Bank Math

PrepBank · পাতা ৯২ / ১৬১ · ৯,১০১–৯,২০০ / ১৬,১২৪

৯,১০১.

Find the compound interest on Tk. 8500 at 4 % per annum for 2 years, compounded annually.

ক
Tk 592.4
খ
Tk 598.8
গ
Tk 693.6
ঘ
Tk 685.3

ব্যাখ্যা

Question: Find the compound interest on Tk. 8500 at 4 % per annum for 2 years, compounded annually.

Solution:
Principal = Tk. 8500, Rate = 4 % per annum, Time = 2 years
Amount = 8500 {1 + (4/100)}²
= Tk. 9193.6

Compound Interest = Total amount - Principal
= 9193.6 - 8500
= 693.6

৯,১০২.

If 15 men can reap the crops of a field in 28 days, in how many days will 5 men reap it?

ক
50 days
খ
60 days
গ
84 days
ঘ
9.333 days

ব্যাখ্যা

Question: If 15 men can reap the crops of a field in 28 days, in how many days will 5 men reap it?

Solution:
Let 5 men can reap a field in x days
So, put the same quantities on the same side.
Men: Days
Now, Men and Days are inversely proportional to each other. If we increase the number of men fewer days will be required to complete the work.
Inversely proportional means = 15 = 1/28, 5 = 1/x
so, 5/15 = 28/x
⇒ 5x = 28 × 15
∴ x = 84

Hence, 5 men can reap a field in 84 days.

৯,১০৩.

A milkman mixed some water with milk to gain 25% by selling the mixture at the cost price. The ratio of water and milk respectively-

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

ব্যাখ্যা

Question: A milkman mixed some water with milk to gain 25% by selling the mixture at the cost price. The ratio of water and milk respectively-

Solution:
Let the milkman has the milk of Tk 100
After mixing the water the mixture sold for Tk 100 + 25 = Tk 125

In Tk 125, Milk is of Tk 100, and water is of Tk 25

So, the ratio of water and milk in the mixture = 25 : 100 = 1 : 4

৯,১০৪.

Find the value of sin(5π/6).

ক
- 1/2
খ
√3/2
গ
1/2
ঘ
- 1/√2

ব্যাখ্যা

Question: Find the value of sin(5π/6).

Solution:
sin(5π/6)
= sin(π - π/6) [যেহেতু (π - θ) দ্বিতীয় চতুর্ভাগে পড়ে এবং দ্বিতীয় চতুর্ভাগে sin ধনাত্মক, তাই sin(π - θ) = sin θ]
= sin(π/6)
= sin(30°)
= 1/2

৯,১০৫.

Rafi, Nabil, and Hasan started a business together. Rafi invested one-fourth of the total capital, Nabil invested one-sixth, and the remaining capital was invested by Hasan. What is the ratio of their profits?

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

ব্যাখ্যা

Question: Rafi, Nabil, and Hasan started a business together. Rafi invested one-fourth of the total capital, Nabil invested one-sixth, and the remaining capital was invested by Hasan. What is the ratio of their profits?

Solution:
Let the total capital be 12x
Then, Rafi's share = 12x × (1/4) = 3x
Nabil's share = 12x × (1/6) = 2x
Hasan's share = 12x - (3x + 2x) = 7x

So, required ratio = 3x : 2x : 7x = 3 : 2 : 7

৯,১০৬.

P is a point lying on the line segment AB. Which of the following relations is applicable for all time?

ক
ক) AP = PB
খ
খ) AB > AP
গ
গ) AB > AP + PB
ঘ
ঘ) AP > PB

ব্যাখ্যা

প্রশ্নানুসারে AB = AP + PB
মূল রেখা সবসময়ই রেখাংশের চেয়ে বড় হবে। সুতরাং, AB > AP
অপশন গ কখনোই সঠিক হবে না এবং অপশন ক এবং ঘ সবক্ষেত্রে সঠিক হবে না।

৯,১০৭.

In an examination paper, there are two groups each containing 5 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

ক
ক) 60
খ
খ) 100
গ
গ) 200
ঘ
ঘ) 288

ব্যাখ্যা

Question: In an examination paper, there are two groups each containing 5 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

Solution:
5 questions can be selected in the following ways,
2 question from first group and 3 question from second group Or 3 question from first group and 2 question from second group.
= (⁵C₂ × ⁵C₃) + (⁵C₃ × ⁵C₂)
= 100 + 100
= 200

৯,১০৮.

A shopkeeper sold an article at a loss of 20%. If he had sold it for Tk. 150 more, he would have made a profit of 10%. The cost price of the article is.

ক
Tk. 480
খ
Tk. 600
গ
Tk. 750
ঘ
Tk. 500

ব্যাখ্যা

Question: A shopkeeper sold an article at a loss of 20%. If he had sold it for Tk. 150 more, he would have made a profit of 10%. The cost price of the article is.

Solution:
Given that,
Loss = 20%
If sold for Tk. 150 more, profit = 10%

Now, Let cost price = Tk. x
Then,
Selling price at 20% loss = x - x of 20% = 0.80x
Selling price at 10% profit = x + x of 10% = 1.10x

According to the question,
⇒ 1.10x - 0.80x = 150
⇒ 0.30x = 150
⇒ x = 150/0.30
∴ x = 500

So, the cost price of the article is Tk. 500.

৯,১০৯.

What is the value of 'm'?
i) The number m yields a remainder p when divided by 14 and a remainder q when divided by 7
ii) p - q = 7

ক
ক) Only i
খ
খ) Only ii
গ
গ) Both i and ii
ঘ
ঘ) Either i or ii
ঙ
ঙ) Cannot be determined

ব্যাখ্যা

What is the value of 'm'?
i) The number m yields a remainder p when divided by 14 and a remainder q when divided by 7
ii) p - q = 7

প্রশ্নে বলা হচ্ছে, m কে 14 দ্বারা ভাগ করলে ভাগশেষ থাকে p এবং 7 দ্বারা ভাগ করলে ভাগশেষ থাকে q। এখন p = q + 7 হলে m এর মান নিচের কোনটি হতে পারে?

এখানে, m এর মান বের করতে হলে শুধু p = 7 + q তথ্য দ্বারা বের করা যাবে না।
এক্ষেত্রে m = 53 হলে 53/14 = 3 অর্থাৎ ভাগশেষ থাকে 11, আবার 7 দ্বারা ভাগ করলে ভাগশেষ থাকে 4.
অর্থাৎ 4 + 7 = 11 যা p এর মান।
এভাবে m এর মান বের করতে (i) এবং (ii) উভয়ই লাগবে।

তাই সঠিক উত্তর: অপশন (গ)

৯,১১০.

At what rate of compound interest per annum will a sum of Tk. 2500 become Tk. 3600 in 2 years?

ক
15%
খ
20%
গ
30%
ঘ
12%

ব্যাখ্যা

প্রশ্ন: At what rate of compound interest per annum will a sum of Tk. 2500 become Tk. 3600 in 2 years?

সমাধান:
দেওয়া আছে,
মূলধন, P = 2500 টাকা
চক্রবৃদ্ধি আসল, C = 3600 টাকা
সময়, n = 2 বছর
মুনাফার হার = r ?

আমরা জানি,
চক্রবৃদ্ধি আসল, C = P(1 + r/100)ⁿ
⇒ 3600 = 2500(1 + r/100)²
⇒ (1 + r/100)² = 3600/2500
⇒ (1 + r/100)² = 36/25
⇒ 1 + r/100 = 6/5
⇒ r/100 = (6/5) - 1
⇒ r/100 = 1/5
⇒ r = (1 × 100) / 5
⇒ r = 20

∴ বার্ষিক চক্রবৃদ্ধি সুদের হার = 20%

৯,১১১.

A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay. Tk. 5,400 interest only for the period, The principal amount borrowed by him was:

ক
ক) Tk. 20,000
খ
খ) Tk. 15,000
গ
গ) Tk. 10,000
ঘ
ঘ) Tk. 5,000

ব্যাখ্যা

Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay. Tk. 5,400 interest only for the period, The principal amount borrowed by him was:

Solution:
Given,
Rate of interest, r = 12%= 12/100
Time, n = 3 years
Interest, I = Tk. 5400

Principal, P =?

We know,
I = Pnr
Or, 5400 = P × 3 × (12/100)
Or, P = (5400 × 100)/(3 × 12)
∴ P = 15000

৯,১১২.

