ব্যাংক মডেল টেস্ট [সাপ্তাহিক]

• Correct sentence: The army reinforced its positions along the LOC lest a surprise offensive should catch them unprepared.
Bangla Meaning: অপ্রত্যাশিত হামলা যেন তাদের অপ্রস্তুত অবস্থায় না ফেলে, তাই সেনাবাহিনী এলওসি'তে অবস্থান শক্তিশালী করে।

• Lest (conjunction)
- "Lest" is used to express the idea of "for fear that" or "in order to prevent".
- শব্দটি মূলত: একটি Conjunction - যার অর্থ পাছে (কোনো কিছু ঘটে) এই ভয়ে।
- Lest এর পরে subject থাকলে subject -এর পূর্বে Should/ might + base form অথবা Should/ might be + V₃ বসে।
- Lest negative অর্থ প্রদান করে, এ কারণে Lest যুক্ত বাক্যে should  -এর পরে no/not/never বসে না Lest এরপর subject থাকলে এর should পূর্বে বসাতে হয়।
- উল্লেখ্য যে, Should না থাকলে might বসবে।

• Structures:
- Lest + 1^st subject + should/might + base form + complement.
- Lest + 1^st subject + should/might + be + V₃ + complement.

• More Examples:
- He spoke in whispers lest anyone should overhear their conversation.
- They left early lest they should get caught in the storm.
- I avoid sugar lest I should fall sick again.

Source: Cambridge Dictionary.

• Complete Sentence: War ends when acquisition turns into reconciliation.
Bangla Meaning: যুদ্ধ তখনই শেষ হয়, যখন জয় শান্তিতে রূপ নেয়।

• Acquisition (noun)
English meaning: the process of getting something.
Bangla meaning: অর্জন, অর্জিত দ্রব্য বা বিষয়।

• Reconciliation (noun)
English meaning: the act of becoming friendly after a disagreement
Bangla meaning: পুনর্মিলন।
 
Source: Cambridge Dictionary.

• শূন্যস্থানে সঠিক উত্তর হবে - of.
Complete Sentence: Both countries, in their rivalry, were envious of each other's technological advancements.

• Envious of
Bangla Meaning: হিংসুক; পরশ্রীকাতর।
- কোন বিষয়ে কারোর প্রতি হিংসা অনুভব করা বুঝাতে envious এরপর appropriate preposition হিসাবে of ব্যবহৃত হয়।

Example:
 - I'm very envious of your new coat - it's beautiful.
- We should not be envious of others' successes.

Source:
1. Cambridge Dictionary
2. Accessible Dictionary by Bangla Academy.

Question: 30% of 50% of 4/7​ of a number is 420. What is 20% of 3/7 of that number?

Solution: 
Let the number be x.

Then,
30% of 50% of 4/7​ of x = 420
⇒ (30/100) × (50/100) × (4/7) × x = 420
⇒ 3/10 × 1/2 × 4/7 × x = 420
⇒ 12x/140 = 420
⇒ 3x/35 = 420
⇒ x = (420 × 35)/3
∴ x = 4900

Now,
20% of 3/7 of x
= (20/100) × (3/7) × 4900
=  (1/5) × (3/7) × 4900
= (3/35) × 4900
= 420

Question: Find the least number which will leaves remainder 5 when divided by 8, 12, 16 and 20.

Solution: 
We have to find the Least number, therefore we find out the LCM of 8, 12, 16 and 20.
8 = 2 × 2 × 2;
12 = 2 × 2 × 3;
16 = 2 × 2 × 2 × 2;
20 = 2 × 2 × 5

∴ LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240

This is the least number which is exactly divisible by 8, 12, 16 and 20.
So, Required number which leaves remainder 5 is = 240 + 5 = 245.

Question: The sum of three consecutive multiples of 4 is 300. What is the largest number?

Solution: 
Let,
First multiple 4x
Second multiple 4(x + 1) = 4x + 4
Third multiple 4(x + 2) = 4x + 8

ATQ,
4x + 4x + 4 + 4x + 8 = 300
⇒ 12x + 12 = 300
⇒ 12x = 288
⇒ x = 288/12
∴ x = 24

So, largest number = 4x + 8
= (4 × 24) + 8
= 104

Question: The sum of the ages of a mother and her daughter is 50 years. The mother’s age is four times the daughter’s age. After how many years will the mother’s age be three times the daughter’s age?

Solution:
Let the daughter's current age be x.
Then, the mother's current age is 4x.

ATC,
x + 4x = 50
⇒ 5x = 50
∴ x = 10

∴ Daughter's current age x = 10 years
and Mother's current age is 4x = 4 × 10 = 40 years

Let, the number of years after which mother’s age will be three times the daughter’s age be t.

So after t years,
The daughter’s age will be 10 + t
The mother’s age will be 40 + t

ATC,
40 + t = 3(10 + t)
⇒ 40 + t = 30 + 3t
⇒ 40 - 30 = 3t - t
⇒ 10 = 2t
⇒ t = 5

∴ After 5 years, the mother’s age will be three times the daughter’s age.

