Bank Math

PrepBank · পাতা ১০ / ১৬১ · ৯০১–১,০০০ / ১৬,১২৪

৯০১.

In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

ক
7500
খ
8000
গ
8900
ঘ
Data inadequate

ব্যাখ্যা

Question: In a competitive examination in State A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each State?

Solution:
Let, the number of candidates appeared from each State was x

0.07x - 0.06x = 80
⇒ 0.01x = 80
⇒ x = 80/0.01
= 8000

৯০২.

The price of rice has fallen by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?

ক
ক) 11kg
খ
খ) 12.5kg
গ
গ) 12kg
ঘ
ঘ) 10.8kg

ব্যাখ্যা

Question: The price of rice has fallen by 20%. How much rice can be bought now with the money that was sufficient to buy 10 kg of rice previously?

Solution:
Let 100Tk is spend on rice initially for 10kg
after 20% fall, the price is needed now is = 100 - (20% of 100)
= 100 - 20
= 80Tk

new price of rice per kg is = 80/10 = 8Tk

at 8Tk per kg, rice can be bought in 100Tk is = 100/8 = 12.5kg

৯০৩.

A train 125 m long passes a person, running at 8 kmph in the same direction in which the train is going in 25 seconds. The speed of the train is:

ক
ক) 22 km/hr.
খ
খ) 36 km/hr.
গ
গ) 30 km/hr.
ঘ
ঘ) 26 km/hr.

ব্যাখ্যা

Speed of the train relative to Person
= (125/25) m/s.
= 5 m/s.

∴ 5 × (18/5) km/hr
= 18 km/hr

Let the speed of the train be x km/hr.
then, relative speed = (x - 8) km/hr.

So, (x - 8) = 18
⇒ x = 26 km/hr.

৯০৪.

Which of the following describes all values of x for which 1 - x² ≥ 0?

ক
x ≤ - 2
খ
x ≤ - 2 or x ≥ 1
গ
- 1 ≤ x ≤ 1
ঘ
x ≥ 1

ব্যাখ্যা

Question: Which of the following describes all values of x for which 1 - x² ≥ 0?

Solution:
1 - x² ≥ 0
⇒ 1 ≥ x²
⇒ x² ≤ 1
⇒ √(x²) ≤ √1
⇒ |x| ≤ 1

We must consider that x can be either positive or negative because the variable x is inside the absolute value sign. Therefore, we’ll need to solve the inequality twice.

When x is positive:
|x| ≤ 1
= x ≤ 1

When x is negative:
|x| ≤ 1
= - x ≤ 1
= x ≥ - 1

We combine the two resulting inequalities to get:
-1 ≤ x ≤ 1

৯০৫.

A and B together complete a piece of work in x days. If A alone completes the work in x + 3 days and B alone completes the piece of work in x + 12 days, what is the value of "x"?

ক
3 days
খ
5 days
গ
6 days
ঘ
9 days
ঙ
Cannot be determined

ব্যাখ্যা

Question: A and B together complete a piece of work in x days. If A alone completes the work in x + 3 days and B alone completes the piece of work in x + 12 days, what is the value of "x"?

Solution:
A's 1 day's work = 1/(x + 3) part
B's 1 day's work = 1/(x + 12) part
and (A + B)'s 1 day's work = 1/x

ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/(x + 3)(x + 12) = 1/x
⇒ (2x + 15)/(x² + 15x + 36) = 1/x
⇒ 2x² + 15x = x² + 15x + 36
⇒ 2x² + 15x - x² - 15x = 36
⇒ x² = 36
∴ x = 6

৯০৬.

The difference between two numbers is 5 and the difference between their squares is 105. What is the larger number?

ক
ক) 10
খ
খ) 13
গ
গ) 16
ঘ
ঘ) 17

ব্যাখ্যা

Question: The difference between two numbers is 5 and the difference between their squares is 105. What is the larger number?

Solution:
Let the numbers be x and y
Then, x - y = 5.........(i)
and x² - y² = 105
Or (x + y)(x - y) = 105 ....... (ii)
Now, deviding (ii) by (i) we get,
x + y = 21 ........(iii)
by adding (i) and (iii) we get,
2x = 26
∴ x = 13
Hence, the larger number is 13

৯০৭.

The difference between the local value and the face value of 7 in the numeral 32675149 is-

ক
75142
খ
64851
গ
5149
ঘ
69993

ব্যাখ্যা

Question: The difference between the local value and the face value of 7 in the numeral 32675149 is-

Solution:
32675149

(Local value of 7) - (Face value of 7)
= 70000 - 7
= 69993

৯০৮.

A sum of money doubles itself in 10 years. How many years will it take to triple itself?

ক
ক) 20
খ
খ) 30
গ
গ) 25
ঘ
ঘ) 40
ঙ
ঙ) 35

ব্যাখ্যা

Let P = 100,
A = 200,
It means I = 100

Now We want A = 300,
means I = 200
Years for I of Tk. 100 = 10
Years for I of Tk. 200 = (10/100) × 200 = 20 Years

Alternative Method:
Assuming simple interest, let the amount be P and rate of interest per annum be R%.

Given that P becomes 2P in 10 years.
=> P + PX10X R/100 = 2P
=> 1 + R/10 = 2
=> R = 10

Let P triple itself in N years:
=> P + PXNX 10/100 = 3P
=> 1 + N/10 = 3
=> N = 20 years

৯০৯.

A bag contains 5 green, 3 yellow, and 2 black balls. If one ball is drawn at random, what is the probability that it will not be a yellow ball?

ক
2/5
খ
7/10
গ
9/10
ঘ
3/10

ব্যাখ্যা

Question: A bag contains 5 green, 3 yellow, and 2 black balls. If one ball is drawn at random, what is the probability that it will not be a yellow ball?

Solution:
Given that,
Green balls = 5
Yellow balls = 3
Black balls = 2

∴ Total balls = 5 + 3 + 2 = 10
∴ Number of non-yellow balls = Green + Black = 5 + 2 = 7

We know,
Probability(not yellow) = favorable outcomes/total outcomes
= 7/10

∴ The probability that the ball drawn is not yellow is 7/10.

৯১০.

At a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years for which the money was invested is =?

ক
7 years
খ
4 years
গ
5 years
ঘ
3 years
ঙ
None of the above

ব্যাখ্যা

Question: At a certain time, the ratio of a certain principal and interest obtained from it are in the ratio 10 : 3 at 10% interest per annum. The number of years for which the money was invested is =?

Solution:
According to the question,
Principal = 10
Interest = 3

We know, T = (100 × S.I.)/(P × R)
= (100 × 3)/(10 × 10)
= 300/100
= 3 years

৯১১.

The LCM of three different numbers is 120. Which of the following cannot be their HCF?

ক
ক) 8
খ
খ) 12
গ
গ) 24
ঘ
ঘ) 35
ঙ
ঙ) Cannot be determined

ব্যাখ্যা

Since HCF is always a factor of LCM, we cannot have three numbers with HCF 35 and LCM 120.

৯১২.

Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are open in how many hours will the tank?

ক
ক) 12 minutes
খ
খ) 30 minutes
গ
গ) 15 minutes
ঘ
ঘ) 60 minutes

ব্যাখ্যা

Part filled by (A and B) pipes in 1 min = (1/20) + (1/30)
= (3 + 2)/60
= 5/60
= 1/12

Time taken to fill the tank = (1 × 12)/1 minutes
= 12 minutes

৯১৩.

In rectangle ABCD, diagonals = 36 unit. Find the value of x, where AE = 2x + 4y and CE = 4x - y.

ক
2
খ
3
গ
4
ঘ
5

ব্যাখ্যা

Question: In rectangle ABCD, diagonals = 36 unit. Find the value of x, where AE = 2x + 4y and CE = 4x - y.

Solution:
Diagonals = 36 unit
Each diagonal segment = 18.
2x + 4y = 18 ......(1)
and 4x - y = 18 .........(2)

From (1) + (2) × 4 we get,
2x + 4y + 16x - 4y = 18 + 72
⇒ 18x = 90
∴ x = 5

৯১৪.