Solve the inequality: 5(x + 2) - 3 ≤ 2(x - 4) + 17

ক
x ≤ 2/3
খ
x > 3/5
গ
x ≤ 3/4
ঘ
x < 3/2
ঙ
None

ব্যাখ্যা

Question: Solve the inequality: 5(x + 2) - 3 ≤ 2(x - 4) + 17

Solution:
Given inequality,
5(x + 2) - 3 ≤ 2(x - 4) + 17
⇒ 5x + 10 - 3 ≤ 2x - 8 + 17
⇒ 5x + 7 ≤ 2x + 9
⇒ 5x - 2x ≤ 9 - 7
⇒ 3x ≤ 2
∴ x ≤ 2/3

৯,১১৩.

In a certain code, AWAKE is written as ZVZJD. How is FRIEND written in that code?

ক
ক) EQHDMC
খ
খ) UOHDMF
গ
গ) UHODMF
ঘ
ঘ) FMDHOU

ব্যাখ্যা

Question: In a certain code, AWAKE is written as ZVZJD. How is FRIEND written in that code?

Solution:
A এর পূর্ববর্তী লেটার Z
W এর পূর্ববর্তী লেটার V
K এর পূর্ববর্তী লেটার J
E এর পূর্ববর্তী লেটার D

তাহলে, FRIEND এর পরিবর্তে লিখা যাবে = EQHDME

৯,১১৪.

The ratio of cost price and selling price is 4 : 5. The profit percentage is

ক
20%
খ
25%
গ
35%
ঘ
30%
ঙ
None

ব্যাখ্যা

Question: The ratio of cost price and selling price is 4 : 5. The profit percentage is

Solution:
Given,
The ratio of cost price (C.P.) to selling price (S.P.) is 4:5.

Let,
The cost price be 4x and the selling price be 5x.

∴ Profit = S.P - C.P. = 5x - 4x = x
∴ Profit percent = (Profit/CP) × 100
= (x/4x) × 100
= (1/4) × 100
= 25%

৯,১১৫.

Krishna invests Tk. 500 in the A Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

ক
ক) Tk. 550
খ
খ) Tk. 540
গ
গ) Tk. 700
ঘ
ঘ) Tk. 800

ব্যাখ্যা

প্রশ্ন: Krishna invests Tk. 500 in the A Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

সমাধান:
Let,
P = Tk. 500
r = 8% = 8/100
n = 5 years

∴ I = Pnr
= 500 × 5 × (8/100)
= 200

∴ total amount after 5 years will be = (500 + 200)
= Tk. 700

৯,১১৬.

The angle between the hands of a clock when the time is 2 : 20 am is?

ক
38°
খ
50°
গ
65°
ঘ
40°
ঙ
75°

ব্যাখ্যা

Question: The angle between the hands of a clock when the time is 2 : 20 am is?

Solution:
Let angle between the hands of clock be x
When the time is 2 : 20 am
Where [M = minutes and H = hours]

Required angle
= 30{(M/5) - H} - (M/2)
= 30{(20/5) - 2} - (20/2)
= 30(4 - 2) - 10
= 30 × 2 - 10
= 60 - 10
= 50°

৯,১১৭.

Out of total expenditure for a month, a man spends 8% on petrol, 15% on his son's education and 52% on his family and the remaining Tk. 2500 for savings. What is the total expenditure?

ক
Tk.15000
খ
Tk.18000
গ
Tk.10000
ঘ
Tk.20000

ব্যাখ্যা

Let the total expenditure = Tk.X
He spends for petrol = 8X/100
For his son's education = 15X/100
For his family = 52X/100
Therefore the remaining amount for savings = Tk. 2500 = X - (8X/100 + 15X/100 + 52X/100)
⇒ X - (8X/100 + 15X/100 + 52X/100) = Tk. 2500
⇒ X - 75X/100 = Tk. 2500
⇒ 25X/100 = Tk. 2500
⇒ 25X = Tk. 2500 × 100
⇒ X = (Tk. 2500 × 100)/25
⇒ X = Tk. 10000
Hence, the total expenditure = Tk. 10000.

৯,১১৮.

Ratul gets 55% of total valid votes in an election. If the total votes were 9000, what is the number of valid votes that the other candidate Sami gets if 30% of the total votes were declared invalid?

ক
6300
খ
4950
গ
3465
ঘ
2835

ব্যাখ্যা

Question: Ratul gets 55% of total valid votes in an election. If the total votes were 9000, what is the number of valid votes that the other candidate Sami gets if 30% of the total votes were declared invalid?

Solution:
Total votes = 9000
Total valid votes = 70% of 9000 = 6300
Shyam gets 45% of 6300 = (45/100) × 6300 = 2835 votes

৯,১১৯.

If 3n³ - 7 = 74, what is the value of n² - n?

ক
3
খ
6
গ
9
ঘ
1

ব্যাখ্যা

Question: If 3n³ - 7 = 74, what is the value of n² - n?

Solution:
3n³ - 7 = 74
⇒ 3n³ = 74 + 7 = 81
⇒ n³ = 81/3 = 27
⇒ n³ = 3³
∴ n = 3

n² - n
= 3² - 3
= 9 - 3
= 6

৯,১২০.

A, B and C enter into a partnership with a certain capital in which A's contribus 5,000. If out of a total profit of Tk. 2000, A gets Tk. 1000, C gets Tk. 400 then B's capital is-

ক
Tk. 1500
খ
Tk. 2000
গ
Tk. 3000
ঘ
Tk. 4500

ব্যাখ্যা

Question: A, B and C enter into a partnership with a certain capital in which A's contribus 5,000. If out of a total profit of Tk. 2000, A gets Tk. 1000, C gets Tk. 400 then B's capital is-

Solution:
Given,,
Total profit is = 2000 Tk
A's profit = 1000 Tk
C's profit = 400 Tk
∴ B's profit is = {Total profit - (A + C)' profit}
= (2000 - 1400) = 600 Tk

∴ Profit Ratio between A, B and C is
= 1000 : 600 : 400
= 5 : 3 : 2

Let their capitals be 5x, 3x, and 2x respectively.

ATQ,
A's contribution is Tk. 5000
∴ 5x = 5000
⇒ x = 1000

∴ B's share = 3x = 3 × 1000 = 3000 Tk

৯,১২১.

Compute the annual interest from a deposit of Tk. 20,000 under an 8% simple interest scheme.

ক
Tk. 1850
খ
Tk. 2100
গ
Tk. 2200
ঘ
Tk. 1600

ব্যাখ্যা

Question: Compute the annual interest from a deposit of Tk. 20,000 under an 8% simple interest scheme.

Solution:
Here,
Principal, P = Tk. 20000
Rate, r = 8%
Time, n = 1 year (since "annual" interest means for one year)

We know,
I = Prn
= 20000 × 8% × 1
= 20000 × (8/100)
= 1600

Thus, the annual interest accrued is Tk. 1600.

৯,১২২.

In triangle ABC, sides AB = AC, and angle ∠C = 35∘. Find the measure of angle ∠A.

ক
110°
খ
90°
গ
70°
ঘ
120°

ব্যাখ্যা

Question: In triangle ABC, sides AB = AC, and angle ∠C = 35^∘. Find the measure of angle ∠A.

Solution:
Since AB = AC, triangle ABC is isosceles with the equal sides being AB and AC. In an isosceles triangle, the angles opposite the equal sides are equal. Therefore ∠B =∠C
Given that ∠C = 35^∘, it follows that, ∠B = 35^∘
The sum of the interior angles in any triangle is 180^∘. Therefore,
⇒ ∠A + ∠B + ∠C = 180^∘
⇒ ∠A + 35^∘ + 35^∘ = 180^∘
⇒ ∠A = (180 - 70)°
∴ ∠A = 110°

৯,১২৩.

If HAPPY is coded as 'JCRRA', then SMILE is coded as-

ক
VNLGH
খ
UOKNG
গ
VHLGN
ঘ
UGONK

ব্যাখ্যা

Question: If HAPPY is coded as 'JCRRA', then SMILE is coded as-

Solution:
Let's first analyze the coding pattern for the word HAPPY:
H - J (Difference 2)
A - C (Difference 2)
P - R (Difference 2)
P - R (Difference 2)
Y - A (Difference 2)
We can see that each letter is replaced by the letter that is two positions ahead in the alphabet.

Now, applying the same rule to the word SMILE:
S - U (Difference 2)
M - O (Difference 2)
I - K (Difference 2)
L - N (Difference 2)
E - G (Difference 2)
Therefore, if HAPPY is coded as JCRRA, then SMILE will be coded as UOKNG.

৯,১২৪.

Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has a larger area and by how much?

ক
ক) Both are equal
খ
খ) circle, 44 cm²
গ
গ) square, 33 cm²
ঘ
ঘ) circle, 33 cm²

ব্যাখ্যা

Perimeter of Square = 44 cm
⇒ Side of square is 11 cm
Area of Square = 11²= 121 cm²

Circumference of Circle = 44 cm
⇒ 2πr = 44
⇒ 2r(22/7) = 44
⇒ r = 7
⇒ Radius of circle is 7 cm
Area of circle =πr²=(22/7) × 7²= 154 cm²

Circle has larger area by 33 cm² than the area of square.

