Bank Asia Ltd Recruitment Test for Management Trainee Examination Held on : 28.04.2017 || 2017

$$\begin{gathered} \frac{x-4}{x-1}+\frac{x-7}{x-3}+\frac{x-2}{x-9}=3 \\ \Rightarrow \frac{x-4}{x-1}+\frac{x-7}{x-3}=3-\frac{x-2}{x-9} \\ \Rightarrow \frac{\left(x-4\right)\left(x-3\right)+\left(x-7\right)\left(x-1\right)}{\left(x-1\right)\left(x-3\right)}=\frac{3\left(x-9\right)-\left(x-2\right)}{x-9} \\ \Rightarrow \frac{x^2-3z-4z+12+x^2-x-7x+7}{x^2-3x-x+3}=\frac{3x-27-x+2}{x-9} \\ \Rightarrow \frac{2x^2-15x+19}{x^2-4x+3}=\frac{2x-25}{x-9} \\ \Rightarrow \left(2x^2-15x+19\right)\left(x-9\right)=\left(x^2-4x+3\right)\left(2x-25\right) \\ \Rightarrow 2x^3-15x^2+19x-18x^2+135x-171=2x^3-8x^2+6x-25x^2+100x-75 \\ \Rightarrow -33x^2+154x-171=-33x^2+106x-75 \\ \Rightarrow -33x^2+33x^2+154x-106x=-75+171 \\ \Rightarrow 48x=96 \\ \therefore x=\frac{96}{48}=2 \end{gathered}$$

Let, Mr. Karim his first borrowings after x years

Interest = 994.5 - 500 - 400= 94.5

According to the question:

$$\begin{gathered} \left(500\times 5\%\times x\right)\left(400\times 3.5\%\times \frac{6}{12}\right)=94.5 \\ \Rightarrow 25x+7=94.5 \\ \Rightarrow 25x=94.5-7 \\ \Rightarrow 25x=87.5 \\ \therefore x=\frac{87.5}{25}=3.5 years \end{gathered}$$

Rahim can do in 80 days = 1 work

Rahim can do in 1 days = $\frac{1}{80}$part of work

Rahim can do in 10 days=$\frac{10}{80}=\frac{1}{80}$ part of work

Remaining work= $1-\frac{1}{8}=\frac{7}{8}$ part of work

Again, Karim can do $\frac{7}{8}$ part in 42 days.

Karim can do 1 part= $\frac{42\times 8}{7}=48$ days

Karim can do in 1 day = $\frac{1}{48}$ part of work

(Rahim + Karim) can do in 1 day = $\frac{1}{80}+\frac{1}{48}=\frac{3+5}{240}=\frac{1}{30}$

So, Rahim + Karim can do the work in 30 days, ans.

Repeat: One Bank Ltd. (SCO) 01.04.2017