If y + (3/y) = 5, what is the value of y³ + (27/y³)?

ক
70
খ
80
গ
100
ঘ
90

ব্যাখ্যা

Question: If y + (3/y) = 5, what is the value of y³ + (27/y³)?

Solution:
দেওয়া আছে y + 3/y = 5

∴ y³ + 27/y³ = (y + 3/y)³ - 3 × (y + 3/y) × 3
= 5³ - 9 × 5
= 125 - 45
= 80

৯১৫.

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

ক
1 : 2
খ
5 : 4
গ
4 : 5
ঘ
3 : 2

ব্যাখ্যা

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

Solution:
Let the third number be x

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

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

৯১৬.

If log₇(x² - x) − log₇(x - 1) = 2, then the value of x is -

ক
49
খ
42
গ
36
ঘ
30

ব্যাখ্যা

Question: If log₇(x² - x) − log₇(x - 1) = 2, then the value of x is -

Solution:
log₇(x² - x) − log₇(x - 1) = 2
⇒ log₇{(x² - x)/(x - 1)} = 2
⇒ log₇{x(x - 1)/(x - 1)} = 2
⇒ log₇x = 2
⇒ x = 7²
∴ x = 49

৯১৭.

Which number replaces the question mark?

ক
2
খ
7
গ
11
ঘ
4

ব্যাখ্যা

Question: Which number replaces the question mark?

Solution:
এখানে,
13 - 8 = 5
22 - 13 = 9
9 - 5 = 4
37 - 22 = 15
15 - 9 = 6
6 - 4 = 2

সুতরাং, প্রশ্নবোধক চিহ্নের স্থানে 2 বসবে।

৯১৮.

The average income of A, B and C is Tk. 12000 per month and average income of B, C and D is Tk. 15000 per month. If the average salary of D be twice that of A, then the average salary of B and C is in Tk.

ক
Tk. 8000
খ
Tk. 9000
গ
Tk. 18000
ঘ
Tk. 13500

ব্যাখ্যা

Question: The average income of A, B and C is Tk. 12000 per month and average income of B, C and D is Tk. 15000 per month. If the average salary of D be twice that of A, then the average salary of B and C is in Tk.

Solution:
Given that,
Average income of A, B, C = 12,000
∴ Total income of A + B + C = 3 × 12000 = 36000 … (1)
Average income of B, C, D = 15,000
∴ Total income of B + C + D = 3 × 15000 = 45000 … (2)
And, D = 2A ....(3)

Now, Subtract equation (1) from (2) than we get,
B + C + D - (A + B + C) = 45000 - 36000
⇒ D - A = 9000
⇒ 2A - A = 9000 ; [from (3)]
∴ A = 9000

Now put a = 9,000 in (i)
9000 + B + C = 36000
⇒ B + C = 36000 - 9000 = 27000
∴ B + C = 27000

∴ Average salary of B and C = (B + C)/2 = 27000/2 = 13500

So the average salary of B and C is Tk. 13500.

৯১৯.

ক
90°
খ
30°
গ
45°
ঘ
60°

ব্যাখ্যা

Question:

Solution:

৯২০.

Find the equation of the vertical line passing through the point (- 3, 5).

ক
y = - 3
খ
x = - 3
গ
y = 5
ঘ
x = 5

ব্যাখ্যা

Question: Find the equation of the vertical line passing through the point (- 3, 5).

Solution:

একটি উল্লম্ব রেখা (vertical line) হলো এমন একটি সরলরেখা যা Y-অক্ষের সমান্তরাল। এই ধরনের রেখার একটি বিশেষ বৈশিষ্ট্য হলো, রেখার উপর অবস্থিত প্রতিটি বিন্দুর x-স্থানাঙ্ক (x-coordinate) একই থাকে, কিন্তু y-স্থানাঙ্ক (y-coordinate) পরিবর্তিত হতে পারে।

উল্লম্ব রেখার সাধারণ সমীকরণ হলো: x = a, যেখানে a একটি ধ্রুবক সংখ্যা এবং রেখার প্রতিটি বিন্দুর x এর মান একই থাকে।

প্রশ্নে বলা হয়েছে রেখাটি (- 3, 5) বিন্দুর মধ্য দিয়ে যায়।
যেহেতু এই বিন্দুর x-স্থানাঙ্ক হলো - 3,
সুতরাং রেখাটির সমীকরণ হবে: x = - 3

৯২১.

The area of the floor of a museum is 500 square meters. How many unbroken tiles of dimension 10 x 20 cm² will be required to cover the floor completely?

ক
18,000 tiles
খ
20,000 tiles
গ
24,000 tiles
ঘ
25,000 tiles

ব্যাখ্যা

Question: The area of the floor of a museum is 500 square meters. How many unbroken tiles of dimension 10 x 20 cm² will be required to cover the floor completely?

Solution:
Area of the floor = 500 square meters

Area of one tile = 10 × 20 cm²
=(10/100) × (20/100) m²
= .10 × .20 m²
= 0.02 m²

Therefore,
Tiles required = 500/.02
= 500/(2/100)
= 250 × 100
= 25,000 tiles

৯২২.

Tk.5000 is deposited in a savings account which pays 7% annual interest compounded semi - annually. To the nearest tk how much is at the end of the year?

ক
ক) 5423
খ
খ) 5356
গ
গ) 5122
ঘ
ঘ) 5247

ব্যাখ্যা

১ম 6 মাসে মুনাফা = 5000 × 6/12 × 7/100 = 175
২য় 6 মাসে মুনাফা = 5175 × 6/12 × 7/100 = 362.25/2 = 181.125
∴ বছর শেষে মোট টাকার পরিমান = 5000 + 175 + 181.125 = 5356.125 ≈ 5356

৯২৩.

There are 28 people in a group. If all shake hands with one another person exactly once, how many handshakes are possible?

ক
378
খ
350
গ
420
ঘ
340
ঙ
368

ব্যাখ্যা

Question: There are 28 people in a group. If all shake hands with one another person exactly once, how many handshakes are possible?

Solution:
Total Handshakes = ²⁸C₂ = 378

৯২৪.

Two pipes A and B would fill the tank in 20 and 30 minutes respectively. Both pipes being open, find when A must be turned off so that the tank may be just filled in 15 minutes.

ক
ক) After 10 mins
খ
খ) After 15 mins
গ
গ) After 20 mins
ঘ
ঘ) After 13 mins

ব্যাখ্যা

Question: Two pipes A and B would fill the tank in 20 and 30 minutes respectively. Both pipes being open, find when A must be turned off so that the tank may be just filled in 15 minutes.

Solution:
Let, after x minutes pipe A must be turned off.
Part fill by (A + B ) in 1 minutes = (1/20+ 1/30) = 1/12
Part fill by (A + B ) in x minutes = x/12

Then, pipe B does the job = (15 - x) minutes
In (15 - x) minutes Pipe B can fill the tank (15 - x) part

ATQ,
x/12 + (15 - x)/30 = 1
⇒ (5x + 30 - 2x)/60 = 1
⇒ 3x + 30 = 60
⇒ 3x = 30
⇒ x = 10

৯২৫.

An outgoing pipe pours water at half the amount of an ingoing pipe. After 6 hours of running both pipes, a tank was filled. If the outgoing pipe was closed, how much time would it take to fill the tank with the ingoing pipe?

ক
2 hours
খ
1.5 hours
গ
3 hours
ঘ
4 hours

ব্যাখ্যা

Question: An outgoing pipe pours water at half the amount of an ingoing pipe. After 6 hours of running both pipes, a tank was filled. If the outgoing pipe was closed, how much time would it take to fill the tank with the ingoing pipe?

Solution:
Let,
ingoing pipe needs X hours,
The outgoing pipe needs 2X hours.

together in one hour, these pipes can fill = (1/X) - (1/2X) = 1/2X

ATQ,
2X = 6
X = 3
∴ Ingoing pipe will take 3 hours to fill the tank.

৯২৬.

The total age of two friends is 40. 5 years back their age ratio was 7 : 8. In 5 years what will be the ratio of their age?