৯,১২৫.

A train traveling at 60 kmph crosses a man in 6 seconds. What is the length of the train?

ক
80 m
খ
85 m
গ
100 m
ঘ
106 m

ব্যাখ্যা

Question: A train traveling at 60 kmph crosses a man in 6 seconds. What is the length of the train?

Solution:
Speed in m/sec = 60 × (5/18) = 50/3 m/sec.
Time taken to cross the man = 6 seconds.

∴ Distance traveled = (50/3) × 6 = 100 m = length of the train.

৯,১২৬.

A train 120 meters long travels at a speed of 54 km/hr. How long will it take to cross a platform 180 meters long?

ক
50 seconds
খ
1 min
গ
25 seconds
ঘ
45 seconds
ঙ
20 seconds

ব্যাখ্যা

Question: A train 120 meters long travels at a speed of 54 km/hr. How long will it take to cross a platform 180 meters long?

Solution:
Total distance = 120 + 180 = 300 meters

∴ Speed = 54 × (5/18) =15 m/s

∴ Time = 300/15 = 20 seconds

৯,১২৭.

ABC : ZYX : : CBA : ?

ক
ক) DCY
খ
খ) BCA
গ
গ) XYZ
ঘ
ঘ) XZY

ব্যাখ্যা

Here A has been used in place of Z, B for Y and C for X everywhere.

৯,১২৮.

The average of two numbers x and y is 16. If x, y, z are non-negative integers such that x < z < y, what is the minimum possible average of x, y, z.

ক
11
খ
11.5
গ
12
ঘ
10.5

ব্যাখ্যা

Question: The average of two numbers x and y is 16. If x, y, z are non-negative integers such that x < z < y, what is the minimum possible average of x, y, z.

Solution:
According to the questions,
(x + y)/2 = 16
x + y = 32
As x, y, z are non-negative integers and x < z < y.

The minimum possible value of these integers are,
X = 0
Z = 1
Y = 32

∴ Average = (0 + 32 + 1)/3
= 11

৯,১২৯.

Samia owns a hairdressing salon. She borrows Tk. 5000 from a bank to improvements to her beauty salon. She is charged 5% per year compound interest. She pays the money back after 2 years. Calculate the total amount Samia must pay to the bank.

ক
ক) Tk. 5820.5
খ
খ) Tk. 5650.5
গ
গ) Tk. 5250.5
ঘ
ঘ) Tk. 5512.5

ব্যাখ্যা

Question: Samia owns a hairdressing salon. She borrows Tk. 5000 from a bank to improvements to her beauty salon. She is charged 5% per year compound interest. She pays the money back after 2 years. Calculate the total amount Samia must pay to the bank.

Solution:
এখানে,
P = 5000 টাকা
r = 5%, = 5/100
n = 2 বছর

চক্রবৃদ্ধি মলধন C = P (1 + r)ⁿ
= 5000(1 + 5/100)²
= 5000 × (105/100)²
= 5000 × 1.1025
= 5512.5

৯,১৩০.

∆ABC is right angled at B. If cosA = 8/17, then what is the value of cotC?

ক
15/8
খ
15/17
গ
8/17
ঘ
17/15

ব্যাখ্যা

Question: ∆ABC is right angled at B. If cosA = 8/17, then what is the value of cotC?

Solution:

cosA = 8/17 = AB/AC
∴ BC = √(AC² - AB²) = √(17² - 8²) = √(289 - 64)
= √225
= 15

cotC = BC/AB = 15/8

৯,১৩১.

A student goes to school at the rate of 3 km/h and reaches 6 min late. If he travels at the speed of 4 km/h he is 12 min early. What is the distance of the school?

ক
ক) 3.6 km
খ
খ) 4 km
গ
গ) 1.2 km
ঘ
ঘ) 5 km

ব্যাখ্যা

Question: A student goes to school at the rate of 3 km/h and reaches 6 min late. If he travels at the speed of 4 km/h he is 12 min early. What is the distance of the school?

Solution:
Here,
A student goes 3 km/h and reaches 6 min late
and goes 4 km/h he is 12 min early
Total time = (12 + 6) min = 18 min

Let the distance between school and home be x km

ATQ,
(x/3) - (x/4) = 18/60
⇒ (4x - 3x)/12 = 3/10
⇒ x/12 = 3/10
⇒ x = (3 × 12)/10
⇒ x = 18/5
∴ x = 3.6

∴ The distance of the school is 3.6 km

৯,১৩২.

k:l = 4:3 and l:m = 5:3, then find k:l:m?

ক
ক) 20 : 15 : 9
খ
খ) 18 : 24 : 11
গ
গ) 9 : 15 : 1
ঘ
ঘ) 21 : 7 : 3

ব্যাখ্যা

Given k : l = 4 : 3 = 20 : 15
and, l : m = 5 : 3 = 15 : 9
∴ k : l : m = 20 : 15 : 9

৯,১৩৩.

A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched 510 taka more. The sum is -

ক
Tk 10,000
খ
Tk 7,000
গ
Tk 9,000
ঘ
Tk 17,000

ব্যাখ্যা

Questoin: A sum was put at simple interest at a certain rate for 3 years. Had it been put at 1% higher rate, it would have fetched 510 taka more. The sum is -

Solution:
Let the sum be Tk x and the original rate be R%
Then, ((x × (R +1) × 3)/100) - {(x × R × 3)/100} = 510
⇒ 3Rx + 3x - 3Rx = 51000
⇒ 3x = 51000
⇒ x = 17000

Hence, sum = Tk 17,000

৯,১৩৪.

Without stoppages, the bus goes 72 kmph, and with stoppages, 60 kmph. Calculate the bus’s stopping time per hour.

ক
12 minutes
খ
10 minutes
গ
8 minutes
ঘ
18 minutes
ঙ
14 minutes

ব্যাখ্যা

Question: Without stoppages, the bus goes 72 kmph, and with stoppages, 60 kmph. Calculate the bus’s stopping time per hour.

Solution:
Including stoppages, it covers = (72 - 60) kmph
= 12 kmph less

Time taken to cover 12 km = {(12/72) × 60} minutes
= 10 minutes

৯,১৩৫.

100 × 10 - 100 + 2000 ÷ 100 = ?

ক
29
খ
780
গ
920
ঘ
979

ব্যাখ্যা

Question: 100 × 10 - 100 + 2000 ÷ 100 = ?

Solution:
100 × 10 - 100 + 2000 ÷ 100
=100 × 10 - 100 + 20
= 1000 - 100 + 20
= 1020 - 100
= 920

৯,১৩৬.

After decreasing 24% in the price of an article the discounted price becomes $1368. Find the actual price of the article?

ক
ক) 1800
খ
খ) 1600
গ
গ) 1200
ঘ
ঘ) 1000

ব্যাখ্যা

Let the products actual price be x
ATQ, 76% of x = 1368
Or, 76x/100 = 1368
Or, x = (1368 × 100) / 76
= 1800

৯,১৩৭.

A man rows at 6 km/hr in still water and 4.5 km/hr against current. His rate along the current is:

ক
9.5 km/hr
খ
7.5 km/hr
গ
7 km/hr
ঘ
5.25 km/hr
ঙ
None of these

ব্যাখ্যা

Question: A man rows at 6 km/hr in still water and 4.5 km/hr against current. His rate along the current is:

Solution:
Speed in still water is 6 km/hr
Speed of the current is x km/hr

against current,
6 - x = 4.5
⇒ x = 6 - 4.5
∴ x = 1.5

along the current,
6 + x
= 6 + 1.5
= 7.5 km/hr

৯,১৩৮.

A man and a boy received Tk. 800 as wages for 5 days for the work they did together. The man's efficiency in the work was thrice times that of the boy. What are the daily wages of the boy?

ক
ক) Tk. 40
খ
খ) Tk. 42
গ
গ) Tk. 48
ঘ
ঘ) Tk. 56

ব্যাখ্যা

Man = 3 boy
Daily wages for them = 800/5
= 160
4 boy (1 man + 1 boy) = 160
4 boy = 160
Or, boy = Tk. 40

৯,১৩৯.

It takes 5 hours to fill a container using machine A. The same container can be filled using machine B in 10 hours. When the container is full, Machine C can fully empty the container in 20 hours. If all three machines start working on the same empty container how long will it take for the container to be completely filled,

ক
ক) 1/2 hours
খ
খ) 4 hours
গ
গ) 2 hours
ঘ
ঘ) 15 hours

ব্যাখ্যা

3 টি মেশিন দ্বারা 1 ঘণ্টায় পূর্ণ হয় = (1/5 + 1/10 − 1/20)
= (4 + 2 − 1) / 20 অংশ
= 5 / 20 অংশ
= 1/4 অংশ

মেশিন 3টি দ্বারা = 1/4 অংশ পূর্ণ হয় 1 ঘণ্টায়
∴ 1 বা সম্পূর্ণ অংশ পূর্ণ হয় (1×4) = 4 ঘণ্টায়

৯,১৪০.

Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 250 kg what is total weight when it was fresh?

ক
1000 kg
খ
1100 kg
গ
1125 kg
ঘ
1225 kg

ব্যাখ্যা

Question: Fresh grapes contain 80 percent water while dry grapes contain 10 percent water. If the weight of the dry grapes is 250 kg what is total weight when it was fresh?

Solution:
Quantity of water in 250 kg dry grapes = 250 × (10/100)
= 25 kg
Then, pulp of grapes = (250 - 25) kg = 225 kg.

We get 20 kg pulp in 100 kg fresh grapes
To get 225 kg pulp, we need fresh grapes = (100 × 225)/20 kg
= 1125 kg.

৯,১৪১.

A student erroneously multiplied a number by 7/10 instead of 7/5. What is the percentage error in the calculation?

ক
60%
খ
50%
গ
45%
ঘ
40%

ব্যাখ্যা

Question: A student erroneously multiplied a number by 7/10 instead of 7/5. What is the percentage error in the calculation?

Solution:
Let
the number be 100.

ATQ,
Actual calculation be: (7/5) × 100 = 140
and error calculation be: (7/10) × 100 = 70

∴ Difference = 140 - 70 = 70

∴ Percentage error = (70/140) × 100 = 50%

৯,১৪২.

At the rate of 8% simple interest, a sum of Tk. 2800 will earn how much interest in 2 years 6 months?

ক
ক) Tk. 580
খ
খ) Tk. 575
গ
গ) Tk. 560
ঘ
ঘ) Tk. 460

ব্যাখ্যা

Question: At the rate of 8% simple interest, a sum of Tk. 2800 will earn how much interest in 2 years 6 months?

Solution:
Given,
Principal, P = 2800 Tk.
Rate of interest, r = 8% = 8/100 = 2/25.
Time, n = 2 years 6 months
⇒ n = 2 + (6/12) years
∴ n = 5/2 years.

We know,
I = Pnr
= 2800 × (5/2) × (2/25)
= 560 Tk.
Simple Interest Tk. 560.

৯,১৪৩.

The difference between the length and the breadth of a table is 8 cm. If the breadth is decreased by 4 cm and the length is increased by 7 cm, the area remains the same. Find the area of the table?

ক
ক) 240 sq.cm
খ
খ) 540 sq.cm
গ
গ) 560 sq.cm
ঘ
ঘ) 660 sq.cm

ব্যাখ্যা

Question: The difference between the length and the breadth of a table is 8 cm. If the breadth is decreased by 4 cm and the length is increased by 7 cm, the area remains the same. Find the area of the table?

Solution:
টেবিলের প্রস্থ = x সে.মি.
টেবিলের দৈর্ঘ্য = x + 8 সে.মি.
টেবিলের ক্ষেত্রফল = x(x + 8) বর্গ সে.মি.
= x² + 8x বর্গ সে.মি.

প্রশ্নমতে
(x - 4)(x + 8 + 7) = x² + 8x
বা, (x - 4)(x + 15) = x² + 8x
বা, x² + 15x - 4x - 60 = x² + 8x
বা, x² - x² + 11x - 8x = 60
বা, 3x = 60
∴ x = 20

টেবিলের প্রস্থ = 20 সে.মি.
টেবিলের দৈর্ঘ্য = 20 + 8 = 28 সে.মি.

টেবিলের ক্ষেত্রফল = 20 × 28 = 560 বর্গসে.মি.

৯,১৪৪.

The sum of 3 consecutive integers is less than 75. What is the greatest possible value of the smallest one?

ক
ক) 16
খ
খ) 19
গ
গ) 22
ঘ
ঘ) 23

ব্যাখ্যা

প্রশ্ন:The sum of 3 consecutive integers is less than 75. What is the greatest possible value of the smallest one?

সমাধান:
ধরি,
সংখ্যা তিনটি যথাক্রমে x, x + 1, x + 2

প্রশ্নমতে,
x + 2 + x + x + 1 < 75
3x + 3 < 75
3x + 3 - 3 < 75 - 3
3x < 72
x/3 < 72/3
x < 24

ছোট সংখ্যাটি = ( 24 - 1 ) = 23

৯,১৪৫.

The length of a rectangular floor is twice its breadth. If the total cost to concrete the floor is Tk 256 at the rate of Tk 2 per sq. meter, what is the length of the floor?

ক
6 meter
খ
8 meter
গ
12 meter
ঘ
14 meter
ঙ
16 meter

ব্যাখ্যা

Question: The length of a rectangular floor is twice its breadth. If the total cost to concrete the floor is Tk 256 at the rate of Tk 2 per sq. meter, what is the length of the floor?

Solution:
Area of the floor = 256/2 = 128 sq. meter
Let breadth = x meter and length = 2x meter

∴ x × 2x = 128
⇒ 2x² = 128
⇒ x² = 64
⇒ x = 8

∴ Length of the floor = (2 × 8) meter
= 16 meter

৯,১৪৬.

If the sum of (3, 7 and x) is 18, then the average of (3, 7 and x) is

ক
6
খ
7
গ
8
ঘ
9
ঙ
None of these

ব্যাখ্যা

Question: If the sum of (3, 7 and x) is 18, then the average of (3, 7 and x) is

Solution:
3 + 7 + x = 18
⇒ x = 18 - 10
∴ x = 8

∴ the average of (3, 7 and 8) is = the sum of (3, 7 and 8)/3 = 18/3 = 6

৯,১৪৭.

If 20% of x is the same as the 10% of y, then x : y is equal to

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

ব্যাখ্যা

Question: If 20% of x is the same as the 10% of y, then x : y is equal to

Solution:
20% of x = 10% of y
⇒ (20/100) × x = (10/100) × y
⇒ 20 x = 10 y
⇒ x/b = 10/20
∴ x : y = 1 : 2

৯,১৪৮.

The reflex angle between the hands of a clock at 10.25 is:

ক
395°/2
খ
397°/2
গ
399°/2
ঘ
393°/2

ব্যাখ্যা

Required angle
= । (11 M - 60 H) / 2 ।°
= । (11 × 25 - 60 × 10) / 2।°
= । (275 - 600) / 2।°
= । -325/2।°
= । 360 -325/2।°
= 395°/2

Angle traced minutes hand in 25 minutes = {(60 × 25)/360}°
=150°

The hour hand traces half a degree in one minute. Hence, angle traced by hour hand at 10 hour and 25 minutes = {(10 × 30) + 25/2}°
=312.5°
Thus, angle between two hands = 312.5 − 150 = 162.5°
Hence, the reflex angle is = (360−162.5)° = 197.5°

৯,১৪৯.

If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be -

ক
less than - 10
খ
greater than - 10
গ
greater than 10
ঘ
between -1/10 and 0

ব্যাখ্যা

Question: If n denotes a number to the left of 0 on the number line such that the square of n is less than 1/100, then the reciprocal of n must be -

Solution:
given,
n < 0
and,
n² < 1/100
or, ।n। < 1/10

but n < 0

∴ n > - 1/10
or, 1/n < - 10

৯,১৫০.

The difference between the two numbers is 1365. When the large number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is :

ক
250
খ
290
গ
270
ঘ
287
ঙ
257

ব্যাখ্যা

Let the numbers be x and (x + 1365)
Then,
⇒ x + 1365 = 6x + 15
⇒ 5x = 1350
⇒ x = 270

৯,১৫১.

A driving wheel makes 250 revolutions per minute to keep a speed of 66 km per hour. What is the diameter of the driving wheel?

ক
ক) 155 cm
খ
খ) 150 cm
গ
গ) 145 cm
ঘ
ঘ) 140 cm

ব্যাখ্যা

Question: A driving wheel makes 250 revolutions per minute to keep a speed of 66 km per hour. What is the diameter of the driving wheel?

Solution:
Total distance of one hour = 66 km = 66 × 1000 m = 66000 × 100 cm = 6600000 cm.
∴ Distance of 1 minute = 6600000/60 cm
= 110000 cm

∴ Distance for 1 revolution = 110000/250 cm
= 440 cm

Let,
The radius of the wheel = r cm
∴ The diameter of the wheel, d = 2r cm

Now,
2πr = 440
⇒ 2r = 440/π
⇒ d = 440 × (7/22)
∴ d = 140

∴ The length of the diameter of the driving wheel is 140 cm

৯,১৫২.

