it, how much did it cost to A?

ক
Tk. 200
খ
Tk. 260
গ
Tk. 300
ঘ
Tk. 400

ব্যাখ্যা

Question: A sells an article to B at gain of 25% B sells it to C at a gain of 20% and C sells it to D at a gain 10%. If D pays Tk. 660 for it, how much did it cost to A?

Solution:
Let,
Cost Price for A was = 100

Then, CP for B = (100 + 25% of 100) = 125
CP for C = (125 + 20% of 125) = 150
CP for D = (150 + 10% of 150 )= 165

But, D pay Tk. 660. Then it must be equal to,
165 = 660
1 = 660/165
∴100 = {660 × (100/165)} = 400

So, CP for A = Tk. 400

৯,৭২২.

If the Average of 7 consecutive positive odd integers is P, then what is the average of next seven consecutive odd integers in terms of P?

ক
ক) p+7
খ
খ) p+12
গ
গ) p+14
ঘ
ঘ) p+25
ঙ
ঙ) None

ব্যাখ্যা

7 টি পরপর ধনাত্মক বিজোড় সংখ্যার গড় p
ধরি, সংখ্যাগুলোঃ p-6, p-4, p-2, p, p+2, p+4, p+6

এবং এর পরবর্তি 7 টি ধনাত্মক বিজোড় সংখ্যা হবেঃ p+8, p+10, p+12, p+14, p+16, p+18, p+20
সুতরাং পরবর্তি 7 টি ধনাত্মক বিজোড় সংখ্যার গড় হবে = (7p+98) / 7 = p+14

৯,৭২৩.

Find the value of k if (x - 1) is a factor of 3x² + 2x² - 6x + k = 0

ক
ক) 1
খ
খ) - 3
গ
গ) - 1
ঘ
ঘ) 3

ব্যাখ্যা

3x² + 2x² - 6x + k = 0
⇒ 3(1)² + 2(1)² - 6(1) + k = 0 [As, x - 1 is a factor]
⇒ 3 + 2 - 6 + k = 0
⇒ k = 1

৯,৭২৪.

The principal that amounts to Tk. 4913 in 3 years at (25/4)% per annum compound interest compounded annually, is-

ক
ক) Tk. 4386
খ
খ) Tk. 4266
গ
গ) Tk. 4096
ঘ
ঘ) Tk. 4566

ব্যাখ্যা

Here
C. P = Tk. 4913
Time = 3 years
Rate = (25/4)% = 25/(4 × 100) = 1/16

Principal (P) = ?
C.P = P(1 + r)ⁿ
4913 =P(1 + 1/16)³
4913 =P(17/16)³
P = 4913/(17/16)³
P = 4913 × (16/17) × (16/17) × (16/17)
P = Tk. 4096

৯,৭২৫.

If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 3 times, what is the probability that it will land heads up on the first 2 flips and not on the last flip?

ক
ক) 1/2
খ
খ) 1/8
গ
গ) 1/16
ঘ
ঘ) 1/32

ব্যাখ্যা

Question: If a certain coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 3 times, what is the probability that it will land heads up on the first 2 flips and not on the last flip?

Solution:
The probability of landing heads and not landing on heads is same = 1/2
The probability of first two heads =(1/2) × (1/2)
The probability of last landing not on heads = 1/2
The total probability =(1/2) × (1/2) × (1/2)
= 1/ 2³
= 1/8

৯,৭২৬.

Three numbers are in the ratio 3 : 4 : 6 and their products is 1944. The smallest number is -

ক
ক) 3
খ
খ) 9
গ
গ) 12
ঘ
ঘ) 18

ব্যাখ্যা

Question: Three numbers are in the ratio 3 : 4 : 6 and their products is 1944. The smallest number is -

Solution:
Let the number be 3x, 4x, 6x.

ATQ,
3x × 4x × 6x = 1944
⇒ 72x³ = 1944
⇒ x³ = 1944/72
⇒ x³= 27
∴ x = 3

So the smallest number = 3x = 3 × 3 = 9

৯,৭২৭.

A cylinder has a radius of 7 cm and a height of 10 cm. What is its volume?

ক
1540 cm³
খ
1078 cm³
গ
1680 cm³
ঘ
780 cm³

ব্যাখ্যা

Question: A cylinder has a radius of 7 cm and a height of 10 cm. What is its volume?

Solution:
Radius, r = 7 cm
Height, h = 10 cm

We know,
Volume = πr²h
= (22/7) × (7)² × 10
= 1540 cm³

৯,৭২৮.

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

ক
ক) 2,520m²
খ
খ) 1,520m²
গ
গ) 2,420m²
ঘ
ঘ) 2,480m²

ব্যাখ্যা

We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103
Solving the two equations, we get: l = 63 and b = 40
∴ Area = (l x b) = (63 x 40) m² = 2520 m²

৯,৭২৯.

In a survey among the readers of newspapers, it was found that 65 persons read the Prothom Alo, 40 persons read the Bhorer Kagoj, 45 read the Janakantho, 52 read the Jugantor. If one person is chosen at random from the readers, what is the probability that the person doesn't read the Jugantor?

ক
ক) 26/101
খ
খ) 5/101
গ
গ) 35/101
ঘ
ঘ) 75/101

ব্যাখ্যা

Question: In a survey among the readers of newspapers, it was found that 65 persons read the Prothom Alo, 40 persons read the Bhorer Kagoj, 45 read the Janakantho, 52 read the Jugantor. If one person is chosen at random from the readers, what is the probability that the person doesn't read the Jugantor?

Solution:
Total persons = 65 + 40 + 45 + 52
= 202

probability of that person reading jugantor = 52/202
= 26/101

the probability that the person doesn't read the Jugantor = 1 - 26/101
= (101 - 26)/101
= 75/101

৯,৭৩০.

A sum of money amount to Tk. 720 in 2 years and Tk. 780 in 3 years. The rate per cent is?

ক
ক) 8%
খ
খ) 9%
গ
গ) 10%
ঘ
ঘ) 7%

ব্যাখ্যা

Question: A sum of money amount to Tk. 720 in 2 years and Tk. 780 in 3 years. The rate per cent is?

Solution:
Simple interest for 1 year = Tk. (780 - 720) = Tk. 60
Simple interest for 2 year = Tk. (60 × 2) = Tk. 120
Sum = Tk. (720 - 120) = Tk. 600

We know,
I = Pnr
⇒ r = I/Pn
= (120 × 100)/(600 × 2)
∴ r = 10%

৯,৭৩১.

Which of the following is irrational?

ক
0.75
খ
√256
গ
2/5
ঘ
√27

ব্যাখ্যা

Question: Which of the following is irrational?