ক
ক) 7 : 8
খ
খ) 12 : 13
গ
গ) 15 : 17
ঘ
ঘ) 3 : 4

ব্যাখ্যা

Question: The total age of two friends is 40. 5 years back their age ratio was 7 : 8. In 5 years what will be the ratio of their age?

Solution:
let, 5 years back their age was 7x and 8x
∴ 7x + 8x = 30
x = 2

after five years their age ratio will be (7 × 2 + 10) : (8 × 2 + 10)
= 24 : 26
= 12 : 13

৯২৭.

What percent of 10 kg is 50 grams?

ক
0.5%
খ
0.25%
গ
5%
ঘ
1%

ব্যাখ্যা

Question: What percent of 10 kg is 50 grams?

Solution:
Required Percentage = {(50gm/10kg) × 100}%
= {(50/10000) × 100}% [1kg = 1000gm]
= (5000/10000)%
= 0.5%

৯২৮.

Arrange the words given below in a meaningful sequence.
1. Crime
2. punishment
3. Police
4. Justice
5. Judgement.

ক
2, 1, 3, 5, 4
খ
1, 3, 4, 5, 2
গ
4, 1, 5, 2, 3
ঘ
1, 5, 4, 3, 2

ব্যাখ্যা

Question: Arrange the words given below in a meaningful sequence.
1. Crime
2. punishment
3. Police
4. Justice
5. Judgement

Solution:
Crime → 1
Police → 3
Justice → 4
Judgement → 5
punishment → 2

so, meaningful sequence is 1, 3, 4, 5, 2

৯২৯.

A does double the work of B in the same time. If they work together, they can dig a canal in 16 days. How many days would B take if he had to dig the same canal working alone?

ক
ক) 36 days
খ
খ) 24 days
গ
গ) 18 days
ঘ
ঘ) 48 days

ব্যাখ্যা

A does double the work of B in the same time

Number of days to dig canal = 16 days

Formula used:
Efficiency = Work done/Time

According to the question
The ratio of efficiency of A to B = 2 ∶ 1
Total work = (2 + 1) × 16 = 48

Number of days B alone takes to dig the canal = 48/1
⇒ 48 days

∴ The number of days B alone takes to dig the canal is 48 days.

৯৩০.

A monkey climbs a 10 meters-high slippery pillar. In his first minute, he climbs 2 meters, and in the next minute, he slip one meter down. In this way, how much time will he take to reach the top of the pillar?

ক
20 min
খ
21 min
গ
17 min
ঘ
19 min

ব্যাখ্যা

Question: A monkey climbs a 10 meters-high slippery pillar. In his first minute, he climbs 2 meters, and in the next minute, he slip one meter down. In this way, how much time will he take to reach the top of the pillar?

Solution:
On first minute monkey climb = 2 m
On the second minute it slips = 1 m
For every two minute, it climbs 1 m
So, average speed = 1 m/2 min For 8 m,
time is taken = 16 min
For the last 2 m jump add 1 min
So time taken = (16 + 1) min
= 17 min

∴ Monkey takes 17 minutes to reach the top of the pole.

৯৩১.

Bananas are bought at Tk. 36 per dozen and sold at a profit of 25%. How much is the selling price of twenty bananas?

ক
ক) Tk. 70
খ
খ) Tk. 72
গ
গ) Tk. 75
ঘ
ঘ) Tk. 65

ব্যাখ্যা

Question: Bananas are bought at Tk. 36 per dozen and sold at a profit of 25%. How much is the selling price of twenty bananas?

Solution:
৩৬ টাকায় ক্রয় করে ১২ টি কলা
∴ ১ টাকায় ক্রয় করে ১২/৩৬ টি কলা
∴ ১০০ টাকায় ক্রয় করে (১২ × ১০০)/৩৬ টি কলা
= ১০০/৩ টি কলা

২৫% লাভে বিক্রয়মূল্য = (১০০ + ২৫) টাকা = ১২৫ টাকা

২৫% লাভ করতে হলে,
১০০/৩ টি কলার বিক্রয়মূল্য ১২৫ টাকা
∴ ১ টি কলার বিক্রয়মূল্য (১২৫ × ৩)/১০০ টাকা
∴ ২০ টি কলার বিক্রয়মূল্য (১২৫ × ৩ × ২০)/১০০ টাকা
= ৭৫ টাকা

৯৩২.

What number should replace the question mark?

ক
ক) 18
খ
খ) 68
গ
গ) 81
ঘ
ঘ) 44
ঙ
ঙ) 52

ব্যাখ্যা

Question: What number should replace the question mark?

Solution:
In first figure:
4 × 8 + 7 = 32 + 7 = 39

In second figure:
6 × 3 + 9 = 18 + 9 = 27

So, in third figure:
9 × 7 + 5 = 63 + 5 = 68

∴ The number is 68

৯৩৩.

If the selling price is tripled and the cost price doubled, the profit would become 65%. What is the present profit (in %)?

ক
90%
খ
100%
গ
10%
ঘ
20%

ব্যাখ্যা

Let, the selling price be = x, Cost price be = y
So profit = 3x- 2y
Profit % = {(3x-2y)/2y} ×100 = 65
So, 300x - 200y = 130y
So 330y = 300x
x/y = 330/300 = 1.1
∴ Present Profit %= 10% .

৯৩৪.

Three rectangular fields having area 60 sq m, 84 sq m and 108 sq m are to be divided into identical rectangular flower beds, each having a length 4m. Find the breadth of each flower bed.

ক
ক) 2m
খ
খ) 3m
গ
গ) 4m
ঘ
ঘ) 1m

ব্যাখ্যা

We need to divide each large field into smaller flower beds such that the area of each bed is same.

So, we find the HCF of the larger fields that gives us the area of the smaller field.

HCF (60, 84, 108) = 12

Now, this HCF is the area (in m²) of each flower bed.

Also, the area of a rectangular field = Length x Breadth

=> 12 = 4 x Breadth

=> Breadth = 3m

Hence, each flower bed would be 3m wide.

৯৩৫.

sinθ√(1 + tan²θ)=?

ক
ক) cosecθ
খ
খ) tanθ
গ
গ) secθ
ঘ
ঘ) cotθ

ব্যাখ্যা

Question: sinθ√(1 + tan²θ)=?

Solution:
sinθ√(1 + tan²θ)
= sinθ√(sec²θ)
= sinθ × secθ
= sinθ × (1/cosθ)
= sinθ/cosθ
= tanθ

৯৩৬.

A bicycle marked at Tk. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:

ক
ক) 1,268
খ
খ) 1,368
গ
গ) 1,468
ঘ
ঘ) 1,568

ব্যাখ্যা

Marked Price = 2000
SP after first Discount of 20% = 2000 - 20% of 2000 = 1600
SP after second Discount of 10% = 1600 - 10% of 1600 = 1440
Now, the final selling price at cash = 1440 - 5% of 1440 = Tk. 1368

৯৩৭.

ক
ক) 100
খ
খ) 100/61
গ
গ) 19/53
ঘ
ঘ) 61

ব্যাখ্যা

Question:

Solution:

৯৩৮.

In a 60-liter mixture, the ratio of juice and water is 5:1. How much water must be added to make the ratio 2:1?

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

ব্যাখ্যা

Question: In a 60-liter mixture, the ratio of juice and water is 5:1. How much water must be added to make the ratio 2:1?

সমাধান:
মোট মিশ্রণের পরিমাণ = ৬০ লিটার
জুস : পানি = ৫ : ১
∴ জুসের পরিমাণ = (৫/৬) × ৬০ = ৫০ লিটার
∴ পানির পরিমাণ = (১/৬) × ৬০ = ১০ লিটার

মনে করি,
ক লিটার পানি যোগ করতে হবে।
⇒ নতুন পানির পরিমাণ = ১০ + ক লিটার
জুস অপরিবর্তিত = ৫০ লিটার

প্রশ্নমতে,
৫০/(১০ + ক) = ২/১
⇒ ৫০ = ২ × (১০ + ক)
⇒ ৫০ = ২০ + ২ক
⇒ ২ক = ৩০
⇒ ক = ১৫

∴ ১৫ লিটার পানি যোগ করতে হবে।

৯৩৯.