The average age of the 20 persons is 19.2 years. After some time two more persons join them and then average is increased by 0.3 years. Find the difference between the age of new persons.

ক
ক) 45 years
খ
খ) 32 years
গ
গ) 22 years
ঘ
ঘ) None of these

ব্যাখ্যা

The average age of the 20 persons is 19.2 years. Therefore, total age = 20 × 19.2 = 384 years
After some time two more persons join them and then average is increased by 0.3 years.
So, average age of (20 + 2) or 22 persons = (19.2 + 0.3) years. Therefore, the total age = 22 × 19.5 = 429 years
Total age of 2 new persons = 429 - 384) = 45 years
It is possible to calculate to find the total age of two new persons but not difference.
--------------------------------------------------------------------------------------------------------------------
২০ জন ব্যক্তির গড় বয়স ১৯.২ বছর। কিছু দিন পর ২ জন নতুন ব্যক্তি যোগ দেওয়ায় গড় বয়স ০.৩ বছর বেড়ে গেলো। তাদের বয়সের বিয়োগফল কত?

২০ জন ব্যক্তির গড় বয়স ১৯.২ বছর হলে মোট বয়স ২০ × ১৯.২ = ৩৮৪ বছর
২ জন নতুন ব্যক্তি যোগ দেওয়ায় (২০ + ২) বা ২২ জনের গড় বয়স ০.৩ বছর বৃদ্ধি পেল। অতএব মোট বয়স = ২২ × (১৯.২ + ০.৩) = ২২ × ১৯.৫ = ৪২৯ বছর
২ জন নতুন ব্যক্তির মোট বয়স = ৪২৯ - ৩৮৪ = ৪৫ বছর
২ জন নতুন ব্যক্তির মোট বয়স বের করা সম্ভব কিন্তু পর্যাপ্ত ডেটা না থাকায় তাদের বয়সের বিয়োগফল বের করা সম্ভব নয়।

৯,১৫৩.

A father is three times as old as his son. After fifteen years father will be twice as old as his son age that time. What is the present age of the son?

ক
ক) 10 years
খ
খ) 15 years
গ
গ) 20 years
ঘ
ঘ) 25 years

ব্যাখ্যা

Question: A father is three times as old as his son. After fifteen years father will be twice as old as his son age that time. What is the present age of the son?

Solution:
Let, the son's age be x years
and the father's age is = 3x years

ATQ,
3x + 15 = 2(x + 15)
⇒ 3x + 15 = 2x + 30
∴ x = 15

∴ Son's age 15 years.

৯,১৫৪.

If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?

ক
60
খ
70
গ
90
ঘ
210

ব্যাখ্যা

Question: If 4 points are indicated on a line and 5 points are indicated on another line that is parallel to the first line, how many triangles can be formed whose vertices are among the 9 points?

Solution:
There are two types of triangles possible:
With two vertices on the line with 4 points and the third vertex on the line with 5 points = ⁴C₂ × ⁵C₁ = 30
With two vertices on the line with 5 points and the third vertex on the line with 4 points = ⁴C₁ ×⁵C₂ = 40

total waya = 30 + 40 = 70

৯,১৫৫.

The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:

ক
30 years
খ
33 years
গ
35 years
ঘ
37 years

ব্যাখ্যা

Question: The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:

Solution:
Let's say A's present age is 3x and B's present age is 5x
After 5 years,
A's age will be = 3x + 5
B's age will be = 5x + 5

ATQ,
(3x + 5)/(5x + 5) = 13/20
⇒ 20(3x + 5) = 13(5x + 5)
⇒ 60x + 100 = 65x + 65
⇒ 60x - 65x = 65 - 100
⇒ - 5x = - 35
∴ x = 7

Since B's present age = 5x = 5 × 7 = 35 years

৯,১৫৬.

In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 5 : 7. If the shop carries 48 cats and bunnies total in stock, how many dogs are there?

ক
9
খ
12
গ
15
ঘ
21

ব্যাখ্যা

Question: In a certain pet shop, the ratio of dogs to cats to bunnies in stock is 3 : 5 : 7. If the shop carries 48 cats and bunnies total in stock, how many dogs are there?

Solution:
5x + 7x = 48
⇒ 12x = 48
⇒ x = 48/12 = 4

number of dogs = 3x
= 3 × 4
= 12

৯,১৫৭.

A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?

ক
5 kmph
খ
7 kmph
গ
3 kmph
ঘ
4 kmph

ব্যাখ্যা

Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?

Solution:
Speed of Man = 4.5 kmph
Speed of stream = 1.5 kmph
Speed in DownStream = 6 kmph
Speed in UpStream = 3 kmph

Average Speed = (2 × 6 × 3)/9 = 4 kmph.

৯,১৫৮.

The slope of a line perpendicular to one with slope 2 is:

ক
2
খ
-1/2
গ
1/2
ঘ
-2

ব্যাখ্যা

Question: The slope of a line perpendicular to one with slope 2 is-

Solution:
দেওয়া আছে,
প্রথম রেখের ঢাল, m₁ = 2

আমরা জানি,
যদি দুটি রেখা পরস্পর লম্ব হলে তাদের ঢালের গুণফল - 1 হয়।
অর্থাৎ,
m₁⋅m₂ = - 1
⇒ 2⋅m₂ = - 1
∴ m₂ = - 1/2

৯,১৫৯.

The ratio of two numbers is 3 : 4 and their sum is 630. The smaller one of the two numbers is

ক
ক) 360
খ
খ) 270
গ
গ) 180
ঘ
ঘ) 120

ব্যাখ্যা

প্রশ্ন: The ratio of two numbers is 3 : 4 and their sum is 630. The smaller one of the two numbers is

সমাধান:
দেয়া আছে ,
দুটি সংখ্যার অনুপাত = 3 : 4

ধরি,
ক্ষুদ্রতম সংখ্যাটি = 3x
বৃহত্তম সংখ্যাটি = 4x
প্রশ্নমতে,
3x + 4x = 630
7x = 630
x = 90
ক্ষুদ্রতম সংখ্যাটি = 3× 90 = 270

৯,১৬০.

What is the simple average of 3³⁰, 3³¹ and 3³²?

ক
3²⁹
খ
13 × (3³⁰)
গ
3³⁰
ঘ
13 × (3²⁹)

ব্যাখ্যা

Question: What is the simple average of 3³⁰, 3³¹ and 3³²?

Solution:
the simple average of 3³⁰ , 3³¹ and 3³² = (3³⁰ + 3³¹ + 3³²)/3
= (3³⁰/3) + (3³¹/3) + (3³²/3)
= 3²⁹ + 3³⁰ + 3³¹
= 3²⁹ (1 + 3 + 32)
= 3²⁹ (1 + 3 + 9)
= 13 × (3²⁹)

৯,১৬১.

Solve the inequality: 4(x - 6) + 4 < 8(x - 4)

ক
x < 3
খ
x > 3
গ
x > 4
ঘ
x < 4

ব্যাখ্যা

Question: Solve the inequality: 4(x - 6) + 4 < 8(x - 4)

Solution:
Given inequality,
4(x - 6) + 4 < 8(x - 4)
⇒ 4x - 24 + 4 < 8x - 32
⇒ 4x - 20 < 8x - 32
⇒ 4x - 8x < - 32 + 20
⇒ - 4x < - 12
∴ x > 3

৯,১৬২.

Ankita deposited Tk. 750 into her savings account. If the interest rate of the account is 4% per year, how much interest will she have made after 5 years?

ক
ক) Tk. 131
খ
খ) Tk. 142
গ
গ) Tk. 150
ঘ
ঘ) Tk. 168

ব্যাখ্যা

We know, I = pnr
= 750 × 5/100 × 4
= 150

৯,১৬৩.

What will come at the place of the question mark?
5, 6, 8, 12, 20, ?

ক
ক) 32
খ
খ) 34
গ
গ) 36
ঘ
ঘ) 38

ব্যাখ্যা

Question: What will come at the place of the question mark?
5, 6, 8, 12, 20, ?

সমাধান:
5 + 1 =6
6 + 2 = 8
8 + 4 = 12
12 + 8 = 20
20 + 16 = 32

৯,১৬৪.

Find the Arithmetic mean of 3, 6, 7, and 4.

ক
5.5
খ
6
গ
4
ঘ
5

ব্যাখ্যা

Question: Find the Arithmetic mean of 3, 6, 7, and 4.

Solution:
The mean is calculated first by taking the sum of all the values 3+6+7+4 = 20
- and then dividing it by, 4 (as we have a total of 4 terms.)
∴ Arithmetic mean = 20/4 = 5
Thus, the arithmetic mean of the given value is 5.

৯,১৬৫.

125 small sphere balls are formed from a big ball with radius 25cm. What will be the surface area of a small ball?