Solution:
একটি সংখ্যা অমূলদ (irrational) হয় যদি এটি p/q আকারে প্রকাশ করা না যায়, যেখানে p এবং q পূর্ণসংখ্যা এবং q ≠ 0।

ক) 0.75 = 75/100 = 3/4 = এটি p/q আকারে প্রকাশ করা যায়, তাই এটি মূলদ সংখ্যা।

খ) √256 = 16 একটি পূর্ণবর্গ সংখ্যা (16² = 256), তাই √256 = 16 একটি মূলদ সংখ্যা।

গ) 2/5 = এটি ইতিমধ্যে p/q আকারে আছে, তাই এটি মূলদ সংখ্যা।

ঘ) √27 = √(9 × 3) = 3√3 একটি পূর্ণবর্গ সংখ্যা নয়, তাই √27 একটি অমূলদ সংখ্যা। এটি p/q আকারে প্রকাশ করা যায় না।

উত্তর: ঘ) √27 একটি অমূলদ (irrational) সংখ্যা।

৯,৭৩২.

If two numbers are in a 3 to 4 ratio and their greatest common factor is 5, what's their least common multiple?

ক
40
খ
48
গ
54
ঘ
60

ব্যাখ্যা

Question: If two numbers are in a 3 to 4 ratio and their greatest common factor is 5, what's their least common multiple?

Solution:
Given:
The ratio of two numbers = 3 : 4
and HCF = 5

So the numbers are:
3 × 5 = 15 and 4 × 5 = 20

We know,
First number × Second number = LCM × HCF
⇒ 15 × 20 = LCM × 5
⇒ LCM × 5 = 300
⇒ LCM = 300 ÷ 5 = 60

৯,৭৩৩.

Three girls have candies in the ratio of 7 : 4 : 5. If the girl with the least number of candies has 12 candies, how many candies does the girl with the greatest number have?

ক
18
খ
21
গ
24
ঘ
28

ব্যাখ্যা

Question: Three girls have candies in the ratio of 7 : 4 : 5. If the girl with the least number of candies has 12 candies, how many candies does the girl with the greatest number have?

Solution:
Let their amounts of candies be 7x, 4x, and 5x.

ATQ,
4x = 12
⇒ x = 3

So, the girl with the greatest number of candies has = 7 × 3
= 21 candies

৯,৭৩৪.

The surface area of hollow cylinder with radius 'r' and height 'h' is measured by -

ক
ক) 2πr - h
খ
খ) 2πr + h
গ
গ) πrh
ঘ
ঘ) 2πrh

ব্যাখ্যা

The surface area of a hollow cylinder with radius 'r' and height 'h' is measured by 2πrh.

৯,৭৩৫.

A coin is tossed twice. What is the probability of getting tail on first toss and head on second toss?

ক
1
খ
1/2
গ
1/3
ঘ
1/4

ব্যাখ্যা

On first toss, the probability of getting tail = 1/2
( প্রথম নিক্ষেপে টেইল পাবার সম্ভাবনা = ১/২)
0n second toss, the probability of getting head = 1/2
( ২য় নিক্ষেপে হেড পাবার সম্ভাবনা = ১/২)

So, the probability of getting tail on first toss and head on second toss = 1/2 × 1/2 = 1/4
(প্রথম নিক্ষেপে টেইল ও ২য় নিক্ষেপে হেড পাবার সম্ভাবনা = ১/২ × ১/২ = ১/৪)

৯,৭৩৬.

Find the number that exceeds 36 by the same amount it falls short of 86.

ক
56
খ
55
গ
61
ঘ
66

ব্যাখ্যা

Question: Find the number that exceeds 36 by the same amount it falls short of 86.

Solution:
Let the number be = x

According to the question,
x - 36 = 86 - x
⇒ x + x = 86 + 36
⇒ 2x = 122
⇒ x = 122/2
⇒ x = 61

৯,৭৩৭.

A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-

ক
8 hours
খ
10 hours
গ
11 hours
ঘ
12 hours

ব্যাখ্যা

Question: A reservoir has two pipes, A and B. A can fill the reservoir 5 hours faster than B. If both together fill the reservoir in 6 hours, the reservoir will be filled by A alone in-

Solution:
Let, A alone can fill the reservoir in x hours
B can fill in x + 5 hours

Both complete in 1 hour = (1/x) + (1/ x + 5)
= (2x + 5)/(x² + 5x)

Now
1/{(2x + 5)/(x² + 5x)} = 1/6
(x² + 5x)/(2x + 5) = 6
⇒ x² + 5x = 12x + 30
⇒ x² - 7x - 30 = 0
⇒ x² - 10x + 3x - 30 = 0
⇒ x (x - 10) + 3 (x - 10) = 0
⇒ (x - 10) (x + 3) = 0
∴ x = 10 or, x = -3 , negative value not possible

A alone can fill the reservoir in 10 hours

৯,৭৩৮.

A sum of Tk. 427 is to be divided among A, B and C in such a way that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal. The share of C is?

ক
64
খ
76
গ
84
ঘ
98
ঙ
87

ব্যাখ্যা

Given total sum = Tk. 427
And given that 3 times A’s share, 4 times B’s share and 7 times C’s share are all equal.
=> 3A = 4B = 7C
But given
=> A + B + C = 427
Now express A and B in terms of C i.e
=> (7C/3) + (7C/4) + C = 427
=> C = 84

৯,৭৩৯.

What percent of a is equal to 3a?

ক
100%
খ
150%
গ
300%
ঘ
350%

ব্যাখ্যা

Question: What percent of a is equal to 3a?

Solution:
Let x% of a = 3a
⇒ (x/100) × a = 3a
⇒ x/100 = 3a/a
⇒ x/100 = 3
⇒ x = 100 × 3
∴ x = 300

৯,৭৪০.

The population of Gotham City increases from 175,000 to 262,500. What is the percentage increase in the population?

ক
45%
খ
55%
গ
50%
ঘ
60%

ব্যাখ্যা

Question: The population of Gotham City increases from 175,000 to 262,500. What is the percentage increase in the population?

Solution:
জনসংখ্যা বৃদ্ধি পেয়েছে
= (262500 - 175000) = 87500

175000 জনে বৃদ্ধি পায় = 87500 জন
∴ 1 জনে বৃদ্ধি পায় = 87500/175000 জন
∴ 100 জনে বৃদ্ধি পায় = (87500 × 100)/175000 = 50 জন

∴ জনসংখ্যা বৃদ্ধির শতকরা হার = 50%

৯,৭৪১.

Bowl S contains only marbles. If (1/4) of the marbles were removed, the bowl would be filled to (1/2) of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

ক
100
খ
200
গ
250
ঘ
300

ব্যাখ্যা

Question: Bowl S contains only marbles. If (1/4) of the marbles were removed, the bowl would be filled to (1/2) of its capacity. If 100 marbles were added, the bowl would be full. How many marbles are in bowl S?

Solution:
Let
there are x number of marbles and capacity of the bowl is y marbles
3x/4 = y/2
⇒ y = 3x/2

x + 100 = y
⇒ x + 100 = 3x/2
⇒ (3x/2) - x = 100
⇒ x/2 = 100
∴ x = 200

৯,৭৪২.