If (a/b) + (b/a) = 3, then (a/b)² + (b/a)² =?

ক
9
খ
6
গ
3
ঘ
7

ব্যাখ্যা

প্রশ্ন: If (a/b) + (b/a) = 3, then (a/b)² + (b/a)² =?

সমাধান:
দেয়া আছে,
(a/b) + (b/a) = 3

(a/b)² + (b/a)² = {(a/b) + (b/a)}² - 2(a/b). (b/a)
= 3² - 2
= 9 - 2
= 7

৯৪০.

In a certain office, the human resources department reports that 60% of the employees in the office commute over an hour on average each day, and that and that 25% of those employees, who commute over an hour on average each day commute by train. If an employee at the office is selected at random, what is the probability that the employee commutes over an hour on average by train?

ক
ক) 0.10
খ
খ) 0.15
গ
গ) 0.20
ঘ
ঘ) 0.25

ব্যাখ্যা

ধরি,
মোট চাকরিজীবী 100 জন
∴ ট্রেনে ভ্রমণ করেন = 60 এর 25%
= 15
∴ সম্ভাব্যতা = 15/100
= 0.15

৯৪১.

If A : B = 3 : 4, and B : C = 12 : 17, then A : C = ?

ক
9 : 17
খ
9 : 12
গ
12 : 17
ঘ
17 : 12

ব্যাখ্যা

A : B = 3 : 4 = (3 × 3) : (4 × 3) = 9 : 12
B : C = 12 : 17
A : B : C = 9 : 12 : 17
Therefore, A : C = 9 : 17

৯৪২.

What is the weight of 1 cubic meter of water?

ক
1000 kg
খ
1000 g
গ
100 kg
ঘ
10 kg

ব্যাখ্যা

Question: What is the weight of 1 cubic meter of water?

Solution:
We know,
The weight of 1 cubic meter of water is 1000 kg.

৯৪৩.

The angle of depression of a point situated at a distance of 50 m from the base of a tower is 30°. What is the height of the tower?

ক
ক) 50√3
খ
খ) 50/√3
গ
গ) 25/√3
ঘ
ঘ) 25√3

ব্যাখ্যা

Question: The angle of depression of a point situated at a distance of 50 m from the base of a tower is 30°. What is the height of the tower?

Solution:

Length of the tower AB = h meter
∠DAC = ∠ACB = 30°
∴ BC = 50

In △ ABC,
tan30° = AB/BC
⇒ 1/√3 = h/50
∴ h = 50/√3

৯৪৪.

Mean proportional of 4 and 36 is x and third proportional of 18 and x is y. Find the value of y.

ক
ক) 9
খ
খ) 12
গ
গ) 8
ঘ
ঘ) 6

ব্যাখ্যা

প্রশ্ন: Mean proportional of 4 and 36 is x and third proportional of 18 and x is y. Find the value of y.

সমাধান:
Given,
Mean proportional of 4 and 36 = x
∴ x² = 4 × 36
⇒ x = 12

Third proportional of 18 and 12 = y
∴ 12² = 18 × y
⇒ 144 = 18 × y
⇒ y = 8

৯৪৫.

Which of the following is the 250% of 1?

ক
ক) 0.25
খ
খ) 2.5
গ
গ) 25
ঘ
ঘ) 0.025

ব্যাখ্যা

Question: Which of the following is 250% of 1?

Solution:
250% of 1 is = 1 × 250%
= 1 × (250/100)
= 2.5

৯৪৬.

The figure above is composed of 6 squares, each with side s centimeters. If the number of centimeters in the perimeter of the figure is equal to the number of square centimeters in its area, what is the value of s?

ক
1
খ
5/3
গ
2
ঘ
5/2
ঙ
7/3

ব্যাখ্যা

Question:

The figure above is composed of 6 squares, each with side s centimeters. If the number of centimeters in the perimeter of the figure is equal to the number of square centimeters in its area, what is the value of s?

Solution:

Area of the figure is 6s² square centimeters, as there are 6 little squares and each has the are of s²

As we can see there are 14 sides exposed, thus the perimeter of the figure is 14s.

ATQ,
14s = 6s²
⇒ 14 = 6s
⇒ 7 = 3s
∴ s = 7/3

৯৪৭.

Tickets numbered 1 to 50 are mixed and one ticket is drawn at random. Find the probability that the ticket drawn has a number which is a multiple of 4 or 7?

ক
9/25
খ
9/50
গ
18/25
ঘ
13/25

ব্যাখ্যা

S = {1, 2, 3,............, 49, 50}
E = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 7, 14, 21, 35, 42, 49}
n(S) = 50
n(E) = 18

P(E) = n(E)/n(S)
= 18/50
= 9/25.

৯৪৮.

Which number is the odd one in oval A and B respectively?

ক
42, 18
খ
42, 52
গ
36, 6
ঘ
48, 52

ব্যাখ্যা

Question: Which number is the odd one in oval A and B respectively?

Solution:
In figure A,
42 is odd because except 42 all the other numbers are divisible by 12

In figure B,
52 is odd because except 52 all the other numbers are divisible by 6

৯৪৯.

In how many ways can the letters of the word 'LEADER' be arranged?

ক
360
খ
420
গ
540
ঘ
620

ব্যাখ্যা

Question: In how many ways can the letters of the word 'LEADER' be arranged?

Solution:
The word 'LEADER' has total 6 letters among them letter L = 1, E = 2, A = 1, R = 1, D = 1

Ways = 6!/2! = 720/2 = 360

৯৫০.

How many number plates of 3 digit can be formed with four digits 1,2,3 and 4?

ক
ক) 18
খ
খ) 24
গ
গ) 28
ঘ
ঘ) 36

ব্যাখ্যা

Here, the order of arrangement of digits does matter.
ⁿP_r= n!/(n-r)!
ⁿP_r= 4!/(4-3)!
⁴P₃= 4!/1!
⁴P₃= 4!
⁴P₃= 24

৯৫১.

A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

ক
3
খ
5
গ
6
ঘ
9
ঙ
10

ব্যাখ্যা

Question: A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished?

Solution:
[(100 × 35) + (200 × 5)]men can finish the work in 1 day
Therefore,
4500 men can finish the work in 1 day.
100 men can finish it in 4500/100 = 45 days.

∴ This is 5 days behind Schedule

৯৫২.

If ‍a² + b² = 63 and ab = 9 then = ?

ক
ক) 1/2
খ
খ) 2
গ
গ) 1
ঘ
ঘ) 1/3

ব্যাখ্যা

Question: If ‍a² + b² = 63 and ab = 9 then = ?

Solution:
দেওয়া আছে,
a² + b² = 63
ab = 9

এখন,
(1/a) + (1/b)
= (b + a)/ab
= √(a + b)²/ab
= √(a² + b² + 2ab)/ab
= √{63 + (2 × 9)}/9
= √81/9
= 9/9
= 1

৯৫৩.

If the cost of p metres of wire is Tk. d, then what is the cost of q metres of wire at the same rate (in Tk)?

ক
pq/d
খ
dp/q
গ
q/pd
ঘ
dq/p

ব্যাখ্যা

If the cost of p metres of wire is Tk. d, then what is the cost of q metres of wire at the same rate (in Tk)?

Solution:
Cost of p metres = Tk. d
Cost of 1 metre = Tk. d/p
Cost of q metres = Tk. dq/p

৯৫৪.

What is the unit digit in the product 84 × 59 × 13 × 77?

ক
ক) 6
খ
খ) 9
গ
গ) 8
ঘ
ঘ) 7

ব্যাখ্যা

প্রশ্ন : What is the unit digit in the product 84 × 59 × 13 × 77?

সমাধান: 84 × 59 × 13 × 77 = 4960956
Without the use of calculator, to count the unit digit = 4 × 9 × 3 × 7 = 756

So, 6 is the unit digit

৯৫৫.

A 20 m long, and 15 m broad hall is surrounded by a verandah with a uniform width of 2.5 m. Find the cost of flooring the verandah at Tk. 3.50 per square meter.