ক
334.16 cm²
খ
324.16 cm²
গ
318.16 cm²
ঘ
314.16 cm²

ব্যাখ্যা

Question: 125 small sphere balls are formed from a big ball with radius 25cm. What will be the surface area of a small ball?

Solution:
converting a big sphere ball to 125 small balls,
the volume will be the same for both case.
let,
small ball radius = r
given, big ball radius, R = 25cm

∴ (4/3)πR³ = 125 × (4/3)πr³
⇒ R³ = 125 × r³
⇒ R = 5 × r
⇒ r = 25/5
r = 5cm

∴ total surface area of a small ball is
a = 4πr²
= 4 × 3.1416 × (5)²
= 314.16 cm²

৯,১৬৬.

A ferry can carry 24 buses or 36 cars at a time. If there are 18 buses on the ferry, how many cars can be loaded onto it?

ক
ক) 6
খ
খ) 8
গ
গ) 9
ঘ
ঘ) 12

ব্যাখ্যা

এখানে 24টি বাস = 36টি গাড়ি
1 টি বাস = 36/24 = 1.5টি গাড়ি
যেহেতু ফেরিটি 18 টি বাস বহন করে ফেলছে, সুতরাং আরো বহন করতে পারবে = 24 - 18 = 6 টি বাস = (6×1.5) টি গাড়ি অর্থাৎ 9 টি গাড়ি।

৯,১৬৭.

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

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

ব্যাখ্যা

Question: A, B, and C invested Tk 50,000 for a business. A invested 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

So A's Share = 35000 × (21/50) = Tk 14700

৯,১৬৮.

A man travels 4 miles towards west, 6 miles towards south, then again 4 miles towards west. What is the direct distance of the destination from the starting point?

ক
10 miles
খ
12 miles
গ
13 miles
ঘ
17 miles
ঙ
20 miles

ব্যাখ্যা

Question: A man travels 4 miles towards west, 6 miles towards south, then again 4 miles towards west. What is the direct distance of the destination from the starting point?

Solution:

Suppose the man starts the journey from A and reaches B.

Here, AB² = 6² + (4 + 4)²
= 36 + 64
= 100

∴ Distance, AB = √100 = 10 miles

৯,১৬৯.

The population of a city grows by 10% every year. If the current population is 50,000, what will the population be after 2 years?

ক
59400
খ
60500
গ
61600
ঘ
63600
ঙ
None

ব্যাখ্যা

Question: The population of a city grows by 10% every year. If the current population is 50,000, what will the population be after 2 years?

Solution:
Here we can use the compound interest based formula,
Population after n years
= P × [1 + (r/100)]n
∴ Population after 2 years = 50000 × [1 + (10/100)]²
= 50000 × (110/100)²
= 50000 × 1.21
= 60,500

৯,১৭০.

A person travels a certain distance at 3 km/hr and reaches 15 min late. If he travels at 4 km/hr, he reaches 15 min earlier. The distance he has to travel is -

ক
ক) 4.5km
খ
খ) 6 km
গ
গ) 7.2 km
ঘ
ঘ) 12 km

ব্যাখ্যা

ATQ,
D/3 - 15/60 = D/4 + 15/60 [As, 60 minutes = 1 hour]
⇒ D/3 - D/4 = 15/60 + 15/60 = 30/60
⇒ D/12 = 1/2
∴ D = 12/2 = 6 km

৯,১৭১.

Niamul, Sabbir, and Mosharaf started a shop by investing Tk 10500, Tk 7000, and Tk 3500 respectively. At the end of the one year, the profit earned was distributed. If Sabbir's gained a profit of Tk 2400, what would be Niamul gain?

ক
ক) 1200 Tk
খ
খ) 3000 Tk
গ
গ) 3600 Tk
ঘ
ঘ) 7200 Tk

ব্যাখ্যা

Question: Niamul, Sabbir, and Mosharaf started a shop by investing Tk 10500, Tk 7000, and Tk 3500 respectively. At the end of the one year, the profit earned was distributed. If Sabbir's gained a profit of Tk 2400, what would be Niamul gain?

Solution:
Let the total profit be Tk x

Now,
Niamul : Sabbir : Mosharaf = 10500 : 7000 : 3500 = 3 : 2 : 1

Sabbir's profit = x × (2/6) = x/3

ATQ,
x/3 = 2400
⇒ x = 7200

Niamul's profit = 7200 × (3/6) = 3600 Tk

৯,১৭২.

A vessel contains 140 litres of milk and water in the ratio of 4 : 3. If 20 litres of milk and 30 litres of water are added to the mixture, the difference between milk and water in the final mixture is Y. Find the value of 7Y?

ক
35
খ
70
গ
84
ঘ
105

ব্যাখ্যা

Question: A vessel contains 140 litres of milk and water in the ratio of 4 : 3. If 20 litres of milk and 30 litres of water are added to the mixture, the difference between milk and water in the final mixture is Y. Find the value of 7Y?

Solution:
Given,
Total mixture = 140 litres
Ratio of milk and water = 4 : 3
Sum of the ratios = 4 + 3 = 7

Initially,
Quantity of milk = 140 × (4/7) = 80 litres
Quantity of water = 140 × (3/7) = 60 litres

After adding 20 litres of milk and 30 litres of water:
New quantity of milk = 80 + 20 = 100 litres
New quantity of water = 60 + 30 = 90 litres

According to the question, the difference between milk and water is Y:
∴ Y = |100 - 90| = 10 litres

∴ The value of 7Y = 7 × 10 = 70

৯,১৭৩.

In a group of people, 35 speak English, 25 speak French, and 12 speak both English and French. How many people are in the group if everyone speaks at least one of these two languages?

ক
36
খ
42
গ
48
ঘ
56
ঙ
64

ব্যাখ্যা

Question: In a group of people, 35 speak English, 25 speak French, and 12 speak both English and French. How many people are in the group if everyone speaks at least one of these two languages?

Solution:
দেওয়া আছে,
ইংরেজি বলে, n(E) = 35 জন
ফরাসি বলে, n(F) = 25 জন
উভয় ভাষা বলে, n(E ∩ F) = 12 জন

যেহেতু সবাই অন্তত একটি ভাষা বলে, তাই মোট ব্যক্তির সংখ্যা হবে n(E ∪ F)।

আমরা জানি,
n(E ∪ F) = n(E) + n(F) - n(E ∩ F)
⇒ n(E ∪ F) = 35 + 25 - 12
⇒ n(E ∪ F) = 60 - 12
⇒ n(E ∪ F) = 48

∴ ঐ গ্রুপে মোট 48 জন ব্যক্তি আছেন।

৯,১৭৪.

The ratio between the perimeter and the length of a rectangle is 5 : 2. If the area of the rectangle is 484 sq. cm, what is the length of the rectangle?

ক
22 cm
খ
33 cm
গ
44 cm
ঘ
55 cm
ঙ
66 cm

ব্যাখ্যা

Question: The ratio between the perimeter and the length of a rectangle is 5 : 2. If the area of the rectangle is 484 sq. cm, what is the length of the rectangle?

Solution:
Let Length = l
& Breadth = b
Perimeter of a rectangle = 2(l + b)

Now,
2(l + b)/l = 5/2
⇒ 4(l + b) = 5l
⇒ l = 4b

Area, l × b = 484
⇒ 4b × b = 484
⇒ b² = 121 = 11²
⇒ b = 11

∴ l = 4 × 11 = 44

So the length of the rectangle is 44 cm.

৯,১৭৫.

150 individuals attended a marathon held in Sylhet. Of those only If x of the 150 individuals were from sythet and z of the individuals participated in the marathon but were not from sylhet. Which of the following represents the number of individuals who did not participate in the marathon and were not from sylhet?

ক
ক) 150-x+z
খ
খ) 150-x-y+z
গ
গ) 150-x+z
ঘ
ঘ) 150-x-z
ঙ
ঙ) None

ব্যাখ্যা

Total = 150
Total ''From-Sylhet'' = x
Total ''Not-from-Sylhet'' = 150-x
Participated & ''Not-from-Sylhet'' = z
Didn't participate & ''Not-from-Sylhet'' = 150-x -z

৯,১৭৬.

Two bus tickets from city A to B and three tickets from city A to C cost Tk. 77 but three tickets from city A to B and two tickets from city A to C cost Tk. 73. What are the fares for cities B and C from A?

ক
Tk. 4, Tk. 23
খ
Tk. 13, Tk. 17
গ
Tk. 15, Tk. 14
ঘ
Tk. 17, Tk. 13

ব্যাখ্যা

Question: Two bus tickets from city A to B and three tickets from city A to C cost Tk. 77 but three tickets from city A to B and two tickets from city A to C cost Tk. 73. What are the fares for cities B and C from A?

