Garments industry is one of the economically important sectors of the country where about 15 laks people are engaged in work. Though they need banking services, 80-90 percent people have no bank accounts for which they are being deprived of banking service. It is proven that mobile banking is more expedient than traditional banking in case of providing the banking services with the working class people. Family members remain in much comfort though the only money breeding keeps for away from family after launching this service. It is possible to get customer service with comparatively low cost through mobile banking It encourages people's savings tendency which has been known from a recent study conducted by IFC. So as soon as the mobile banking activities flourish services will be cheaper as well.

প্রশ্নে বলা হচ্ছে, A, B এবং C একটি কাজ যথাক্রমে 16.32 এবং 48 দিনে করতে পারে। তারা একসাথে কাজ করা শুরু করল। কাজ শুরুর 4 দিন পর C কাজ ছেড়ে চলে গেল এবং B কাজ শেষ হবার 2 দিন আগে কাজ ছেড়ে চলে গেল। কাজটি কত দিনে সম্পন্ন হয়েছিলো?

Let, total work has been completed in x days.

A do the work = x days

B do the work = (x-2) days &

 C do the work = 4 days

 According to the question, 

$$\begin{gathered} \frac{x}{16}+\frac{x-2}{32}+\frac{4}{48}=1 \\ \Rightarrow \frac{6x+3\left(x-2\right)+8}{96}=1 \\ \Rightarrow 6x+3x-6+8=96 \\ \Rightarrow 9x+2=96 \\ \Rightarrow 9x=96-2=94 \\ \Rightarrow x=\frac{94}{9}=10.44 \\ \therefore x=10.44 \end{gathered}$$

So, the work will be completed in 10.44 days. ans.

বলা হচ্ছে যে, দুটি ঘড়ির একত্রে ক্রয়মূল্য 840 টাকা। একটি ঘড়ি 16% লাভে এবং অপরটি 12% ক্ষতিতে বিক্রয় করলে লাভ/ক্ষতি কোনটাই হয় না। প্রতিটি ঘড়ির ক্রয়মূল্য কত?

Let, the cost price of one watch is x Tk. 

The cost price of another watch is (840-x) Tk.

 Selling price at 16% profit=$x+16\% of x= x+\frac{16x}{100}=\frac{116x}{100}TK.$

Again, price at 12% loss

$$\begin{gathered} = (840-x)-12\% of (840-x) Tk \\ =\left(840-x\right)-\frac{12\left(840-x\right)}{100}TK. \\ =\left(840-x\right) - \frac{2520-3x}{25}TK. \\ = \frac{2100-25x-2520+3x}{25}TK. \\ = \frac{18480-22x}{25}TK. \end{gathered}$$

According to the question, 

$$\begin{gathered} \frac{116x}{100}+\frac{18480-22x}{25}=840 \\ \Rightarrow \frac{116x+73920-88x}{100}=840 \\ \Rightarrow 28x+73920=84,000 \\ \Rightarrow 28x=84,000-73,920 \\ \Rightarrow 28x=10,080 \\ \Rightarrow x=\frac{10080}{28} \\ \therefore x=360 \end{gathered}$$

The cost price of one watch is 360 Tk.

The cost price of another watch = (840-360)= 480 Tk. 

ans. The cost price of one watch is 360 Tk. & another watch is 480 Tk.

বলা হচ্ছে যে, একটি বর্গাকৃতির মাঠের পরিসীমা একটি আয়তাকৃতির মাঠের পরিসীমার সমান। আয়তাকার মান দৈর্ঘ্য এর প্রস্থের তিনগুণ এবং ক্ষেত্রফল 768 বর্গমিটার। 80cm দৈর্ঘ্যের বর্গাকৃতির Tiles দিয়ে বর্গাকার মাঠটিকে ঢাকতে কতগুলো Tiles লাগবে?

Let, the width of a rectangular field is x meter

The length of a rectangular field is 3x meter 

Area = $(x \times 3x)=3x²$

According to the question, 

$$\begin{gathered} 3x^2=786 \\ \Rightarrow x^2=\frac{786}{3} \\ \Rightarrow x^2=256 \\ \Rightarrow x=\sqrt{256} \\ \Rightarrow x=16 \end{gathered}$$

Width = 16 meter

Length = 3x =3 * 16=48 meter

Perimeter = 2(48+ 16)= 2*64 = 128 meter

Let, a is the arm of a square

4a will be the perimeter of the square

 According to the question, 

$$\begin{gathered} 4a=128 \\ \Rightarrow a=\frac{128}{4} \\ \therefore a=32 \end{gathered}$$

Area of the square field = (32)² = 1,024

Length of tiles = 80cm=0.8m

Area of tiles = (0.8)² = 0.64

Require tiles = $\frac{1024}{0.64}=1,600$ ans

$$\begin{gathered} \frac{1}{x+2}+\frac{1}{x+5}=\frac{1}{x+4}+\frac{1}{x+3} \\ \Rightarrow \frac{1}{x+2}-\frac{1}{x+4}=\frac{1}{x+3}-\frac{1}{x+5} \\ \Rightarrow \frac{x+4-x-2}{x^2+4x+2x+8}=\frac{x+5-x-3}{x^2+5x+3x+15} \\ \Rightarrow \frac{2}{x^2+6x+8}=\frac{2}{x^2+8x+15} \\ \Rightarrow \frac{1}{x^2+6x+8}=\frac{1}{x^2+8x+15} \\ \Rightarrow x^2+8x+15=x^2+6x+8 \\ \Rightarrow x^2+8x-x^2-6x=8-15 \\ \Rightarrow 2x=-7 \\ \Rightarrow x=\frac{-7}{2} \\ \therefore x=\frac{-7}{2} \end{gathered}$$