ক
Tk. 500
খ
Tk. 600
গ
Tk. 700
ঘ
Tk. 800

ব্যাখ্যা

Question: A 20 m long, and 15 m broad hall is surrounded by a verandah with a uniform width of 2.5 m. Find the cost of flooring the verandah at Tk. 3.50 per square meter.

Solution:
Length of the hall = 20 m,
Breadth of hall = 15 m,
Area of hall = 20 × 15 = 300 m²

Length of hall with verandah = 20 + 2.5 + 2.5 = 25 m,
Breadth of hall with verandah = 15 + 2.5 + 2.5 = 20 m,
Area of hall with verandah = 25 × 20 = 500 m²

Area of verandah = area of hall with verandah - area of hall
= 500 - 300 = 200 m²

Cost of flooring the verandah is Tk. 3.50 per square meter.
So, the cost of flooring the entire verandah = 3.50 × 200 = Tk. 700

৯৫৬.

Find the value of the expression a² - 2ab + b² for a = 1, b = 1.

ক
1
খ
- 1
গ
2
ঘ
0

ব্যাখ্যা

Question: Find the value of the expression a² - 2ab + b² for a = 1, b = 1.

Solution:
a² - 2ab + b²
= (a - b)²
= (1 - 1)²
= (0)²
= 0

৯৫৭.

The average price of three items of furniture is Tk 14200. If their prices are in the ratio 3 : 2 : 5, then the price of the most expensive item is-

ক
25620 Tk
খ
16540 Tk
গ
21300 Tk
ঘ
18150 Tk

ব্যাখ্যা

প্রশ্ন: The average price of three items of furniture is Tk 14200. If their prices are in the ratio 3 : 2 : 5, then the price of the most expensive item is-

সমাধান:
ধরি,
ফার্নিচার তিনটির মূল্য যথাক্রমে 3a, 2a এবং 5a
অনুপাতগুলোর যোগফল = 3a + 2a + 5a = 10a

প্রশ্নমতে,
10a = 14200 × 3
⇒ a = 43600/10
∴ a = 4260

অতএব, সবচেয়ে দামি ফার্নিচারটির মূল্য = 5 × 4260
= 21300 টাকা

৯৫৮.

If 3^2x . 9^{x + 1} = 27^{x - 1}, what is the value of x?

ক
- 5
খ
-1
গ
3
ঘ
5

ব্যাখ্যা

Question: If 3^2x . 9^{x + 1} = 27^{x - 1}, what is the value of x?

Solution:
3^2x . 9^{x + 1} = 27^{x - 1}
⇒ 3^2x . (3²)^{x + 1} = (3³)^{x - 1}
⇒ 3^2x . 3^{2(x + 1)} = 3^{3(x - 1)}
⇒ 3^2x . 3^{2x + 2} = 3^{3x - 3}
⇒ 3^{2x + 2x + 2} = 3^{3x - 3}
⇒ 3^{4x + 2} = 3^{3x - 3}
⇒ 4x + 2 = 3x - 3
⇒ 4x - 3x = - 3 - 2
∴ x = - 5

৯৫৯.

A mother said to her daughter "I was as old as you are at present at the time of your birth". If the mother's age is 38 years now, the daughters age five years back was-

ক
ক) 19
খ
খ) 15
গ
গ) 14
ঘ
ঘ) 33

ব্যাখ্যা

দেয়া আছে,
মাতার বর্তমান বয়স 38 বছর।
মেয়ের বর্তমান বয়স = 38 /2 = 19 বছর।

5 বছর আগে মেয়ের বয়স ছিল = 19 - 5 = 14 বছর।

বিকল্প

ধরি,
মেয়ের বর্তমান বয়স = x বছর।
মাতার বর্তমান বয়স (x + x) = 2x বছর

শর্তমতে,
2x = 38
x=19

5 বছর পূর্বে মেয়ের বয়স ছিল = (19 - 5) বছর
= 14 বছর।

৯৬০.

If x > 2 and x < 5, then which of the following expressions is positive?
I. (x - 2)(x - 5)
II. (2 - x)(x - 5)
III. (2 - x)(5 - x)

ক
I only
খ
II only
গ
III only
ঘ
I and III
ঙ
None of these

ব্যাখ্যা

Question: If x > 2 and x < 5, then which of the following expressions is positive?
I. (x - 2)(x - 5)
II. (2 - x)(x - 5)
III. (2 - x)(5 - x)

Solution:
Given,
x > 2 and x < 5

For expression I: (x - 2)(x - 5)
Since x > 2, (x - 2) will be positive.
Since x < 5, (x - 5) will be negative.
(x - 2)(x - 5) = positive × negative = negative

For expression II: (2 - x)(x - 5)
Since x > 2, (2 - x) will be negative.
Since x < 5, (x - 5) will be negative.
(2 - x)(x - 5) = negative × negative = positive

For expression III: (2 - x)(5 - x)
Since x > 2, (2 - x) will be negative.
Since x < 5, (5 - x) will be positive.
(2 - x)(5 - x) = negative × positive = negative

∴ Only expression II is positive.

৯৬১.

If p + 3 + 1/p = 0 then what is the value of p² + 1/p² = ?

ক
11
খ
7
গ
8
ঘ
9

ব্যাখ্যা

Question: If p + 3 + 1/p = 0 then what is the value of p² + 1/p² = ?

Solution:
Given,
p + 3 + 1/p = 0
⇒ p + 1/p = - 3
⇒ (p + 1/p)² = (- 3)² [
⇒ p² + 2. p. 1/p + 1/p² = 9
⇒ p² + 1/p² = 9 - 2
∴ p² + 1/p² = 7

৯৬২.

How many different selections of 4 books can be made from 10 different books, if 2 particular books are never selected?

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

ব্যাখ্যা

Question: How many different selections of 4 books can be made from 10 different books, if 2 particular books are never selected?

Solution:
Number of different books =10
Number of books to be formed = 4

If two particular books are never selected,
∴ Number of ways = ⁸C₄
=8!/4!(8 -4)!
= 8 × 6 × 7 × 5 × 4!/4! × 4 × 3 × 2
= 70 ways

৯৬৩.

A farm rears geese and dogs. The headcount in the farm is 84 and the leg count is 282. How many geese are there?

ক
27
খ
30
গ
54
ঘ
57

ব্যাখ্যা

Let geese be denoted by 'G' and Dogs by 'D'
Geese have 2 legs; Dogs have 4 legs.

Total Heads = G + D = 84 ------------------------- (1)
Total Legs = 2G + 4D = 282 --------------------- (2)

Divide equation 2 by 2, we get,
G + 2D = 141 -------------------------------------- (3)
Equation 3 - Equation 2
G + 2D - G - D = 141 - 84
∴ D = 57

So, Geese = 84 - 57 = 27

৯৬৪.

A and B together have Tk. 500. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

ক
ক) 200
খ
খ) 250
গ
গ) 300
ঘ
ঘ) 350

ব্যাখ্যা

Question: A and B together have Tk. 500. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does A have?

Solution:
Here,
(4/15)A = (2/5)B
A/B = 30/20
A : B = 3 : 2

Hence,
The amount of A = (500 × 3/5)
= 1500/5
= 300

৯৬৫.

The average speed of a bus is one-third of the speed of a train. The train covers 1200 km in 16 hours. How much distance will the bus cover in 48 minutes?

ক
ক) 30 km
খ
খ) 25 km
গ
গ) 20 km
ঘ
ঘ) 50 km

ব্যাখ্যা

Question: The average speed of a bus is one-third of the speed of a train. The train covers 1200 km in 16 hours. How much distance will the bus cover in 48 minutes?

Solution:
Speed of the train = (1200/16) km/hr.
= 75 km/hr.

Speed of the bus = (1/3)×75 km/hr.
= 25 km/hr.

Distance covered by the bus in 60 min = 25 km
Distance covered by the bus in 48 min =(25/60) × 48 = 20 km

৯৬৬.

Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is

ক
ক) 27
খ
খ) 33
গ
গ) 49
ঘ
ঘ) 55

ব্যাখ্যা

Let the numbers be 3x and 5x.
Then, (3x-9)/(5x - 9) = 12/23
⇒ 23(3x - 9) = 12(5x - 9)
⇒ 69x - 207 = 60x - 108
⇒ 9x = 99
⇒ x = 11.
∴ The smaller number = (3×11) = 33

৯৬৭.