Solution:
Let,
Tk. x be the fare of city B from city A
Tk. y be the fare of city C from city A.

Then,
2x + 3y = 77 ........(i)
3x + 2y = 73 ........(ii)

Multiplying (i) by 3 and (ii) by 2 and subtracting, we get:
6x + 9y - 6x - 4y = 231 - 146
⇒ 5y = 85
∴ y = 17

Putting y = 17 in (i), we get:
2x + 51 = 77
⇒ 2x = 77 - 51
⇒ 2x = 26
∴ x = 13.

৯,১৭৭.

If 5^a = 125, then 5^{a - 3} =?

ক
ক) 0
খ
খ) 1
গ
গ) 2
ঘ
ঘ) 3

ব্যাখ্যা

প্রশ্ন: If 5^a = 125, then 5^{a - 3} =?

সমাধান:
5^a = 125
⇒ 5^a 5^-3 = 5³.5^-3
⇒ 5^{a - 3} = 1

৯,১৭৮.

A mixture contains two liquids 'A' and 'B' are in the ratio 4 : 1. If 10 litres of mixture is withdrawn and replaced with 10 litres of 'B', then the ratio becomes 2 : 3. What was the initial quantity of A?

ক
24 ltr.
খ
16 ltr.
গ
20 ltr.
ঘ
12 ltr.

ব্যাখ্যা

Question: A mixture contains two liquids 'A' and 'B' are in the ratio 4 : 1. If 10 litres of mixture is withdrawn and replaced with 10 litres of 'B', then the ratio becomes 2 : 3. What was the initial quantity of A?

Solution:
ধরি, মিশ্রণের প্রাথমিক পরিমাণ = 5x লিটার

A এর পরিমাণ = 4x লিটার
B এর পরিমাণ = x লিটার

∴ 10 লিটার মিশ্রণ তুলে নেওয়ার পর,
A এর পরিমাণ = 4x - (4/5) × 10 = 4x - 8 লিটার
B এর পরিমাণ = x - (1/5) × 10 = x - 2 লিটার

আবার,
B তে 10 লিটার যোগ করার পর,
B এর পরিমাণ = x - 2 + 10 = x + 8 লিটার

∴ প্রদত্ত অনুপাত,
⇒ (4x - 8)/(x + 8) = 2/3
⇒ 12x - 24 = 2x + 16
⇒ 10x = 16 + 24
⇒ x = 40/10
⇒ x = 4

∴ A এর পরিমাণ = 4 × 4 = 16 লিটার

৯,১৭৯.

A man has Tk. 480 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

ক
60
খ
80
গ
120
ঘ
90

ব্যাখ্যা

Question: A man has Tk. 480 in the denominations of one-taka notes, five-taka notes and ten-taka notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

Solution:
Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
⇒ 16x = 480
∴ x = 30.

Hence, total number of notes = 3x = 90

৯,১৮০.

Two students are selected from a class of 5 girls and 12 boys. Find the probability that a particular pair of girl and boy is selected.

ক
1/72
খ
1/136
গ
5/136
ঘ
1/17

ব্যাখ্যা

Question: Two students are selected from a class of 5 girls and 12 boys. Find the probability that a particular pair of girl and boy is selected.

Solution:
total number of students is = 12 + 5 = 17
a pair of students can be chosen from 17 students in = ¹⁷C₂ ways
= (17!)/(2!15!)
= 136 ways

there is one probability that a particular pair of girl and boy is selected.

total probability = 1/136

৯,১৮১.

A train travels 180 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1/2 hour less for the same journey. Find the speed of the train.

ক
40 km/hr
খ
45 km/hr
গ
50 km/hr
ঘ
42 km/hr

ব্যাখ্যা

Question: A train travels 180 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1/2 hour less for the same journey. Find the speed of the train.

Solution:
Given distance = 180 km.
Let,
The speed of the train be x km/hr.
Speed when increased by 5 km/hr will be = (x + 5) km/hr

ATQ,
(180/x) - 180/(x + 5) = 1/2
⇒ [180x + 900 - 180x]/{x(x+5)} =1/2
⇒ 900/(x² + 5x) = 1/2
⇒ x² + 5x = 900 × 2
⇒ x² + 5x - 1800 = 0
⇒ x² + 45x - 40x - 1800 =0
⇒ x(x + 45) - 40(x + 45)=0
⇒ (x - 40)(x + 45)=0
⇒ x = 40, - 45

The speed of the train is 40 km/hr.

৯,১৮২.

Tha value of is

ক
0
খ
1
গ
∞
ঘ
Can not be determined

ব্যাখ্যা

Question: The value of is
(Senior Officer 2022 অনুযায়ী)

Solution:
As x → 0, we know cosx → 1 [cos0 = 1]
So the expression becomes x/1 = x near 0

Applying the limit,

৯,১৮৩.

A Company employs 20 persons, each working 42 hours a week. If 5 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?

ক
56 hours
খ
46 hours
গ
52 hours
ঘ
60 hours

ব্যাখ্যা

Question: A Company employs 20 persons, each working 42 hours a week. If 5 persons are absent, how many hours a week would the rest of the persons have to work to make up the time lost?

Solution:
একটি কোম্পানি ২০ জন কর্মচারী নিয়োগ দেয়। প্রত্যেকে ৪২ ঘণ্টা কাজ করে।

∴ মোট কাজ হয় = (২০ × ৪২)
= ৮৪০ ঘণ্টা
৫ জন অনুপস্থিত থাকলে, বাকি থাকে = ২০ - ৫ = ১৫ জন

∴ প্রত্যেকের কাজ করতে হবে ৮৪০/১৫ ঘণ্টা
= ৫৬ ঘণ্টা

৯,১৮৪.

The average of 10 numbers is 52. Later it is found that two numbers have been wrongly added. The first one is 20 greater than the actual number and the second number added is 15 instead of 31. Find the correct average-

ক
51.1
খ
51.6
গ
52.2
ঘ
52.5

ব্যাখ্যা

Question: The average of 10 numbers is 52. Later it is found that two numbers have been wrongly added. The first one is 20 greater than the actual number and the second number added is 15 instead of 31. Find the correct average -

Solution:
১০টি সংখ্যার প্রকৃত সমষ্টি = (52 × 10 - 20 + 31 - 15)
= 516

∴ প্রকৃত গড় = (516/10) = 51.6

৯,১৮৫.

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

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

ব্যাখ্যা

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

Solution:

Suppose, first pipe alone takes x hours to fill the tank .

Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.

ATQ,
1/x + 1/(x - 5) = 1/(x - 9)

⇒ (x - 5 + x)/x(x - 5) = 1/(x - 9)
⇒ (2x - 5)(x - 9) = x(x - 5)

⇒ x² - 18x + 45 = 0

⇒ x² - 15x - 3x + 45 = 0
⇒ x(x - 15) - 3(x - 15) = 0
⇒ (x - 15)(x - 3) = 0
∴ x = 15 [neglecting x = 3]

৯,১৮৬.

If 40% of all women are voters and 52% of the population is women, what percent of the population are women voters?

ক
20.8
খ
19.2
গ
26.4
ঘ
40.0
ঙ
None of these

ব্যাখ্যা

Question: If 40% of all women are voters and 52% of the population is women, what percent of the population are women voters?

Solution:
Let,
There are 100 number of population

∴ The number of women is 52
∴ Women voters in number 40% of 52 = 20.8

∴ 20.8% of the population are women voters.

৯,১৮৭.

A and B started a business investing Tk. 22,500 and Tk. 35,000 respectively. Out of a total profit of Tk. 13,800. B's share is-

ক
ক) 5400
খ
খ) 7200
গ
গ) 8400
ঘ
ঘ) 9600

ব্যাখ্যা

Question: A and B started a business investing Tk. 22,500 and Tk. 35,000 respectively. Out of a total profit of Tk. 13,800. B's share is-

Solution:
A এবং B এর বিনিয়োগের অনুপাত = 22,500 : 35,000
= 9 : 14

অনুপাতের রাশিগুলোর যোগফল = (9 + 14) = 23
ব্যবসায়ে মোট লাভের পরিমাণ = 13,800 টাকা

B এর লাভের পরিমাণ = (13,800 এর 14/23) টাকা
= 8400 টাকা

৯,১৮৮.

The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 208 cm. The length of the long side is -

ক
ক) 92 cm
খ
খ) 96 cm
গ
গ) 72 cm
ঘ
ঘ) 78 cm

ব্যাখ্যা

Question: The sides of a triangle are in the ratio 1/2 : 1/3 : 1/4 and its perimeter is 208 cm. The length of the long side is -

Solution:
Ratio of sides = 1/2 : 1/3 : 1/4
= (1/2) × 12 : (1/3) × 12 : (1/4) × 12
= 6 : 4 : 3

Let, the sides be 6x, 4x, and 3x

Then,
6x + 4x + 3x = 208
⇒ 13x = 208
⇒ x = 208/16
⇒ x = 16

The length of the long side is = 16 × 6 = 96 cm

৯,১৮৯.