12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The radius of each sphere is-

ক
ক) 4 cm
খ
খ) 2 cm
গ
গ) 1 cm
ঘ
ঘ) 5 cm

ব্যাখ্যা

Question: 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The radius of each sphere is-

Solution:
Let the radius of each sphere be r cm

∴ Volume of 12 spheres = Volume of cylinder
⇒ 12 × (4/3)π × r³ = π × 8² × 2
⇒ r³ = (8 × 8 × 2 × 3)/(12 × 4)
⇒ r³ = 8
⇒ r = 2 cm

৯,৭৪৩.

What is the average of 1², 2², 3², 4², 5², 6^2, 7²?

ক
ক) 20
খ
খ) 25
গ
গ) 30
ঘ
ঘ) 40

ব্যাখ্যা

Question: What is the average of 1², 2², 3², 4², 5², 6^2, 7²?

Solution:
Average = (1² + 2² + 3² + 4² + 5²+6²+7²)/7
= (1 + 4 + 9 +16 + 25 + 36 + 49)/7
= 140/7
= 20

Alternative Solution:
Sum = {n(n + 1)(2n + 1)}/6
= {7(7 + 1)(14 + 1)}/6
= (7 × 8 × 15)/6
= 140

Average = 140/7 = 20

৯,৭৪৪.

An officer was appointed on maximum daily wages on contract money of Tk. 6720. But on being absent for some days, he was paid Tk. 5600. For how many days was he absent?

ক
5 days
খ
4 days
গ
3 days
ঘ
1 days

ব্যাখ্যা

Question: An officer was appointed on maximum daily wages on contract money of Tk. 6720. But on being absent for some days, he was paid Tk. 5600. For how many days was he absent?

Solution:
Maximum daily wages of the officers = H.C.F of Tk. 6720 and Tk. 5600

H.C.F of 6720 & 5600 = 1120

Maximum daily wage = Tk. 1120
Total days appointed = 6720 ÷ 1120 = 6 days

Days present = 5600 ÷ 1120 = 5 days
Absent days = 6 − 5 = 1

৯,৭৪৫.

If the sum of the interior angels of a regular polygon measures 1440°, how many sides does the polygon have?

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

ব্যাখ্যা

Question: If the sum of the interior angels of a regular polygon measures 1440°, how many sides does the polygon have?

Solution:
দেয়া আছে,
একটি সুষমভুজের অন্ত:কোণের সমষ্টি 1440°
n সংখ্যক বাহু দ্বারা সীমাবদ্ধ ক্ষেত্রের সকল অন্তঃস্থ কোনের সমষ্টি
= (n - 2) × 180°

প্রশ্নমতে,
(n - 2) × 180° =1440°
n - 2 = 1440°/180°
n - 2 = 8
n = 2 + 8
n = 10

৯,৭৪৬.

On selling 17 balls at Tk. 840 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

ক
Tk. 85
খ
Tk. 50
গ
Tk. 60
ঘ
Tk. 70

ব্যাখ্যা

Question: On selling 17 balls at Tk. 840 there is a loss equal to the cost price of 5 balls. The cost price of a ball is-

Solution:
Let,
The cost price of 1 ball is = Tk. x
The cost price of 17 balls is = Tk. 17x

We know,
Cost price - Selling price = Loss
17x - 840 = 5x
⇒ 12x = 840
⇒ x = 840/12
∴ x = 70

∴ The cost price of 1 ball is Tk. 70

৯,৭৪৭.

Calculate the simple interest if the principal amount is Tk. 50000 and the rate is 2% for 4 years.

ক
Tk. 4000
খ
Tk. 40000
গ
Tk. 40
ঘ
Tk. 400

ব্যাখ্যা

Question: Calculate the simple interest if the principal amount is Tk. 50000 and the rate is 2% for 4 years.

Solution:
S.I. = PNR/100
⇒ S.I. = (50000 × 2 × 4)/100
= 4000

৯,৭৪৮.

A person buys goods worth tk 600. He sells half of it at a gain of 10%. At what gain % must he sell the remaining goods to achieve an overall gain of 15%?

ক
15%
খ
20%
গ
25%
ঘ
30%

ব্যাখ্যা

Question: A person buys goods worth tk 600. He sells half of it at a gain of 10%. At what gain % must he sell the remaining goods to achieve an overall gain of 15%?

Solution:
To gain 15% on the whole, he must sell all goods for = 600 + 15% of 600
= 690 tk

He sells half at a 10% gain = 300 + 10% of 300
= 330 tk
Required balance = 690 - 330 = 360 tk
He must gain tk 60 on the remaining tk 300.

∴ % gain on remainder goods= (60 × 100) / 300 = 20%

৯,৭৪৯.

What is the minimum number of chocolates that must be added to an existing stock of 966 chocolates, so the total stock can be equally distributed among 6, 7, 8 or 9 person?

ক
42
খ
36
গ
48
ঘ
32

ব্যাখ্যা

Question: What is the minimum number of chocolates that must be added to an existing stock of 966 chocolates, so the total stock can be equally distributed among 6, 7, 8 or 9 person?

Solution:
LCM of 6, 7, 8 or 9 is,
6 = 2 × 3
7 = 7
8 = 2 × 2 × 2
9 = 3 × 3
∴ LCM = 2³ × 3² × 7 = 8 × 9 × 7 = 504

Double of the chocolates = 2 × 504 = 1008
The chocolate to be added = 1008 - 966 = 42

So the minimum number of chocolates that must be added to the stock of 966 is 42.

৯,৭৫০.

The L.C.M of 3/4, 6/7, 9/8 is:

ক
ক) 3
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 18

ব্যাখ্যা

Required L.C.M = (L.C.M of 3, 6, 9)/(H.C.F of 4, 7, 8)
=18/1 = 18
Answer : 18

৯,৭৫১.

A man completes a certain journey in 8 hours. He covers one-third distance at 60 kmph and the rest at 80 kmph. The length of the journey-

ক
ক) 320 km
খ
খ) 360 km
গ
গ) 480 km
ঘ
ঘ) 576 km

ব্যাখ্যা

Question: A man completes a certain journey in 8 hours. He covers one-third distance at 60 kmph and the rest at 80 kmph. The length of the journey-

Solution:
Let, the length of the journey be x km
he covers x/3 km at 60 kmph
he covers (x - x/3) = 2x/3 at 80 kmph

ATQ,
(x/3)/60 + (2x/3)/80 = 8
x/180 + x/120 = 8
5x/360 = 8
x = 576 km

৯,৭৫২.

If the sum of seven consecutive odd integers is 385, what is the largest number?

ক
55
খ
61
গ
65
ঘ
71

ব্যাখ্যা

Question: If the sum of seven consecutive odd integers is 385, what is the largest number?

Solution:
ধরি, মাঝের সংখ্যাটি = x

সুতরাং, 7টি ক্রমিক বিজোড় সংখ্যা হবে যথাক্রমে: x - 6, x - 4, x - 2, x, x + 2, x + 4 এবং x + 6

প্রশ্নমতে,
(x - 6) + (x - 4) + (x - 2) + x + (x + 2) + (x + 4) + (x + 6) = 385
⇒ 7x = 385
⇒ x = 55

∴ মাঝের সংখ্যা, x = 55

∴ সবচেয়ে বড় সংখ্যা = x + 6 = 55 + 6 = 61

৯,৭৫৩.