The probability that an integer in the set 1, 2, 3, ....86 is divisible by 2 and not divisible by 3 is __________.

ক
ক) 17/86
খ
খ) 29/86
গ
গ) 21/86
ঘ
ঘ) 23/86

ব্যাখ্যা

প্রশ্ন : The probability that an integer in the set 1, 2, 3, ....86 is divisible by 2 and not divisible by 3 is __________.

সমাধান :

The set is (1, 2, 3, ....86)

Number divided by 2 = 86/2 = 43
So, 43 numbers are divisible by 2

The number which is divisible by 2 and 3
Both i.e, divisible by 6 → (6, 12, 18, ....86) = 14

So, only divisible by 2 not 3 = 43 - 14 = 29

Required probability = 29/86
∴ The required answer is 29/86

৯৬৮.

If x² + y² = 40 and xy = 12, what is the value of (x - y)²?

ক
12
খ
16
গ
10
ঘ
15

ব্যাখ্যা

Question: If x² + y² = 40 and xy = 12, what is the value of (x - y)²?

Solution:
We are given:
x² + y² = 40
xy = 12

Use the identity:
(x - y)² = x² + y² - 2xy

Substitute the values:
⇒ (x - y)² = x² + y² - 2xy
⇒ (x - y)² = 40 - 2 × 12
⇒ (x - y)² = 40 - 24
∴ (x - y)² = 16

৯৬৯.

The sum of the digits of a two-digit number is 12 and the difference between the two digits of the two-digit number is 6. What is the two-digit number?

ক
75
খ
95
গ
39
ঘ
84

ব্যাখ্যা

Question: The sum of the digits of a two-digit number is 12 and the difference between the two digits of the two-digit number is 6. What is the two-digit number?

Solution:
Let, the two-digit number be 10a + b where a > b.

ATQ,
a + b = 12 ------- (1)
a - b = 6 --------- (2)

On adding equation (1) & (2)
21 =18
∴ a = 9

Putting this value in (1) we get,
9 + b = 12
∴ b = 3

So the number is 10a + b = 9 . 10 + 3 = 93

When, a < b, Then the required number is 39

৯৭০.

A 60-meter cable is attached from the top of a vertical pole down to the ground. If the cable makes an angle of 30 degrees with the ground, find the height of the pole.

ক
36 m
খ
16.92 m
গ
20 m
ঘ
30 m
ঙ
None of these

ব্যাখ্যা

Question: A 60-meter cable is attached from the top of a vertical pole down to the ground. If the cable makes an angle of 30 degrees with the ground, find the height of the pole.

Solution:

Let,
Height, AB = h

Given that,
AC = 60m
∠ACB = 30°

∴ sin30°= AB/AC
⇒ 1/2 = h/60
⇒ h = 60 × (1/2)
∴ h = 30 m

So the height of the pole is 30 meters

৯৭১.

The average wage of a worker during a fortnight comprising 15 consecutive working days was Taka 90 per day. During the first 7 days, his average wage was Taka 87 per day and the average wage during the last 7 days was Taka 92 per day. What was his wage on the 8th day?

ক
ক) 83
খ
খ) 90
গ
গ) 92
ঘ
ঘ) 97

ব্যাখ্যা

15 দিনের কাজের মোট বেতন (15 × 90) = 1350 টাকা
১ম 7 দিন ও শেষ 7 দিনের কাজের মোট বেতন (7×87 + 7×92) = 609 + 644 = 1253 টাকা।
∴ অষ্টম দিনের কাজের বেতন = (1350 - 1253) = 97 টাকা

৯৭২.

ক
7
খ
14
গ
49
ঘ
50

ব্যাখ্যা

Question:
Solution:

৯৭৩.

If two jeans and three shirts cost Tk. 4000 and three jeans and two shirts cost Tk. 3500, then how much does a jeans-

ক
400 taka
খ
500 taka
গ
800 taka
ঘ
1000 taka

ব্যাখ্যা

Question: If two jeans and three shirts cost Tk. 4000 and three jeans and two shirts cost Tk. 3500, then how much does a jeans

Solution:
মনেকরি
১টি jeans এর দাম = x টাকা
১টি shirt এর দাম = y টাকা

এখানে
2x + 3y = 4000.......................(1)
3x + 2y = 3500.........................(2)

(1) × 2 - (2) × 3 ⇒
4x + 6y - 9x - 6y = 8000 - 10500
- 5x = - 2500
x = 500

১টি jeans এর দাম = 500 টাকা

৯৭৪.

If the height of Rasel is less by 20% than Maruf, the height of Maruf will be greater than that of Rasel by how many percent?

ক
25%
খ
28%
গ
30%
ঘ
32%

ব্যাখ্যা

Question: If the height of Rasel is less by 20% than Maruf, the height of Maruf will be greater than that of Rasel by how many percent?

Solution:
Let the height of Maruf is x and height of Rasel is y.
Then, height of Rasel = x - 20% of x
y = x - (20x)/100
⇒ y = x - x/5
⇒ y = (5x - x)/5
⇒ y = 4x/5
∴ x = 5y/4

Now,
height of Maruf - height of Rasel
= 5y/4 - y
= (5y - 4y)/4
= y/4

∴ Height of Suresh will be greater than that of Ramesh by = {(y/4)/y} × 100
= (y/4) × (1/y) × 100
= 25%

৯৭৫.

Working alone, pump A can empty a pool in 3 hours. Working alone, pump B can empty the same pool in 2 hours. Working together, how many minutes will it take pump A and pump B to empty the pool?

ক
ক) 72
খ
খ) 75
গ
গ) 84
ঘ
ঘ) 96

ব্যাখ্যা

Pump A can empty the pool in 3 hours therefore the rate at which it empties is 1/3 pool/hour
Pump b can empty the pool in 2 hours therefore the rate at which it empties is 1/2 pool/hour.
If they work together, the resulting rate is the addition of both rates (1/3 +1/2)pool/hour = 5/6 pool/hour

Now we have the following: (5/6pool)/60min = 1pool/x
Or, x = 72minutes

৯৭৬.

In how many ways can 5 books be selected from 12 books, with 2 particular books always left out?

ক
192
খ
235
গ
252
ঘ
280

ব্যাখ্যা

Question: In how many ways can 5 books be selected from 12 books, with 2 particular books always left out?

Solution:
মোট বস্তু, n = 12
সর্বদা বাদ বা বর্জন থাকবে, m = 2
এবং প্রতিবার নিতে হবে, r = 5

∴ সমাবেশ = ^{(n - m)}C_r = ^{(12 - 2)}C₅
= ¹⁰C₅
= 10!/[5!(10 - 5)!]
= (10 × 9 × 8 × 7 × 6)/(5 × 4 × 3 × 2 × 1)
= 252

৯৭৭.

The area of lawn is 460 m². If the length is 15 percent more than the breadth of the rectangular field. What is the length of the field?

ক
ক) 15 m
খ
খ) 26 m
গ
গ) 34.5 m
ঘ
ঘ) None of these

ব্যাখ্যা

Let, Breadth = x
So, length = x + 15% of x = x + 3x/20 = 23x/20
ATQ,
23x/20 × x = 460
Or, x² = (460×20)/23 = 400
Or, x = 20
So, length = (23×20)/20 = 23 m

৯৭৮.

The LCM and the HCF of the numbers 28 and 42 are in the ratio-

ক
ক) 5 : 1
খ
খ) 2 : 3
গ
গ) 3 : 2
ঘ
ঘ) 6 : 1

ব্যাখ্যা

প্রশ্ন: 28 এবং 42 এর ল.সা.গু ও গ.সা.গু এর অনুপাত কত?

সমাধান:
28 ও 42 এর ল.সা.গু= 84
28 ও 42 এর গ.সা.গু = 14

∴ ল.সা.গু : গ.সা.গু = 84 : 14 = 6 : 1

৯৭৯.