Walking 3/4 of his normal speed, Rafi is 12 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office-

ক
18 min
খ
24 min
গ
36 min
ঘ
48 min
ঙ
56 min

ব্যাখ্যা

Question: Walking 3/4 of his normal speed, Rafi is 12 minutes late in reaching his office. The usual time taken by him to cover the distance between his home and office-

Solution:
Let s be Rafi's normal speed, t be his usual time, and t' be his new time.

Since the distance to the office is constant, d = s × t
When Rafi walks at his normal speed his new time is expressed as, d = (3/4)s × t'

Again, since the distance is the same,
st = (3/4)s × t'
⇒ t' = (4/3)t

ATQ,
t' - t = 12
⇒ (4/3)t - t = 12
⇒ (4t - 3t)/3 = 12
⇒ t/3 = 12
∴ t = 36 min

৯,১৯০.

A can complete a work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

ক
7 days
খ
9 days
গ
12 days
ঘ
10 days

ব্যাখ্যা

Question: A can complete the work in 24 days and B in 16 days. They work together for 6 days. How many more days will A take alone to finish the remaining work?

Solution:
A একা কাজটি করতে পারে = 24 দিনে
∴ A এর একদিনের কাজ = 1/24 অংশ
এবং,
B একা কাজটি করতে পারে = 16 দিনে
∴ B এর একদিনের কাজ = 1/16 অংশ

∴ A ও B একসাথে একদিনের কাজ = (1/24) + (1/16) = (2 + 3)/48 = 5/48 অংশ
তারা 6 দিনে একসাথে কাজ করে = 6 × (5/48) = 5/8 অংশ

বাকি কাজ = 1 - (5/8) = 3/8 অংশ

অতএব,
A, 1/24 অংশ কাজ করে 1 দিনে
∴ 3/8 অংশ কাজ করে = (24 × 3)/8 = 9 দিনে

অতএব, A একা বাকি কাজ শেষ করতে 9 দিন লাগবে।

৯,১৯১.

By how many of the following numbers is 2¹² - 1 divisible?
2, 3, 5, 7, 10, 11, 13, 14

ক
7
খ
4
গ
6
ঘ
2

ব্যাখ্যা

Question: By how many of the following numbers is 2¹² - 1 divisible?
2, 3, 5, 7, 10, 11, 13, 14

Solution:
(2¹² - 1) = (4096 - 1) = 4095, which is clearly divisible by 3, 5, 7 and 13

∴ 4 numbers in all.

৯,১৯২.

If tan(θ - 45°) = 1, then what is the value of sinθ?

ক
1/2
খ
√2/2
গ
√3/2
ঘ
1
ঙ
None

ব্যাখ্যা

Question: If tan(θ - 45°) = 1, then what is the value of sinθ?

Solution:
Given that,
tan(θ - 45°) = 1

We know,
tan45° = 1

So,
tan(θ - 45°) = tan45°
⇒ (θ - 45°) = 45°
⇒ θ = 90°

Now,
∴ sinθ = sin90° = 1

৯,১৯৩.

A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

ক
Taka 15,000
খ
Taka 20,000
গ
Taka 10,000
ঘ
Taka 11,000

ব্যাখ্যা

Question: A vendor purchased 200 books for Taka 150 each and sold them for Taka 200 each. Calculate the total profit.

Solution:
Cost Price of 200 books = 200 × Taka 150 = Taka 30,000
Selling Price of 200 books = 200 × Taka 200 = Taka 40,000
Total Profit = Selling Price - Cost Price = Taka 40,000 - Taka 30,000 = Taka 10,000

৯,১৯৪.

A person who spends (200/3)% of his income is able to save Tk.1500 per month. His monthly expenses ( in Tk.) are-

ক
ক) Tk. 2600
খ
খ) Tk. 3200
গ
গ) Tk. 3000
ঘ
ঘ) Tk. 4500

ব্যাখ্যা

Let
The monthly income be Tk. x
Now
{100 - (200/3)}% of x = 1500
{(300 - 200)/3}% of x = 1500
(100/3) % of x = 1500
(100/3) × (1/100) × x = 1500
x/3 = Tk.1500
x = Tk.4500

His monthly expense = Tk. (4500 - 1500)
= Tk. 3000

৯,১৯৫.

A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 784 Tk, what was his profit?

ক
72 Tk.
খ
144 Tk.
গ
148 Tk.
ঘ
164 Tk.

ব্যাখ্যা

Question: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of 784 Tk, what was his profit?

Solution:
Given,
Selling price = 784 Tk.

For a gain of 22.5%,
The cost price can be = 122.5

Cost price = (100/122.5) × 784 Tk.
= (1000/1225) × 784 Tk.
= 640 Tk

Therefore, Profit = 784 - 640 Tk.
= 144 Tk.

৯,১৯৬.

There is 45% increase in an amount in 4 years 6 months at simple interest. What will be the compound interest of Tk. 10000 after 4 years at the same rate?

ক
Tk. 4000
খ
Tk. 4641
গ
Tk. 14641
ঘ
Tk. 14000

ব্যাখ্যা

Question: There is 45% increase in an amount in 4 years 6 months at simple interest. What will be the compound interest of Tk. 10000 after 4 years at the same rate?

Solution:
Let,
P = Tk. 100.
∴ Simple interest, I = Tk. 45
n = 4 years 6 months = 4.5 years
Rate = r

We know that,
I = Pnr
∴ r = I/(Pn)
= (45 × 100)/(100 × 4.5) %
= 10%

Now,
P = Tk. 10000
n = 4 years
r = 10%

C = P(1 + r)ⁿ
= 10000 × (1.1)⁴
= 10000 × 1.1 × 1.1 × 1.1 × 1.1
= 14641

∴ The compound interest = Tk. (14641 - 10000) = Tk. 4641

৯,১৯৭.

⁷P_r = 210 and ⁷C_r = 35 then what is the value of r?

ক
3
খ
6
গ
4
ঘ
5

ব্যাখ্যা

Question: ⁷P_r = 210 and ⁷C_r = 35 then what is the value of r?

Solution:
Given that,
⁷P_r = 210 and ⁷C_r = 35

We know that,
ⁿP_r = r! × ⁿC_r
⇒ 210 = r! × 35
⇒ r! = 210/35
⇒ r! = 6
⇒ r! = 3!
∴ r = 3

৯,১৯৮.

If dividing P(x) = 2x³ + 5x² + ax - 7 by (x - 2) results in the remainder 15, then find the value of a.

ক
- 7
খ
20
গ
- 2/9
ঘ
- 9

ব্যাখ্যা

Question: If dividing P(x) = 2x³ + 5x² + ax - 7 by (x - 2) results in the remainder 15, then find the value of a.

Solution:
Dividing P(x) by (x - 2), we get the remainder P(2).

∴ P(2) = 2(2)³ + 5(2)² + a(2) - 7
= 2(8) + 5(4) + 2a - 7
= 16 + 20 + 2a - 7
= 29 + 2a

According to the question,
29 + 2a = 15
⇒ 2a = 15 - 29
⇒ 2a = -14
∴ a = - 7

৯,১৯৯.

Students of a class stand in a queue. Suppose Rakib is 13th from the start and 7th from the end. How many students are there?

ক
18
খ
19
গ
20
ঘ
21

ব্যাখ্যা

Question: Students of a class stand in a queue. Suppose Rakib is 13th from the start and 7th from the end. How many students are there?

Solution:
যেহেতু রাকিব শুরু থেকে ১৩তম অবস্থানে আছে, তাই শুরু থেকে রাকিব সহ মোট ছাত্র আছে ১৩ জন।

আবার যেহেতু রাকিব শেষ থেকে ৭ম অবস্থানে আছে, তাই শেষ থেকে রাকিব ছাড়া ছাত্র আছে ৬ জন।

∴ মোট ছাত্র = ১৩ + ৬ = ১৯ জন।

৯,২০০.

A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

ক
10 sec
খ
12 sec
গ
6 sec
ঘ
3 sec

ব্যাখ্যা

Question: A train 110 m long is running at the speed of 60 km/hr. In what time will it pass a man who is running at the speed of 6 km/hr in the opposite direction in which the train is moving?

Solution:
Relative speed = 60 km/hr + 6 km/hr
= 66 km/hr
= 66 ×1000/3600 m/sec
= 66 × 5/18 m/sec
= 55/3 m/sec

Time needed = 110 /55/3 sec
= 110 × 3/55 sec
= 6 sec