Rahim is 12 years old. He is three times older than Karim. What will be the age of Rahim when he is two times older than Karim?

ক
ক) 15 years
খ
খ) 16 years
গ
গ) 17 years
ঘ
ঘ) 18 years

ব্যাখ্যা

Question: Rahim is 12 years old. He is three times older than Karim. What will be the age of Rahim when he is two times older than Karim?

Solution:
Rahim is 12 years old.
He is three times older than Karim.

karim is = 12 / 3 years
= 4 years

let, Rahim's age will be two times than karim after x years

(12 + x) = 2 (4 + x)
⇒ 12 +x = 8 + 2x
⇒ 2x - x = 12 - 8
∴ x = 4

Rahim's age will be = 12 + 4 years
= 16 years

৯,৭৫৪.

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) 4
খ
খ) 5
গ
গ) 6
ঘ
ঘ) 8

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

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

৯,৭৫৫.

If 15% of 40 is greater than 25% of a number by 2, then the number is-

ক
ক) 12
খ
খ) 16
গ
গ) 20
ঘ
ঘ) 24

ব্যাখ্যা

প্রশ্ন: If 15% of 40 is greater than 25% of a number by 2, then the number is-

সমাধান:
15% of 40
= 40 × 15/100
= 6

ধরি, সংখ্যাটি x

প্রশ্নমতে,
6 = x × 25% + 2
⇒ 6 = (x × 25/100) + 2
⇒ 6 = (x/4) + 2
⇒ (x/4) = 6 - 2 = 4
∴ x = 4 × 4
= 16

৯,৭৫৬.

If the workforce is tripled, how much longer will it take to finish the task?

ক
2 times
খ
1/2 times
গ
1/5 times
ঘ
1/3 times

ব্যাখ্যা

Question: If the workforce is tripled, how much longer will it take to finish the task?

Solution:
ধরি,
শ্রমিক সংখ্যা = x, এর তিনগুণ = ৩x,
সময় = n
x জন কাজটি করে n সময়ে

১ জন কাজটি করে = xn সময়ে
∴ ৩x জন কাজটি করে = xn/৩x
= n/৩ সময়ে বা ১/৩ সময়ে।

৯,৭৫৭.

Fahim's regular pay is Taka 40 per hour up to 30 hours. Overtime is 2.5 times the payment for regular time. If he was paid Taka 1680, how many hours of overtime did he work?

ক
8
খ
6
গ
5
ঘ
4

ব্যাখ্যা

30 ঘণ্টার জন্য regular payment = (30 * 40) টাকা = 1200 টাকা
Overtime এর টাকার পরিমান = (1680 - 1200) টাকা = 480 টাকা
Over time এর প্রতিদিনের টাকার পরিমান regular payment এর 2.5 গুণ।
সুতরাং নির্ণেয় মোট সময় = 480 / (2.5 * 40) = 480/100 = 4.8 ঘণ্টা = 4 ঘণ্টা 48 মিনিট যা 5 ঘণ্টার কাছাকাছি।

৯,৭৫৮.

75 employees have been able to finish only one-third of the project in 40 hours. The time committed by the management to complete the project was 90 hours. How many more employees should join the team to complete the project on time?

ক
ক) 45
খ
খ) 55
গ
গ) 100
ঘ
ঘ) 150

ব্যাখ্যা

Remaining work = 1 - (1/3) = 2/3
Let number of more employees needed be E
Thus (75+E) employees complete 2/3 works in 50 hours.
∴ 75 employes × 40 hours × (2/3) = (75 + E) × 50 hours × (1/3)
∴ E = 45 = these many more employees are needed.

৯,৭৫৯.

A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time to fill the cistern completely?

ক
ক) 9 hours
খ
খ) 10 hours
গ
গ) 4 hours
ঘ
ঘ) None of above

ব্যাখ্যা

Question: A pipe can fill a cistern in 16 hours. After half the tank is filled, three more similar taps are opened. What is the total time to fill the cistern completely?

Solution:
Time is taken to fill half of the tank = (1/2) × 16 = 8 hrs
In 1 hour pipe can fill = 1/16 part filled by 4 pipes in1 hour = 4 × (1/16) = 1/4 part
So, remaining half part = 4 × (1/2) = 2 hours
∴ Total time = 8 + 2 = 10 hours.

৯,৭৬০.

Calculate the volume of a cylinder that is 12 cm tall with a base diameter of 7 cm.

ক
147π cm³
খ
142π cm³
গ
47π cm³
ঘ
252π cm³

ব্যাখ্যা

Question: Calculate the volume of a cylinder that is 12 cm tall with a base diameter of 7 cm.
(12 সে.মি. উচ্চতা বিশিষ্ট একটি সিলিন্ডারের ভূমির ব্যাস 7 সে.মি.। সিলিন্ডারটির আয়তন কত?)

Solution:
সিলিন্ডারের উচ্চতা h = 12 সে.মি.
সিলিন্ডারের ভূমির ব্যাস 7 সে.মি.
সিলিন্ডারের ভূমির ব্যাসার্ধ r = 7/2 সে.মি.

সিলিন্ডারটির আয়তন = πr²h
= π × (7/2)² ×12
= π × (49/4) × 12
= 147π ঘন সে.মি.

৯,৭৬১.

The difference between the two numbers is 20% of the larger number. If the smaller number is 12, the larger one is:

ক
10
খ
15
গ
20
ঘ
25

ব্যাখ্যা

Question: The difference between the two numbers is 20% of the larger number. If the smaller number is 12, the larger one is:

Solution:
Let the number be x

Then,
x − 12 = 20% of x
⇒ x − 12 = x/5
⇒ x − x/5 = 12
⇒ 4x/5 = 12
⇒ x = (12 × 5)/4
∴ x = 15

৯,৭৬২.

Sharif travelled a distance of 41 km in 9 hours. He travelled partly on foot 3 km/hr and partly on bicycle 9 km/hr. The distance travelled on bicycle is:

ক
ক) 22 km.
খ
খ) 21 km.
গ
গ) 24 km.
ঘ
ঘ) 25 km.

ব্যাখ্যা

Question: Sharif travelled a distance of 41 km in 9 hours. He travelled partly on foot 3 km/hr and partly on bicycle 9 km/hr. The distance travelled on bicycle is:

Solution:
Let,
the distance travelled on bicycle be x km.
distance travelled on foot = (41 -x) km.

ATQ,
Or, (x/9) + (41 − x)/3 = 9
Or, x + 123 − 3x = 81
Or, 2x = 42
Or, x = 21

৯,৭৬৩.

The factor of 2x² + x - 3 is -

ক
ক) (3x + 2)(x - 3)
খ
খ) (2x + 3)(2x - 1)
গ
গ) (2x + 3)(x - 1)
ঘ
ঘ) (3x + 1)(x - 2)

ব্যাখ্যা

2x² + x - 3
2x² + 3x - 2x - 3
x(2x + 3) - 1(2x + 3)
(2x + 3)(x - 1)

৯,৭৬৪.