A box contains 12 poles and 7 pieces of net. Each piece of net weighs 0.2 gm: each pole weighs 1.1gm. The box and its contents together weigh 16.25 gm. How much does the empty box weigh?

ক
ক) 1.2 gm
খ
খ) 1.65 gm
গ
গ) 2.75 gm
ঘ
ঘ) 6.15 gm

ব্যাখ্যা

Weight of 7 nets = (7 × 0.2) gm = 1.4 gm
And, Weight of 12 poles = (12 × 1.1) gm = 13.2 gm
Total weight of net and pole = (1.4 + 13.2) gm = 14.6 gm
∴ Empty box's weight = (16.25 – 14.6) = 1.65 gm

৯৮০.

The average monthly income of Rakib and Sunny is Tk. 5050. The average monthly income of Sunny and Rabbi is Tk. 6250 and the average monthly income of Rakib and Rabbi is Tk. 5200. What is the monthly income of Rakib?

ক
3000
খ
6000
গ
4000
ঘ
2500

ব্যাখ্যা

Question: The average monthly income of Rakib and Sunny is Tk. 5050. The average monthly income of Sunny and Rabbi is Tk. 6250 and the average monthly income of Rakib and Rabbi is Tk. 5200. What is the monthly income of Rakib?

Solution:
Rakib + Sunny (total income) = 5050 × 2 = 10100 .............. (i)
Sunny + Rabbi (total income) = 6250 × 2 = 12500 .............. (ii)
Rakib + Rabbi (total income) = 5200 × 2 = 10400 ................. (iii)

Adding (i), (ii) and (iii), we get:
2(Rakib + Sunny + Rabbi) = 10100 + 12500 + 10400
⇒ 2(Rakib + Sunny + Rabbi) = 33000
⇒ Rakib + Sunny + Rabbi = 16500 ........... (iv)

Subtracting (ii) from (iv), we get
Rakib = 16500 - 12500
∴ Rakib = 4000

∴ Rakib's monthly income = Tk. 4000.

৯৮১.

Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

ক
Tk. 150.2
খ
Tk. 170.8
গ
Tk. 184.5
ঘ
Tk. 190

ব্যাখ্যা

Question: Tea worth Tk. 126 per kg and Tk. 135 per kg are mixed with a third variety in the ratio 1 : 2 : 2. If the mixture is worth Tk. 153 per kg, the price of the third variety per kg will be:

Solution:
let, price of third variety x tk per kg
126y + 135 × 2y + x × 2y = 153 (y + 2y + 2y)
⇒ 126 + 270 + 2x = 765
⇒ 2x = 369
∴ x = 184.5 tk

৯৮২.

What is the total interest on Tk 2,000 at 12.5% per annum for 9 months (in taka)?

ক
Tk. 150
খ
Tk. 210.5
গ
Tk. 187.5
ঘ
Tk. 190

ব্যাখ্যা

Question: What is the total interest on Tk 2,000 at 12.5% per annum for 9 months (in taka)?

সমাধান:
আসল, P = 2,000 টাকা
সুদের হার, r = 12.5% = 12.5/100 = 1/8
সময়, n = 9 মাস = 9/12 = 3/4 বছর

সুদ, I = Pnr
⇒ সুদ, I = 2,000 × (3/4) × (1/8)
∴ সুদ, I = 187.5 টাকা

৯৮৩.

A problem is given to three students whose chances of solving it are 1/3, 1/4 and 1/5 respectively. What is the probability that the problem will be solved?

ক
1
খ
1/2
গ
5/4
ঘ
3/5
ঙ
None of these

ব্যাখ্যা

Question: A problem is given to three students whose chances of solving it are 1/3, 1/4 and 1/5 respectively. What is the probability that the problem will be solved?

Solution:
Probability of 1st student solving the problem = 1/3
Probability of 1st student not solving the problem = 1 - (1/3) = 2/3

Probability of 2nd student solving the problem = 1/4
Probability of 2nd student not solving the problem = 1 - (1/4) = 3/4

Probability of 3rd student solving the problem = 1/5
Probability of 3rd student not solving the problem = 1 - (1/5) = 4/5

Probability that none of the students solve the problem = (2/3) × (3/4) × (4/5)
= 2/5

∴ Probability that the problem will be solved = 1 - (2/5)
= 3/5

∴ The probability that the problem will be solved is 3/5

৯৮৪.

Solve the inequality |1 - 2x| < 7

ক
3 < x < 2
খ
- 3 < x < 4
গ
4 < x < - 3
ঘ
- 3 < x < 3

ব্যাখ্যা

Question: Solve the inequality |1 - 2x| < 7

Solution:
Given that,
|1 - 2x| < 7
⇒ - 7 < 1 - 2x < 7
⇒ - 7 - 1 < 1 - 1 - 2x < 7 - 1
⇒ - 8 < - 2x < 6
⇒ - 4 < - x < 3 (dividing by - 2 and reversing the inequality signs)
⇒ 4 > x > - 3
∴ - 3 < x < 4

৯৮৫.

The top and bottom of a flag on a building subtend angles of 60° and 30° respectively at a point B which is 48 meter away from the building. Find the height of the flag?

ক
32 m
খ
16 m
গ
18.49 m
ঘ
32√3 m

ব্যাখ্যা

Question: The top and bottom of a flag on a building subtend angles of 60° and 30° respectively at a point B which is 48 meter away from the building. Find the height of the flag?

Solution:

Let height of building be AC = X and height of flag be CD = h.

In ΔDAB
tan60° = (X + h)/48
⇒ √3 = (X + h)/48
⇒ X + h = 48√3
∴ h = 48√3 - X ..................(1)

In ΔCAB
tan30° = X/48
⇒ 1/√3 = X/48
∴ X = 48/√3

From (1) we get,
h = 48√3 - 48/√3
= (48 × 3 - 48)/√3
= (144 - 48)/√3
= 96/√3
= (32 × 3)/√3
= 32√3

৯৮৬.

A salesman receives daily wage of Tk. 500 and earns a commission of 10% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1200?

ক
Tk. 5000
খ
Tk. 6500
গ
Tk. 7700
ঘ
Tk. 7000

ব্যাখ্যা

Question: A salesman receives daily wage of Tk. 500 and earns a commission of 10% on all sales he makes. How much taka worth of sales does he need to make in order to bring his total daily income of Tk. 1200?

Solution:
দৈনিক মোট আয় করতে হবে = 1200 টাকা
দৈনিক মজুরি = 500 টাকা
অবশিষ্ট= (1200 - 500) টাকা
= 700 টাকা

সেলস কমিশন 10 টাকা যখন সেলস = 100 টাকা
সেলস কমিশন 1 টাকা যখন সেলস = 100/10 টাকা = 10 টাকা
সেলস কমিশন 700 টাকা যখন সেলস = 10 × 700 টাকা
= 7000 টাকা

৯৮৭.

Running at the same constant rate, 10 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce in 30 minutes?

ক
ক) 120
খ
খ) 135
গ
গ) 150
ঘ
ঘ) 160

ব্যাখ্যা

Question: Running at the same constant rate, 10 identical machines can produce a total of 180 bottles per hour. How many bottles could 15 such machines produce in 30 minutes?

Solution:
In 60 minutes 10 machines can produce = 180 bottles
In 1 minute 1 machine can produce = 180/(60 × 10) bottles
In 30 minutes 15 machines can produce = (180 × 15 × 30)/(60 × 10) bottles
= 135 bottles

৯৮৮.

sec²17° - (1/tan²73°) - sin17°sec73°

ক
ক) 2
খ
খ) 1
গ
গ) 0
ঘ
ঘ) - 1

ব্যাখ্যা

Question: sec²17° - (1/tan²73°) - sin17°sec73°

Solution:
sec²17° - (1/tan²73°) - sin17°sec73°
= sec²17° - cot²73° - sin17°sec(90° - 17°)
= sec²17° - cot²(90° - 17°) - sin17°cosec17°
= sec²17° - tan²17° - 1
= 1 - 1 [sec²θ - tan²θ = 1]
= 0

৯৮৯.

