NCC Bank Ltd. || Management Trainee Officer Examination (30-03-2018) || 2018

প্রশ্নে বলা হচ্ছে, ৪% হার সুদে কোনো আসলের 2 বছরে সরল সুদ ও বাৎসরিক চক্রবৃদ্ধি সুদের পার্থক্য 12.80 টাকা হলে আসল কত?

Let, the principal be Tk. x

∴ Amount of compound interest

$$\begin{gathered} = x {\left(1 + \frac{8}{100}\right)}^2 -x \\ = x {\left(\frac{100 + 8}{100}\right)}^2 \\ = x {\left(\frac{108}{100}\right)}^2 -x \\ = x {\left(\frac{27}{25}\right)}^2 -x \\ = x \times \frac{729}{625} -x =\frac{729x}{625} -x = \frac{729x-625x}{625} = \frac{104x}{625}Tk. \end{gathered}$$

And amount of simple interest $= \left(x \times 2 \times \frac{8}{100}\right) =\frac{4x}{25}Tk.$ 

According to the question, $\frac{104x}{625} - \frac{4x}{25} = 12.80$

$$\begin{gathered} \Rightarrow \frac{104x - 100x}{625} = 12.80 \\ \Rightarrow 4x = 625 \times 12.80 \\ \Rightarrow x = \frac{625 \times 12.80}{4} = 625 \times 3.20 \\ \therefore x = 2, 000 Tk. \\ Principal amount is Tk. 2,000 \left(answer\right) \end{gathered}$$

প্রশ্নে বলা হচ্ছে, Jaya এক মিনিটে 40 টি Pancake তৈরী করে। Sally এক মিনিটে 40 টির অর্ধেক Pancake তৈরী করে। 150 টি Pancake তৈরী করতে কত সময় লাগবে, যদি ইতোমধ্যেই Sally 30 টি Pancake তৈরী করে থাকে?

Sally takes 1 minute to make $= \frac{40}{2}$ = 20 pancakes.

Sally makes 20 pancakes in 1 minute.

∴ Sally makes 30 pancakes in $= \frac{30 \times 1}{20}$ = 1.5 minute.

∴ Remaining (150-30)= 120 pancakes are made by both of them.

Now, Jaya and Sally takes 1 minute to make = 40+ 20 = 60 pancakes.

That means, 1 pancake is made by them in $= \frac{1}{60}$ minutes

∴ 120 pancake is made by them in  $= \frac{1 \times 120}{600}$ = 2 minutes

∴ Total time taken by them to make 150 pancakes is = 2 min +1.5 min = 3.5 minutes. (ans)