If x = 0.1039, then the value of √(4x² - 4x + 1) + 3x is:

ক
ক) - 1.1139
খ
খ) 0.1039
গ
গ) 1.9339
ঘ
ঘ) 1.1039

ব্যাখ্যা

Given that
x = 0.1039
Now
√(4x² - 4x + 1) + 3x
=√{(1)² + (2x)² - 2 x 1 x 2x} + 3x
= √(1 - 2x)² + 3x
= 1 - 2x + 3x
= 1 + x
= 1 + 0.1039
= 1.1039

৯,৭৬৫.

The square root of (4 + 3√5)(4 - 3√5) is:

ক
11i
খ
i√11
গ
i√29
ঘ
i√7

ব্যাখ্যা

Question: The square root of (4 + 3√5)(4 - 3√5) is:

Solution:
Using the identity (a + b)(a - b) = a² - b²

We get,
(4 + 3√5)(4 - 3√5) = 4² - (3√5)²
= 16 - 45
= -29

Since the result is negative,
√(-29) = i√29

Therefore, the square root is i√29.

৯,৭৬৬.

If rsinθ = 1, rcosθ = √3 then the value of √3tanθ + 3 = ?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 3√3

ব্যাখ্যা

Question: If rsinθ = 1, rcosθ = √3 then the value of √3tanθ + 3 = ?

Solution:
দেওয়া আছে,
rsinθ = 1 ......... (1)
rcosθ = √3 .............. (2)

(1) ÷ (2) হতে পাই
rsinθ/rcosθ =1/√3
⇒ tanθ = 1/√3
⇒ √3√tanθ = 1

এখন, √3tanθ + 3 = 1 + 3
∴ √3tanθ + 3 = 4

৯,৭৬৭.

The number n yields a remainder p when divided by 15 and a remainder q when divided by 5. If p = q + 10, then which one of the following could be the value of n?

ক
24
খ
32
গ
43
ঘ
50

ব্যাখ্যা

Question: The number n yields a remainder p when divided by 15 and a remainder q when divided by 5. If p = q+10, then which one of the following could be the value of n?

Solution:
প্রদত্ত শর্ত অনুযায়ী, আমাদের এমন একটি সংখ্যা n খুঁজে বের করতে হবে, যাকে 15 দ্বারা ভাগ করলে ভাগশেষ p এবং 5 দ্বারা ভাগ করলে ভাগশেষ q পাওয়া যায়, যেখানে p = q + 10।

• অপশন (ক):
ধরা যাক n = 24
24 ÷ 15 = 1 এবং ভাগশেষ p = 9।
24 ÷ 5 = 4 এবং ভাগশেষ q = 4।
শর্ত অনুযায়ী, p = q + 10। এখানে 9 ≠ 4 + 10 ; সুতরাং, এই অপশনটি সঠিক নয়।

• অপশন (খ):
ধরা যাক n = 32
32 ÷ 15 = 2 এবং ভাগশেষ p = 2।
32 ÷ 5 = 6 এবং ভাগশেষ q = 2।
শর্ত অনুযায়ী, p = q + 10। এখানে 2 ≠ 2 + 10 ; সুতরাং, এই অপশনটি সঠিক নয়।

• অপশন (গ):
ধরা যাক n = 43
43 ÷ 15 = 2 এবং ভাগশেষ p = 13।
43 ÷ 5 = 8 এবং ভাগশেষ q = 3।
শর্ত অনুযায়ী, p = q + 10। এখানে 13 = 3 + 10 = 13, যা সত্য। সুতরাং, এই অপশনটি সঠিক।

• অপশন (ঘ):
ধরা যাক n = 50
50 ÷ 15 = 3 এবং ভাগশেষ p = 5।
50 ÷ 5 = 10 এবং ভাগশেষ q = 0।
শর্ত অনুযায়ী p = q + 10। এখানে 5 ≠ 0 + 10 ; সুতরাং, এই অপশনটি সঠিক নয়।

৯,৭৬৮.

If 3x + 2y = 8 and 2x - 2y = 2, then find the value of (4 + 3x).

ক
- 2
খ
6
গ
12
ঘ
10

ব্যাখ্যা

Question: If (3x + 2y) = 8 and (2x - 2y) = 2, then find the value of (4 + 3x).

Solution:
3x + 2y = 8........(1)
⇒ (2x - 2y) = 2
⇒ 2(x - y) = 2
⇒ x - y = 1
x = 1 + y ..............(2)

x এর মান (1) নং এ বসিয়ে পাই
3x + 2y = 8
⇒ 3(1 + y) + 2y = 8
⇒ 3 + 3y +2y = 8
⇒ 3 + 5y = 8
⇒ 5y = 8 - 3
⇒ 5y = 5
∴ y = 1

y এর মান (2) নং এ বসিয়ে পাই
x = 1 + y
⇒ x= 1 + 1
∴ x = 2

প্রদত্ত রাশি = 4 + 3x = 4 + 3 × 2 = 4 + 6 = 10

৯,৭৬৯.

A 144 liters of mixture contains milk and water in the ratio of 5 : 7. How much milk needs to be added to this mixture so that the new ratio is 23 : 21 respectively?

ক
ক) 30
খ
খ) 32
গ
গ) 34
ঘ
ঘ) 36
ঙ
ঙ) 38

ব্যাখ্যা

Milk = 144 × 5/12 = 60L
Water = (144 - 60) = 84 L
ATQ,
(60 + x)/(144 + x) = 23/44
Or, 2640 + 44x = 3312 + 23x
Or, 21x = 672
Or, x = 672/21
or, x = 32L

Solution 2:
ATQ,
(60 + x)/84 = 23/21
Or, 60×21 + 21x = 23×84
Or, 21x = 672
or, x = 32 L

৯,৭৭০.

There are 12 true-false questions in an examination, these questions can be answered in-

ক
4096
খ
2048
গ
1024
ঘ
None of these

ব্যাখ্যা

Question: There are 12 true-false questions in an examination, these questions can be answered in-

Solution:

There are 12 true-false questions.

Each question can be answered in two ways i.e. true or false.

Therefore, the total number of ways is
= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
= (2 × 2 × 2 × 2) × (2 × 2 × 2 × 2) × (2 × 2 × 2 × 2)
= 2⁴ × 2⁴ × 2⁴
= 16 × 16 × 16
= 4096

∴ There are 12 true-false questions in an examination, these questions can be answered in- 4096 ways.

৯,৭৭১.

A sum of money amounts to 3300 in 2 years and Tk. 3600 in 5 years. What is the principal amount?

ক
Tk. 3100
খ
Tk. 2950
গ
Tk. 2850
ঘ
Tk. 2700

ব্যাখ্যা

Question: A sum of money amounts to 3300 in 2 years and Tk. 3600 in 5 years. What is the principal amount?

Solution:
After two years the amount is Tk. 3300 and in the next three years it becomes Tk. 3600.

Therefore, S.I for three years = 3600 - 3300 = 300
S.I for one year = 300/3 = 100
S.I for two years = 100 × 2 = 200

∴ Principal = 3300 - 200 = 3100

৯,৭৭২.

