ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Let the required number of revolutions made by larger wheel be x.
Then, More cogs, Less revolutions (Indirect Proportion)
14 : 6 :: 21 : x       
14 x x = 6 x 21
x =(6 x 21)/14
x = 9.

Let the required number of days be x.
Less persons, More days (Indirect Proportion)
More working hours per day, Less days (Indirect Proportion)
Persons  30:39                   ⟩ ::12 : x
Working hours/day 6:5        ⟩
30 x 6 x x = 39 x 5 x 12
x =(39 x 5 x 12)/(30 x 6)
x = 13.

Let original Cost price is x
Its Selling price = 105/100 × x = 21x/20
New Cost price = 95/100 × x = 19x/20
New Selling price = 110/100 × 19x/20 = 209x/200
[(21x/20) - (209x/200)] = 1
=> x = 200

Let the C.P. = x,
Then S.P. = (120/100)x = 6x/5
New S.P. = 2(6x/5) = 12x/5
Profit = 12x/5 - x = 7x/5
Profit% = (Profit/C.P.) × 100
=> (7x/5) × (1/x) × 100 = 140 %

C.P. of 56 kg rice = Tk. (26 x 20 + 30 x 36) = Tk. (520 + 1080) = Tk. 1600.
S.P. of 56 kg rice = Tk. (56 x 30) = Tk. 1680.
Gain = (80/1600)x 100% = 5%.

Out of the woods means Out of the danger
Example : He was very serious but now he is out of the woods

Kick the bucket means to die
Example : He kicked the bucket after long illness.

Hold and corner means a secret
Example : Many successful entrepreneurs have a hold and corner method for dealing with people.

Grease the palm means to bribe
Example : You will have to grease the palm of clerk for quick action on this file.

Fish in troubles waters means to take advantage of trouble of others
Example : Clever businessmen fish in troubled water when there is scarcity of things.

Call a spade a spade means To speak plainly
Example : He never manipulate things, he always call a spade a spade

Blaze the trail means To start a movement.
Example : All great people names are written in history who blazed the trail for their nations.

Black and Blue means To beat very badly
Example : Ramesh was beaten black and blue by my friends when he was trying to steal my bike.

By hook or by crook means by any means
Example : I want to win this match, by hook or by crook.

Let the rate of interest during the second year be R%.
Given, 
4500 × {(100 + 12)/100} × {(100 + R)/100} = 5544 
R = 10%

Let the sum be Tk. x,
then it becomes Tk. 4x in eight years
Tk. 3x is the interest on x for eight years.
R = (100 × 3x)/(x × 8)
= 300/8 %
If the sum becomes ten times itself, then interest is 9x.
The required time period = (100 × 9x)/(x × 300/8)
= (100 × 9x × 8)/(x × 300)
= 24 years.

T = (100 × 16500)/(15 × 5000)
= 22 years

90 = (450×4×R)/100
R = 5%
I = (450×6×5)/100 = 135
so, 450 + 135 = 585

P = (P×5×R)/100
R = 20 year

A = 7500(26/25)² = 8112

SI = 40 + 40
CI = 40 + 40 + 1.6 = 81.6

441 = P(21/20)²
P = 400

Tk.1440 - 1200 = Tk.240 is the interest on Tk.1200 for one year. 
Rate of interest = (100 × 240) / (100 ×1) = 20% p.a

S.I. = (1200 × 10 × 1)/100 = Tk. 120 
C.I. = [1200 × (1 + 5/100)² - 1200] 
= Tk. 123 
Difference = (123 - 120) = Tk. 3.

Let the numbers be x and y
Then,
x+y=33.....(i)
And,
x−y=15.....(ii)
Solving (i) and (ii), we get :
x = 24, y = 9
∴ Smaller number = 9

LCM of (12, 15, 18, 27)
⇒ 4 × 3 × 5 × 3 × 3 = 540
largest 4-digits number = 9999 on dividing by 540 to number = 9999/540
remainder = 279
Required number = 9999 - 279 = 9720

The greatest length of pipes of same size will be HCF of 1.5 m and 1.2 m.
So HCF of 15 and 12 is 3, then HCF of 1.5 and 1.2 is 0.3 m

Greatest prime number = 97
Least prime number = 2
So, their difference 97 - 2 = 95

Take LCM of 10 and 13 = 130
Any number divisible by 130 will be divisible by 13 and 10
i.e., 130, 260, 390, 520, 650, 780 & 910
⇒ total numbers are 7

Prime numbers between 0 and 50 are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47
Their number is 15

In 5ⁿ we have 5 as unit digit and in 6^m we have 6 as unit digit.
∴ 5 + 6 = 11(i.e unit digit always be 1)

শব্দের মধ্যে কোনাে ব্যঞ্জনধ্বনি লােপ পেলে তাকে অন্তর্হতি বলে।
যেমন- আলাহিদা > আলাদা, ফাল্গুন > ফাগুন, ফলাহার > ফলার ইত্যাদি।
উৎসঃ বাংলা ভাষা ও সাহিত্য জিজ্ঞাসা, ড. সৌমিত্র শেখর।

আকাশ শব্দটির সমার্থক শব্দ হলো ব্যোম, নভঃ, অম্বর, গগন ইত্যাদি।
হুতাশন শব্দটির সমার্থক শব্দ হলো আগুন, অনল, পাবক ইত্যাদি।
উৎসঃ বাংলা ভাষা ও সাহিত্য জিজ্ঞাসা-ড. সৌমিত্র শেখর

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বাংলা ভাষায় যে অব্যয় শব্দগুলাে কখনাে স্বাধীন পদ রূপে, আবার কখনাে শব্দ বিভক্তির ন্যায় বাক্যে ব্যবহৃত হয়ে বাক্যের অর্থ প্রকাশে সাহায্য করে, সেগুলােকে অনুসর্গ বা কর্মপ্রবচনীয় বলে।
অনুসর্গগুলাে কখনাে প্রাতিপদিকের পরে ব্যবহৃত হয়, আবার কখনাে বা 'কে' এবং 'র' বিভক্তিযুক্ত শব্দের পরে বসে।
যেমন-
বিনা : দুঃখ বিনা সুখ লাভ হয় কি মহীতে? (প্রাতিপদিকের পরে)
দিয়ে : তােমাকে দিয়ে আমার চলবে না। (দ্বিতীয়ার কে' বিভক্তিযুক্ত শব্দের পরে)
সনে : ময়ূরীর সনে নাচিছে ময়ূর। (ষষ্ঠী বিভক্তিযুক্ত শব্দের পরে)
(রেফারেন্সঃ ৯ম-১০ম শ্রেণির বাংলা ভাষার ব্যাকরণ)