Bangladesh Bank || Assistant Director (General) (27-07-2018) || 2018

প্রশ্নে বলা হচ্ছে, এক ব্যক্তি 11.5% হারে 50 লক্ষ টাকা ব্যাংকে জমা রাখলেন। প্রতি 6 মাস অন্তর তিনি তার আসল হতে 2 লক্ষ টাকা এবং 6 মাসে যে সুদ পান সেই পরিমাণ টাকা তুলে নেন। 2 বছর পরে তার আসল কত থাকবে?

In two years, he withdraws $= 4 \times 2,00,000 = 8,00,000 Lac taka.$

We will not calculate the amount of interest charged against 50 lac taka as he also withdraws interest amount.

So, after two years the principal amount will be = 5000000-800000=4200000 Taka

ans. 4200000 Taka is the principal amount for the investment after two years.

প্রশ্নে বলা হচ্ছে, একটি বৃত্তে একটি বর্গ অন্তর্লিখিত আছে। বৃত্তটির ব্যাস 10cm হলে বর্গটির ক্ষেত্রফল কত?

First, let us depict an inscribed square in a circle

As, radius of the circle is 10 cm

∴ Diameter $= 2 \times 10 = 20$cm

Here, diameter of the circle will be the diagonal of the square.

So, the length of the diagonal = 20cm.

If 'a' is one arm of a square, then the length of the diagonal will be $a\sqrt{2}$

According to question,  $a\sqrt{2} = 20$

$$\begin{gathered} \Rightarrow a\sqrt{2} = 20 \\ \Rightarrow a = \frac{20}{\sqrt{2}} \\ \therefore a^2 = {\left(\frac{20}{\sqrt{2}}\right)}^2 = \frac{400}{2} = 200 c{m}^2 \end{gathered}$$

Therefore, area of the square is $200 c{m}^2.$ ans.

এটি সমান্তর ধারার অঙ্ক। এখানে A.P. হলো Arithmatic Progression যার অর্থ সমান্তর ধারা। প্রশ্নটিতে বলা হচ্ছে, একটি সমান্তর ধারার 3টি সংখ্যা x, y এবং z এর সমষ্টি 30 এবং সংখ্যাগুলোর বর্গের সমষ্টি 308 হলে সংখ্যা 3টি কত?

As the numbers are in Arithmatic Progression, their common difference will always be same. Here, we denote common difference by 'd'.

$$\begin{gathered} So, y-x=z-y \\ \Rightarrow y + y = x + z \\ \Rightarrow 2y = x + z.............. \left(i\right) \end{gathered}$$

Now, according to the first condition,

$$\begin{gathered} x + y + z = 30 \\ \Rightarrow y+x+z=30 \\ \Rightarrow y + 2y = 30 \\ \Rightarrow 3y = 30 \\ \Rightarrow y = \frac{30}{3} = 10 \\ \therefore y = 10 \end{gathered}$$

So, the second number = y = 10

As, common difference is d

∴ First number x = 10-d & Third number z = 10 + d

Now, according to the second condition $x^2+ y^2+z^2 = 308$

$$\begin{gathered} \Rightarrow {(10-d)}^2+{\left(10\right)}^2 + {(10+ d)}^2 = 308 \Rightarrow 100-20d + d^2 + 100+ 100+ 20d + d^2 = 308 \\ \Rightarrow 2d^2+300 = 308 \\ \Rightarrow 2d^2 = 308-300 = 8 \\ \Rightarrow d^2 = \frac{8}{2} = 4 \\ \Rightarrow d = \sqrt{4} = \pm 2 \end{gathered}$$

∴ The common difference will be '+2' Or '-2'

When the common difference d = 2

Then, the first number x = 10-2 = 8; Second number y = 10 & Third number z = 10+2 = 12

Again, when the common difference d = -2

Then, the first number x = 10-(-2)=10+2 = 12

Second number y = 10 & Third number z = 10+ (-2)=10-2=8

So, the numbers of the arithmatic progression may be 8, 10, 12 or 12, 10, 8

50 daily workers done by 40 day's 

∴ 1 daily workers done by 40×50 days

∴  30 daily workers done by 40×50/30= 200/3 days.

In 2 days, the worked done by (1/40+3/200)= 1/25 parts. 

   1/25 parts done by 2 days 

∴ 1 part done by 25×2= 50 days. 

So, days will be required in (50-40)= 10 days. (answered)

Man, by born, is weak. But as the time passes, he gathers some strength by experiencing new and confronting difficulties. As a human being, I have some strength and weaknesses. Some of them described below:

Strength:

• I'm hard working, self-motivated and take both success and failure in a balanced way; 
• I have positive attitude and am eager to learn new things and I'm a hard worker;
• I'm quick learner, honest, punctual, inquisitive and pro-active; 
• I have good communication skill, problem solving approach and creativity;
• I like to work in a team.

Weaknesses:

• I can not adapt to a new environment quickly.
• I trust people easily. 
• I feel impatient and uncomfortable until I finish work on time. 
• can not work in night; 
• I am very much serious about criticism for which I gave my best performance; 
• Over thinking;
• I am straightforward.