- 1 হতে কত বিয়োগ করলে বিয়োগফল 0 (শূণ্য) হবে?

ক
2
খ
- 1
গ
1
ঘ
4

ব্যাখ্যা

প্রশ্ন: -1 হতে কত বিয়োগ করলে বিয়োগফল 0 (শূণ্য) হবে?

সমাধান:
- 1 - ( - 1)
= - 1 + 1
= 0

অর্থাৎ, -1 হতে -1 বিয়োগ করলে বিয়োগফল 0 (শূণ্য) হবে।

৯,৭৭৩.

The dimensions of a certain machine are 48'' X 30'' X 52''. If the size of the machine is increased proportionately until the sum of its dimensions equals 156''. What will be the increase in the shortest side?

ক
ক) 6
খ
খ) 13
গ
গ) 26
ঘ
ঘ) 32
ঙ
ঙ) Cannot be determined

ব্যাখ্যা

Sum of present dimension 48+30+52 = 130.
New dimension = 156.
Increase in dimension = 26.
Ratio of dimensions = 48:30:52 ⇒ 24:15:26.
Therefore, increase in the shortest side = 15×(26)/(24+15+26) = 6.

৯,৭৭৪.

If x * y = x² + y² - xy, then the value of 13*2 is?

ক
ক) 147
খ
খ) 157
গ
গ) 126
ঘ
ঘ) 137

ব্যাখ্যা

Question: If x * y = x² + y² - xy, then the value of 13*2 is?

Solution:
13*2 = (13)² + (2)² - (13 × 2)
= 169 + 4 - 26
= 147

৯,৭৭৫.

The simple interest on a sum of money at 10% per annum for 4 years is half the sum. What is the value of the sum?

ক
Tk. 5000
খ
Tk. 8000
গ
Tk. 10000
ঘ
Data is inadequate

ব্যাখ্যা

Question: The simple interest on a sum of money at 10% per annum for 4 years is half the sum. What is the value of the sum?

Solution:
ধরি, আসল = P
মুনাফার হার, r = 10%
সময়, n = 4 বছর
মুনাফা, I = P/2

আমরা জানি,
I = Pnr/100
⇒ P/2 = (P × 4 × 10)/100
⇒ P/2 = 40P/100
⇒ P/2 = 2P/5
⇒ (P/2) - (2P/5) = 0
⇒ (5P - 4P)/10 = 0
⇒ P/10 = 0
⇒ P = 0

যেহেতু আসলের মান 0 হতে পারে না, তাই প্রদত্ত তথ্যটি সঠিক নয় বা অপর্যাপ্ত।

৯,৭৭৬.

Two trains start from station P and Q and travel towards each other at speeds of 60 km/hr and 80 km/hr respectively. At the time of their meeting, the second train has traveled 80 km more than the first. The distance between P and Q is:

ক
450 km
খ
520 km
গ
560 km
ঘ
610 km

ব্যাখ্যা

Question: Two trains start from station P and Q and travel towards each other at speeds of 60 km/hr and 80 km/hr respectively. At the time of their meeting, the second train has traveled 80 km more than the first. The distance between P and Q is:

সমাধান:
দ্বিতীয় ট্রেনের গতিবেগ বেশি = (80 - 60) কিমি/ঘন্টা
= 20 কিমি/ঘন্টা।

দ্বিতীয় ট্রেনটি প্রথম ট্রেনের চেয়ে 80 কিমি বেশি ভ্রমণ করেছে।
এই বাড়তি দূরত্ব অতিক্রম করার সময় = দূরত্ব/গতিবেগ
= 80 কিমি/20 কিমি/ঘন্টা
= 4 ঘন্টা

যেহেতু ট্রেন দুটি একই সময়ে যাত্রা শুরু করেছিল, তাই তাদের মিলিত হতে 4 ঘন্টা সময় লেগেছে।

ট্রেন দুটির আপেক্ষিক গতিবেগ (Relative speed) = (60 + 80) কিমি/ঘন্টা
= 140 কিমি/ঘন্টা।

সুতরাং, মোট অতিক্রান্ত দূরত্ব = আপেক্ষিক গতিবেগ × সময়
= 140 কিমি/ঘন্টা × 4 ঘন্টা
= 560 কিমি

সুতরাং, P এবং Q স্টেশনের মধ্যবর্তী দূরত্ব হলো 560 কিমি।

৯,৭৭৭.

Abir, Babul, and Chandan invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If Chandan's share of profit is Tk. 54000, find the total profit earned.

ক
Tk. 120000
খ
Tk. 120050
গ
Tk. 130000
ঘ
Tk. 130500

ব্যাখ্যা

Question: Abir, Babul, and Chandan invest 63000, 56000, and 84000 respectively to start a business. After one year, the profit is distributed in the ratio of their investments. If Chandan's share of profit is Tk. 54000, find the total profit earned.

Solution:
Let the total profit = x
The ratio of investment = 63000 : 56000 : 84000
= 63 : 56 : 84
= 9 : 8 : 12
Now, sum of the ratios = 29

Chandan's share = (12/29) × x = 54000
⇒ x = (54000 × 29)/12
x = 130500

Hence, the total profit = Tk. 130500

৯,৭৭৮.

After decreasing 24% in the price of an article the discounted price becomes Tk. 912. Find the actual price of the article?

ক
ক) Tk.1400
খ
খ) Tk.1300
গ
গ) Tk.1200
ঘ
ঘ) Tk.1100

ব্যাখ্যা

ধরি,
পণ্যটির প্রকৃত মূল্য x টাকা

প্রশ্নমতে,
x এর 76%= 912
76x /100 = 912
76x = 91200
x = 91200/76
x = 1200

পণ্যটির প্রকৃত মূল্য 1200 টাকা

৯,৭৭৯.

A container contains 64 litres of milk. From this container 16 litres of milk was taken out and replaced by water. This process was repeated overall three times. How much milk is now contained by the container?

ক
ক) 20
খ
খ) 37
গ
গ) 27
ঘ
ঘ) 34

ব্যাখ্যা

Question: A container contains 64 litres of milk. From this container 16 litres of milk was taken out and replaced by water. This process was repeated overall three times. How much milk is now contained by the container?

Solution:
After first replacement the ratio of milk and water is 48 : 16 = 3 : 1

After second replacement,
remaining milk = 48 - (3/4 of 16) = 48 - 12 = 36
water = 16 +12= 16 + 12 = 28
∴ ratio = 36 : 28 = 9 : 7

After third replacement,
remaining milk = 36 - (9/16 of 16) = 36 - 9 = 27
water = 28 + 9 = 37
∴ ratio = 27 : 37

shortcut,
after three replacement the reamining milk will be = 64 × (3/4)³
= 64 × 27/64
= 27

৯,৭৮০.

The banker's gain on a sum due 3 years hence at 12% per annum is Tk. 360. The banker's discount is:

ক
ক) 1360
খ
খ) 1000
গ
গ) 360
ঘ
ঘ) 640

ব্যাখ্যা

BG = Tk. 360
T = 3 years
R = 12%
TD = (BG×100)/TR
= (360×100)/(3×12)
= Tk. 1000
BG = BD - TD
⇒ BD = BG + TD = 360 + 1000 = Tk. 1360

৯,৭৮১.