Question: In a class, the number of girls is 5/6​ of the number of boys. The total students of the class is 121. If 5 more girls join the class, what will be the new ratio of girls to boys?

Solution: 
Let the number of boys be x
Then, number of girls = 5/6 of x = 5x/6

ATC,
x + (5x/6) = 121
⇒ (6x + 5x)/6 = 121
⇒ 6x + 5x = 6 × 121
⇒ 11x = 6 × 121
⇒ x = (6 × 121)/11
∴ x = 66

So, number of boys = x = 66 
number of girls = 5/6 of x = 5/6 of 66 = 55 

Now, 5 more girls join,
∴ New number of girls = 55 + 5 = 60

∴ ratio (girls : boys) = 60/66
= 10/11
= 10 : 11

Question: Two trains are 150 meters and 180 meters long. They are running on parallel tracks in the same direction. The faster train runs at 90 km/h and the slower at 54 km/h. How much time will the faster train take to completely pass the slower train?

Solution:
Given,
Length of first train = 150 meters
Length of second train = 180 meters
Speed of faster train = 90 km/h 
= (90 × 1000)/3600 = 25 m/s
Speed of slower train = 54 km/h
= (54 × 1000)/3600 = 15 m/s

Since they are moving in the same direction,
∴ Relative speed = 25 - 15 = 10 m/s

To pass completely, the faster train must cover the length of both trains.
∴ Total lenght = 150 + 180 = 330 meters

Now,
Time = Distance / Speed
= 330/10 = 33 seconds

Question: The length of a rectangular plot is 10 meters less than three times its breadth. If the cost of fencing the plot at Tk 50 per meter is Tk 15000, what is the length of the plot in meters?

Solution:
Let the breadth of the plot be x meters.
Then, the length of the plot is 3x - 10 meters.

Perimeter of the rectangle = 2 × (Length + breadth)
= 2 × (x + 3x - 10 )
= 2 × (4x - 10 )
= 8x - 20

Given,
Cost of fencing per meter = Tk 50
Total cost = Tk 15000

So, Perimeter × 50 = 15000
⇒ (8x - 20) × 50 = 15000
⇒ 8x - 20 = 15000/50
⇒ 8x = 300 + 20
⇒ 8x = 320 
∴ x = 40

∴ Breadth = 40 meters.
and length = 3x - 10 = 3 × 40 - 10 = 110 meters.

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

Question: If the average of x and y is 70 and the average of y and z is 90. What is the value of z - x?

Solution: 
(x + y)/2 = 70
∴ x + y = 140 .........(1)

Again,
(y + z)/2 = 90
∴ y + z = 180 .........(2)

From (2) - (1) we get,
y + z - x - y = 180 - 140
∴ z - x = 40

Question: The average age of a group of 20 employees is 30 years. If 10 more employees join the group, the average age increases by 3 years. Find the average age of the new employees?

Solution:
Here,
Total age of the 20 employees,
= 20 × 30=600 years

After joining 10 new employees, average age increases by 3 years.
So, New average age = 30 + 3 = 33 years

Total age of the 30 employees,
= 30 × 33 = 990 years

∴ Total age of the 10 new employees = (990 - 600) years
= 390 years

∴ Average age of the 10 new employees = 390/10 = 39 years

Question: ∠A and ∠B are supplementary angle to each other. If ∠A = 40° + 3x and ∠B = 2x, what is the value of ∠B?

Solution:
We are given:
∠A = 40° + 3x
∠B = 2x

Since ∠A and ∠B are supplementary:
∠A + ∠B = 180°
⇒ (40° + 3x) + 2x = 180°
⇒ 40° + 5x = 180°
⇒ 5x = 180° - 40°
∴ 5x = 140°
∴ x = 28°

∴ ∠B = 2x = 2 × 28° = 56°

Question: If 3 less than twice the number is equal to 2 more than 3 times the number, then 5 less than 5 times the number is:

Solution:
Let the number be x

ATQ,
2x - 3 = 3x + 2
∴ x = - 5

∴ Five times the number = 5 × (- 5)
= - 25
∴ Five less than this = - 25 - 5
= - 30

Question: If log⁡_y81 = 4/2​, what is the value of y?

Solution: 
log⁡_y81 = 4/2
⇒ log⁡_y81 = 2
⇒ y² = 81  [log_ba = c ⇒ b^c = a]
⇒ y² = 9²
∴ y = 9

Question: At what profit percent must an article be sold so that by selling it at two-thirds of that price, there will be a loss of 20%?

Solution:
Let,
Cost Price be x .
Selling Price be y.

Selling at 2/3 of y, causes 20% loss,
So, 2y/3 = x - 20% of x
⇒ 2y/3 = x - (20x/100)
⇒ 2y/3 = x{(1 - (20/100)}
⇒ 2y/3 = x × (80/100)
∴ y = 6x/5

Profit = Selling Price - Cost Price
= (6x/5) - x
= (6x - 5x)/5
= x/5

∴ Profit Percentage = (Profit/Cost Price) × 100%
= {(x/5)/x} × 100%
= 20%

A, B and C are partners of a company. During a particular year A received one-fifth of the profit, B received one-third of the profit and C received the remaining Tk 5600. How much did B receive?