A natural number when increased by 12, equals 160 times its reciprocal. The number is-

ক
20
খ
15
গ
12
ঘ
8

ব্যাখ্যা

Question: A natural number when increased by 12, equals 160 times its reciprocal. The number is-

Solution:
Let the number be x. Then,
x + 12 = 160 × (1/x)
⇒ x² + 12x - 160 = 0
⇒ x² + 20x - 8x - 160 = 0
⇒ x(x + 20) - 8(x + 20) = 0
⇒ (x + 20)(x - 8) = 0
⇒ x= - 20, 8

Therefore, the required number is 8.

৯৯০.

The LCM and HCF of two numbers are 495 and 5. If the sum of the numbers is 100, what is the difference of the numbers?

ক
10
খ
15
গ
20
ঘ
5

ব্যাখ্যা

Question: The LCM and HCF of two numbers are 495 and 5. If the sum of the numbers is 100, what is the difference of the numbers?

Solution:
let,
one number is x
∴ another number is (100 - x)

ATQ,
x(100 - x) = 5 × 495
⇒ 100x - x² = 2475
⇒ x² - 100x + 2475 = 0
⇒ x² - 55x - 45x + 2475 = 0
⇒ x(x - 55) - 45(x - 55) = 0
⇒ (x - 55)(x - 45) = 0
∴ x = 45, 55

∴ the numbers are 45 and 55. difference = 55 - 45 = 10

৯৯১.

Two-fifths of one-fourth of three-seventh of a number is 15. What is the Three-fifths of the number?

ক
150
খ
190
গ
210
ঘ
250

ব্যাখ্যা

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

Solution:
Let the number be x

ATQ,
(2/5) × (1/4) × (3/7) × x = 15
⇒ (1/10) × (3/7) × x = 15
⇒ (3/70) × x = 15
⇒ x = (15 × 70)/3
∴ x = 350

The Three-fifths of the number = (3 × 350)/5
= 210

৯৯২.

ক
4
খ
2
গ
3.96
ঘ
8

ব্যাখ্যা

Question:

Solution:

৯৯৩.

2, 8, 14, 20, 26, 32, 38, ... choose which pair of numbers comes next?

ক
44, 50
খ
42, 48
গ
2, 46
ঘ
32, 26

ব্যাখ্যা

Question: 2, 8, 14, 20, 26, 32, 38, ... choose which pair of numbers comes next?

Solution:
This is an arithmetic sequence where each term increases by 6.
Check the differences,
8 - 2 = 6
14 - 8 = 6
20 - 14 = 6
26 - 20 = 6
32 - 26 = 6
38 - 32 = 6
So the pattern is very clear that add 6 each time.

Next two numbers after 38 is-
38 + 6 = 44, 44 + 6 = 50

Therefore, the next pair is 44, 50.

৯৯৪.

A machine is sold at a profit of 20%. Had it been sold for Tk. 60 less, there would have been a loss of 20%. What was the cost price?

ক
Tk. 150
খ
Tk. 240
গ
Tk. 260
ঘ
Tk. 320

ব্যাখ্যা

Question: A machine is sold at a profit of 20%. Had it been sold for Tk. 60 less, there would have been a loss of 20%. What was the cost price?

Solution:
ধরি, মেশিনটির ক্রয়মূল্য = x টাকা

20% লাভে বিক্রয়মূল্য = x + x এর 20%
= x + 20x/100
= 12x/10

20% ক্ষতিতে বিক্রয়মূল্য = x - x এর 20%
= x - 20x/100
= 8x/10

প্রশ্নমতে,
(12x/10) - (8x/10)= 60
⇒ 4x/10 = 60
⇒ 4x = 60 × 10
⇒ x = (60 × 10)/4
∴ x = 150

∴ মেশিনটির ক্রয়মূল্য = 150 টাকা

৯৯৫.

A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

ক
10%
খ
10.8%
গ
20%
ঘ
28%
ঙ
None

ব্যাখ্যা

Question: A towel, when bleached, was found to have lost 20% of its length and 10% of its breadth. The percentage of decrease in area is:

Solution:
Let,
The length be 10x cm
The breadth be 10y cm
The area of the rectangle be 10x × 10y = 100xy

After reduction the length is = 10x × (80/100) = 8x
After reduction the breadth is = 10y × (90/100) = 9y
New area after reduction = 8x × 9y = 72xy

Change in area = 100xy - 72xy = 28xy
Change in Percentage = (28xy/100xy) × 100 = 28%

∴ Decreases in the area is 28%

৯৯৬.

If a 34 meter ladder is placed against a 17 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is:

ক
20º
খ
25º
গ
30º
ঘ
45º

ব্যাখ্যা

Question: If a 34 meter ladder is placed against a 17 meter wall such that it just reaches the top of the wall, the angle of elevation of the wall is:

Solution:
Given that
Ladder's length = 34m
Wall's height = 17m

perpendicular = Wall's height = 17m
Hypotenuse = Ladder's length = 34m

We know,
sinθ = perpendicular/hypotenuse
⇒ sinθ = 17/34
⇒ sinθ = 1/2
⇒ sinθ = sin 30º
⇒ θ = 30º

৯৯৭.

A is 30% more efficient than B. How much time will they, working together, take to complete a job which A alone could have done in 23 days?

ক
ক) 11 days
খ
খ) 13 days
গ
গ) 20(3/17) days
ঘ
ঘ) 15 days
ঙ
ঙ) None of these

ব্যাখ্যা

Ratio of times taken by A and B = 100:130 = 10:13
Suppose B takes x days to do the work.
Then,
10:13 :: 23:x
⇒ x = (23 × 13)/10
⇒ x = 299/10
A's 1 day's work = 1/23
B's 1 day's work = 10/299
(A + B)'s 1day's work = 1/23 + 10/299
= 23/299
= 1/13
∴ A and B together can complete the work in 13 days.

৯৯৮.

A sum of TK. 800 amounts to TK. 920 in 3 years at simple interest. What will it amount to if the rate of interest is increased by 3%?

ক
Tk. 1012
খ
TK. 972
গ
Tk. 980
ঘ
Tk. 992

ব্যাখ্যা

Question: A sum of TK. 800 amounts to TK. 920 in 3 years at simple interest. What will it amount to if the rate of interest is increased by 3%?

Solution:
Principal (P) = 800 TK.
Amount after 3 years = 920 TK.
∴ Simple Interest (SI) for 3 years = 920 - 800 = 120 TK.

Now, SI = (P × n × r)/100
⇒ 120 = (800 × 3 × r)/100
⇒ 120 = 24r
⇒ r = 120/24
∴ r = 5%

New Interest Rate = 5% + 3% = 8%
New simple interest for 3 years = (800 × 3 × 8) / 100 = 192 TK.
New Amount = Principal + New Interest = 800 + 192 = 992 TK.

Alternative Shortcut Method:
Additional Interest for 3% increase in 3 years = (800 × 3 × 3)/100 = 72 TK.
∴ New Amount = 920 + 72 = 992 TK.

৯৯৯.

Two dice are thrown together. What is the probability that the sum of the numbers on the two faces is divisible by 4 or 6?

ক
ক) 2/7
খ
খ) 7/18
গ
গ) 3/18
ঘ
ঘ) 5/7

ব্যাখ্যা

Clearly,
n(S) = 6 × 6
= 36.
Let,
E be the event that the sum of the numbers on the two faces is divisible by 4 or 6.
Then, E = {(1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (5, 1), (5, 3), (6, 2), (6, 6)}
∴ n(E) = n(E)/n(S)
= 14/36
= 7/18.

১,০০০.

The length, breadth, and height of a brick are 10 cm, 4 cm, and 3 cm, respectively. Find the surface area of the brick?

ক
154 cm²
খ
156 cm²
গ
160 cm²
ঘ
164 cm²

ব্যাখ্যা

Question: The length, breadth, and height of a brick are 10 cm, 4 cm, and 3 cm, respectively. Find the surface area of the brick?

Solution:
Surface area of a Cuboid = 2(lb+ bh+ hl) cm²
So,
Surface area of a brick = 2(10 × 4 + 4 × 3 + 3 × 10) cm²
= 2(82) cm²
= 164 cm²