In a class, 54 students are good in Bangla only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Bangla and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in either Bangla or Mathematics but not in English?

ক
135
খ
98
গ
108
ঘ
116
ঙ
125

ব্যাখ্যা

Question: In a class, 54 students are good in Bangla only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Bangla and Mathematics. 10 students are good in all three subjects. What is the number of students who are good in either Bangla or Mathematics but not in English?

Solution:

No. of students who are good in either Bangla or Mathematics but not in English = 54 + 18 + 63 = 135
Let B₁M₁E₁ denote the set of students studying Bangla, Mathematics and English.
No. of students of English only = 41
No. of students of Bangla only = 63
No. of students of Maths only = 54
n(B ∩ M ∩ E) = 10
n(B ∩ M) = 18
No. of students who study 'B' or 'M' but not 'E' = 63 + 54 + 18 - 10 = 125

৯,৭৮২.

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

ক
ক) 75
খ
খ) 82
গ
গ) 100
ঘ
ঘ) 110
ঙ
ঙ) 120

ব্যাখ্যা

Originally let there be x men.

Less men, More days (Indirect Proportion)

Therefore, (x - 10) : x :: 100 :110

=> (x - 10) × 110 = x × 100
=> x = 110

৯,৭৮৩.

If January 1, 1996, was Monday, what day of the week was January 1, 1997?

ক
Thursday
খ
Wednesday
গ
Friday
ঘ
Sunday

ব্যাখ্যা

Question: If January 1, 1996, was Monday, what day of the week was January 1, 1997?

Solution:
The year 1996 is divisible by 4, so it is a leap year with 2 odd days.

As per the question, the first day of the year 1996 was Monday, so the first day of the year 1997 must be two days after Monday. So, it was Wednesday.

৯,৭৮৪.

What number will replace the '?' mark?

ক
88
খ
76
গ
68
ঘ
65

ব্যাখ্যা

Question: What number will replace the '?' mark?

Solution:
এখানে,
নিচের ১ম সংখ্যা + নিচের দুই সংখ্যার পার্থক্য = উপরের সংখ্যা।

১ম চিত্রে,
25 + (25 - 10) = 40

২য় চিত্রে,
55 + (55 - 20) = 90

একইভাবে,
৩য় চিত্রে, 45 + (45 - 14) = 76

৯,৭৮৫.

In a primary school the average weight of male students is 65.9 kg and the average weight of female students is 57 kg. If the average weight of all the students (both male and female) is 60.3 kg and the number of male students in the school is 66, what is the number of female students in the school?

ক
ক) 162
খ
খ) 168
গ
গ) 180
ঘ
ঘ) 112

ব্যাখ্যা

Let the number of female students be x
Let the weight of female students = 57x
Number of male students = 66
Total weights of male students = 65.9 × 66
The average weight of all the students = 60.3 kg
Total weights of all the students = 60.3 (66 + x)

According to the given information,
Then,
⇒ 60.3 (66 + x) = 66 × 65.9 + 57x
⇒ 60.3 × 66 + 60.3x = 66 × 65.9 + 57x
⇒ 60.3x - 57x = 66 (65.9 - 60.3)
⇒ 3.3x = 66 × 5.6

∴ x = (66 × 5.6)/3.3
⇒ x = 2 × 56
⇒ x = 112

৯,৭৮৬.

How many points are both 4 units from the origin and also 2 units from the line y = 4?

ক
1
খ
2
গ
3
ঘ
4

ব্যাখ্যা

Question: How many points are both 4 units from the origin and also 2 units from the line y = 4?

Solution:
১ম শর্ত:
মূলবিন্দু (0, 0) থেকে 4 ইউনিট দূরত্বে থাকা বিন্দুগুলো একটি বৃত্ত তৈরি করে, যার সমীকরণ x² + y² = 4²। এই বৃত্তটি y-অক্ষে সর্বোচ্চ (0, 4) এবং সর্বনিম্ন (0, -4) বিন্দু পর্যন্ত বিস্তৃত।

২য় শর্ত:
y = 4 রেখা থেকে ২ ইউনিট দূরত্বে থাকা বিন্দুগুলো দুটি সমান্তরাল রেখা তৈরি করে।

একটি রেখা হবে: y = 4 + 2 = 6
অন্য রেখাটি হবে: y = 4 - 2 = 2

এখন ছেদবিন্দু পরীক্ষা:
১. y = 6 রেখাটি বৃত্তের সীমানার (y = 4) বাইরে অবস্থিত, তাই এটি বৃত্তকে কোথাও ছেদ করবে না।
২. y = 2 রেখাটি বৃত্তের ব্যাসার্ধের (৪) ভেতরে অবস্থিত। আমরা জানি, একটি সরলরেখা বৃত্তের ভেতর দিয়ে গেলে তা বৃত্তকে ঠিক ২ টি বিন্দুতে ছেদ করে।

অতএব, উভয় শর্ত পূরণকারী বিন্দুর সংখ্যা মোট ২ টি।

৯,৭৮৭.

The monthly incomes of two persons are in the ratio 5 : 4 and their monthly expenditures are in the ratio of 9 : 7. If each saves BDT 50 per month, what would be the total amount of their monthly expenditure?

ক
900 tk
খ
800 tk
গ
750 tk
ঘ
850 tk

ব্যাখ্যা

Question: The monthly incomes of two persons are in the ratio 5 : 4 and their monthly expenditures are in the ratio of 9 : 7. If each saves BDT 50 per month, what would be the total amount of their monthly expenditure?

Solution:
Let,
Their monthly income 5a and 4a
Their monthly expenses 9b and 7b

ATQ,
5a - 9b = 50 ..............(1)
4a - 7b = 50 ...............(2)

Multiply equation (1) and (2) by 4 and 5 respectively,
20a - 36b = 200 .............(3)
20a - 35b = 250 ..............(4)

(3) - (4) ⇒
20a - 36b- 20a + 35b = 200 - 250
or, - b = - 50
∴ b = 50

Hence, their total monthly expenditure = 9 × 50 + 7 × 50 = 450 + 350 = 800 tk

৯,৭৮৮.

20 litres of a mixture contains milk and water 4 : 1. Then the amount of water to be added to the mixture so as to have milk and water in ratio 2 : 1 is-

ক
7 litres
খ
4 litres
গ
5 litres
ঘ
6 litres

ব্যাখ্যা

Question: 20 litres of a mixture contains milk and water 4 : 1. Then the amount of water to be added to the mixture so as to have milk and water in ratio 2 : 1 is-

Solution:
In 20 litres of mixture,
quantity of mik = 20 × (4/5) = 16 litres
quantity of water = 20 × (1/5) = 4 litres
Let,
The quantity of water be added m litres
ATQ,
16 : (4 + m) = 2 : 1
or, 16/(4 + m) = 2/1
or, 2m + 8 = 16
or, 2m = 16 - 8
or, 2m = 8
∴ m = 8/2 = 4

∴ 4 litres water to be added to the mixture.