Solution:
Let the total profit be Tk x.

Now, Total profit - A's share - B's Share = C's share
⇒ x - (x/5 + x/3) = 5600
⇒ x - {(3x + 5x)/15} = 5600
⇒ x - (8x/15) = 5600
⇒ (15x - 8x)/15 = 5600
⇒ 7x/15 = 5600
⇒ 7x = 5600 × 15
⇒ 7x = 84000
⇒ x = 84000/7
∴ x = 12000

So, B's share = 12000 × 1/3 = 4000

Question: A is thrice as good a workman as B and so takes 40 days less than B for doing a job. The time in which they can do the job together is - 

Solution:
Let A alone takes x days 
and B alone takes 3x days to complete the job.

ATQ,
3x - x = 40
⇒ 2x = 40
⇒ x = 20

So, A alone takes 20 days and B alone takes 3 × 20 = 60 days to complete the job.

(A + B)'s 1 days work = (1/20 + 1/60) = 1/15 part

∴ A and B together can do the work in 15 days.

Question: If x + (1/x) = 3, then x - (1/x) = ?

solution: 
Given,
x + (1/x) = 3

We know,
{x - (1/x)}² = {x + (1/x)}² - 4 . x . 1/x
⇒ {x - (1/x)}² =  3² - 4
⇒ {x - (1/x)}² = 9 - 4
⇒ {x - (1/x)}² = 5
∴ x - (1/x) = √5

Question: A jar contains 5 blue, 8 green, and 6 orange marbles. If a marble is picked at random, what is the probability that the marble drawn will be either blue or green?

Solution:
Total number of marbels = 5 + 8 + 6 = 19

If one marbel is picked at random.

P(blue) = 5/19
P(green) = 8/19

P(blue or green) = 5/19 + 8/19
= (5 + 8)/19
= 13/19

⇒ সোসাইটি ফর ওয়ার্ল্ডওয়াইড ইন্টারব্যাংক ফাইন্যান্সিয়াল টেলিকমিউনিকেশন কী?
- a monetary transfer tool

সুইফট:
- SWIFT এর পূর্ণরূপ Society for Worldwide Interbank Financial Telecommunication.
- SWIFT একটি বিশ্বব্যাপী আর্থিক বার্তা আদান-প্রদানকারী নেটওয়ার্ক, যা আন্তর্জাতিক লেনদেনের নিরাপত্তা ও দক্ষতা নিশ্চিত করে।
- এর মাধ্যমে ব্যাংক ও আর্থিক প্রতিষ্ঠানগুলো দ্রুত, নির্ভুল ও নিরাপদভাবে লেনদেনের নির্দেশনা আদান-প্রদান করতে পারে।
- SWIFT ১৯৭৩ সালে বেলজিয়ামে প্রতিষ্ঠিত হয়।
- এটি একটি সমবায় ভিত্তিক প্রতিষ্ঠান, যা এর সদস্য ব্যাংক ও আর্থিক প্রতিষ্ঠানের মালিকানাধীন।

- বিশ্বব্যাপী ব্যাংক বা আর্থিক প্রতিষ্ঠানের মধ্যে আর্থিক লেনদেন করতে এই নেটওয়ার্ক ব্যবহার করা হয়।
- আর্থিক লেনদেনের বিষয়ে তথ্য আদান প্রদানের জন্য সুইফটকে একটি নিরাপদ নেটওয়ার্ক হিসেবে বিবেচনা করা হয়।
- প্রতিষ্ঠানটি মূলত একটি তাৎক্ষণিক মেসেজিং ব্যবস্থা, যা কোনো লেনদেনের ব্যাপারে গ্রাহককে তৎক্ষণিক জানিয়ে দেয়। বিশ্বের অধিকাংশ ব্যাংক নিজেদের মধ্যকার বার্তা আদান প্রদানের কাজে সুইফট নেটওয়ার্ক ব্যবহার করে।
- সুইফট নেটওয়ার্ক দিয়ে সরাসরি অর্থ প্রেরণ করা যায় না, এটা শুধু অনলাইনে পেমেন্ট অর্ডার প্রেরণ করে। একটি ব্যাংক তাদের সুইফট নেটওয়ার্কে সংযুক্ত অন্য একটি ব্যাংককে অর্থ পরিশোধের অনুরোধ পাঠায় এবং সংশ্লিষ্ট ব্যাংক সেই আদেশ গ্রহণ করে সে অনুযায়ী কাজ করে।
বিশ্বব্যাপী খুবই গুরুত্বপূর্ণ অর্থনৈতিক ভূমিকা রাখলেও কোনো দেশের ওপর অবরোধ আরোপের আইনি ক্ষমতা নেই এই প্রতিষ্ঠানটির।

তথ্যসূত্র - Britannica.com