৯,৭৮৯.

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

ক
4 years
খ
5 years
গ
6 years
ঘ
7 years

ব্যাখ্যা

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

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

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

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

৯,৭৯০.

The volume of two cubes are in the ratio 64 : 27 . The ratio of their surface area is-

ক
ক) 8 : 9
খ
খ) 4 : 6
গ
গ) 16 : 9
ঘ
ঘ) 25 : 9

ব্যাখ্যা

Question: The volume of two cubes are in the ratio 64 : 27 . The ratio of their surface area is-

Solution:
The ratio of the volume of two cubes = 64 : 27
Let
a and b the sides of the first cube and second cube respectively
Now
a³ : b³ = 64 : 27
⇒ a³ : b³ = 4³ : 3³
⇒ a/b = 4/3

Surface area of cubes =6(side)2

6a²/6b² = a²/b²
= 4²/3²
= 16/9
= 16 : 9

৯,৭৯১.

A man can row 1.8 kilometer against the stream in 15 minutes and down the stream in 3 minutes. The speed (in m/sec) of the man in still water is-

ক
6 m/sec
খ
9 m/sec
গ
10 m/sec
ঘ
15 m/sec

ব্যাখ্যা

Question: A man can row 1.8 kilometer against the stream in 15 minutes and down the stream in 3 minutes. The speed (in m/sec) of the man in still water is-

Solution:
1.8 kilometer = 1800 meters
15 minutes = 15 × 60
= 900 sec
3 minutes = 3 × 60
= 180 sec
Rate upstream = 1800/900 m/sec
= 2 m/sec
Rate downstream = 1800/180 m/sec
= 10 m/sec
∴ Rate in still water = (1/2)(2 + 10) m/sec
= 6 m/sec

৯,৭৯২.

Arif and Mahir can clean the garage together in 6 hours. If it takes Arif 8 hours working alone, how long will it take Mahir working alone?

ক
ক) 12 hours
খ
খ) 16 hours
গ
গ) 18 hours
ঘ
ঘ) 24 hours

ব্যাখ্যা

দুই জন একত্রে ১ ঘণ্টায় কাজ করতে পারে ১/৬ অংশ।
আরিফ ১ ঘণ্টায় কাজ করতে পারে ১/৮ অংশ।
মাহির একা ১ ঘণ্টায় করতে পারে (১/৬ - ১/৮) = (৮-৬)/৪৮ = ১/২৪ অংশ।
∴ মাহির একা পুরো কাজটি করতে পারবে = ২৪ ঘণ্টায়

৯,৭৯৩.

How much time does a train 50 m long, moving at 68 km/hr takes to pass another train 75 m long moving at 50 km/hr in the same direction?

ক
ক) 5 sec
খ
খ) 15 sec
গ
গ) 25 sec
ঘ
ঘ) 30 sec

ব্যাখ্যা

Question: How much time does a train 50 m long, moving at 68 km/hr takes to pass another train 75 m long moving at 50 km/hr in the same direction?

Solution:
Total distance covered by the length of both trains = (50 + 75) m = 125 m
And, their relative speed in same direction = (68 - 50) = 18 km/hr

Then, the time to cross each other will be = 125 m/18 km/hr.
= (125 × 3600)/(18 × 1000) s
= 25 sec

৯,৭৯৪.

The angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 12.4 m away from the wall. The length of the ladder is:

ক
ক) 14.8 m
খ
খ) 68.2m
গ
গ) 12.5 m
ঘ
ঘ) 24.8 m

ব্যাখ্যা

Consider the diagram shown above where PR represents the ladder and RQ represents the wall.
cos⁡60∘=PQ/PR
1/2=12.4/PR
PR=2×12.4=24.8m

৯,৭৯৫.

An unbiased die is tossed. Find the probability of getting a multiple of 3.

ক
1/2
খ
1/8
গ
1/3
ঘ
2/7

ব্যাখ্যা

Question: An unbiased die is tossed.Find the probability of getting a multiple of 3.

Solution:
Here S = {1, 2, 3, 4, 5, 6}
Let E be the event of getting the multiple of 3
Then,
E = {3,6}
P(E) = n(E)/n(S)
= 2/6
= 1/3

৯,৭৯৬.

On a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4?

ক
1/6
খ
1/3
গ
1/2
ঘ
1/4

ব্যাখ্যা

Question: On a six-sided die, each side has a number between 1 and 6. What is the probability of throwing a 3 or a 4?

Solution:
On a six-sided die, the probability of throwing any number is 1 in 6.
The probability of throwing a 3 = 1/6
The probability of throwing a 4 = 1/6

Therefore, the probability of throwing either a 3 or 4 is 1/6 + 1/6 = (1+1)/6 = 2/6 = 1/3

৯,৭৯৭.

Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

ক
6 years
খ
4 years
গ
8 years
ঘ
12 years

ব্যাখ্যা

Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

Solution:
Ayesha's brother is 4 years younger than her.

Ayesha's mother was 36 years old when her brother was born.

So, the age of Ayesha's mother when she was born = 36 - 4 years = 32 years.

And when Ayesha was born her father's age = 38 years

∴ The difference between the ages of her parents = 38 - 32 years

= 6 years

৯,৭৯৮.

It was Tuesday on January 1, 2008. What was the day of the week on Jan 1, 2009?

ক
Wednesday
খ
Thursday
গ
Sunday
ঘ
Saturday

ব্যাখ্যা

Question: It was Tuesday on January 1, 2008. What was the day of the week on Jan 1, 2009?

Solution:
The year 2008 is a leap year. So, it has 2 odd days.
Given,1st day of the year 2008 is Tuesday
So, 1st day of the year 2009 is 2 days beyond Tuesday.
Hence, it will be Thursday.

৯,৭৯৯.

If x + y = 8 and xy = 20, then what is the value of x³ + y³?

ক
32
খ
-32
গ
512
ঘ
None of these

ব্যাখ্যা

Question: If x + y = 8 and xy = 20, then what is the value of x³ + y³ = ?

Solution:
Given that,
x + y = 8 and xy = 20

We know,
x³ + y³ = (x + y)³ - 3xy(x + y)
= (8)³ - 3 × 20 × 8
= 512 - 480
= 32

৯,৮০০.

The sum of the salaries of A and B is Tk. 2100. A spends 80% of his salary and B spends 70% of his salary. If their savings are in the proportion of 4 : 3, then the salary of A?

ক
ক) Tk.1700
খ
খ) Tk.1400
গ
গ) Tk.1600
ঘ
ঘ) Tk.1800

ব্যাখ্যা

A and B savings are 20% and 30%
Let the salaries of A and B be x and y respectively

Now
(20% of x)/(30% of y) = 4/3
(x/5)/(3y/10) = 4/3
(x/5)×(10/3y) = 4/3
2x/3y = 4/3
x/3y = 2/3
x/y = 2
x = 2y

Again
x + y = 2100
2y + y = 2100
3y = 2100
y = 700

A's salaries = x = 2y
= 2 × 700
=Tk.1400