Sonali & Janata Bank Ltd. Recruitment Test for Senior Officer (IT/ICT)) Examination Held On: 29.06.2018 || 2018

Given, total rods = 75

Now, we will find the probability.

A. Probability of a blue rod from the box = $\frac{Total blue rods}{Total rods}=\frac{35}{75}=\frac{7}{15}$

B. Probability of a clear rod from the box = $\frac{Total blue rods}{Total rods}=\frac{10+10}{75}=\frac{20}{75}=\frac{4}{15}$

C. Probability of a blue twisted rod = $\frac{Total blue rods}{Total rods}=\frac{25}{75}=\frac{1}{3}$

D. Probability of a clear red rod =  $\frac{Total blue rods}{Total rods}=\frac{10}{75}=\frac{2}{15}$

E. Probability of a twisted rod = $\frac{Total blue rods}{Total rods}=\frac{25+30}{75}=\frac{55}{75}=\frac{11}{15}$ 

Let, A took x seconds
B took (170-x) seconds.
According to question, 

$$\begin{gathered} \Rightarrow 340-2x-10+170-x=170 \\ \Rightarrow 330=3x \\ \Rightarrow 3x=330 \\ \Rightarrow x=\frac{300}{3}=110 \\ A=110 \end{gathered}$$

A took 110 seconds and B took (170-110)= 60 seconds.

Let, Fahim's age be x year

Shakib is 2x years old.

4 years ago Fahim was (x-4) years old and 4 years ago Shakib was (2x-4) years old

According to question

$$\begin{gathered} 3\left(x-4\right)-6=2x-4 \\ \Rightarrow 3x-12-6=2x-4 \\ \Rightarrow 3x-18=2x-4 \\ \Rightarrow 3x-2x=18-4=14 \\ \therefore x=14 \end{gathered}$$

After 2 years, Fahim will be = 14+2 = 16 years old 

And Shakib will be = $2 \times 14) + 2 = 28+ 2 = 30$ years old

Total amount of charity = $20 \times 4 = 80 Tk.$

Here, maximum 3 students can give = 25 Tk.

Total = $3 \times 25 = 75 Tk.$

Minimum amount contributed by one student = $80-75 =5 Tk.$

The sum of 15 consecutive integers will 88.

only when there are some positive and negative consecutive integers. 

So, we let, the numbers are $(x-7), (x-6), (x-5), (x-4) (x-3), (x-2) (x-1) x, (x + 1), (x+2), (x+3), (x+4), (x+5), (x+6) (x+7).$

According to question 

$x+(x+1)+(x+2)+(x+3)+(x+4)+(x+5)+(x+6)+(x+7)+(x-7) + (x -6) + (x -5) + (x - 4)+(x-3)+(x-2)+(x-1)=88$
$$\begin{gathered} \Rightarrow 15x+28-28 = 88 \\ \Rightarrow 15x = 88 \\ \therefore x=\frac{88}{15} \end{gathered}$$

The largest number is $(x+7)= \frac{88 }{15}+7=\frac{88+105}{15}=\frac{193}{15}$
But, here $\frac{193}{15}$ is not a integer. 

So the data given in the question may not be consistent.

$$\begin{gathered} x^2-12x+27<0 \\ \Rightarrow x^2-9x-3x+27<0 \\ \Rightarrow x\left(x-9\right)-3\left(x-3\right)<0 \\ Here, if we take x<3 \\ Then, \left(x^2-12x+27\right)<0 will not be true and if we take x<9. \\ So, x must lie between 3<x<9, \\ Because for each value between 3<x<9, (x^2-12x+27)<0 will be true. \\ \mathit{a}\mathit{n}\mathit{s}. 3 <x<9. \end{gathered}$$

$$\begin{gathered} x^2-13x+40\ge 0 \\ \Rightarrow x^2-8x-5x+40\ge 0 \\ \Rightarrow x(x-8)-5(x-8)\ge 0 \\ \Rightarrow (x-8) (x-5)\ge 0 \\ Here, the product of (x-8) and (x-5) is grater than zero or equal to zero. \\ So the value of these must be both positive or negative. \\ When both positive, (x-8)\ge 0 \\ \Rightarrow x>8; (x-5)\ge 0 \\ \Rightarrow x\ge 5 [It is not true] \\ When both negative, -(x-8)\ge 0 \\ \Rightarrow x\le 8; [It is not true] \\ -(x-5)\ge 0 \\ \Rightarrow x\le 5; \\ So, the range x\ge 8 Or, x\le 5. \end{gathered}$$

The number of 10 seat room = x 

The number of 20 seat room = 40- x

According to question

$$\begin{gathered} 10x+20(40-x) = 600 \\ \Rightarrow 10x+800- 20x = 600 \\ \Rightarrow -10x=600-800=-200 \\ \therefore x=\frac{-200}{-10} =20 \end{gathered}$$

Number of 10 seat room = 20 and number of 20 seat room = 40-20=20. 

The ratio of the number of 10 seat room to the number of 20 seat room = 20 : 20= 1 : 1. ans.

Given, total football players 85

Do not score a goal = 85 - 42 = 43 players

Do not receive a yellow card = 85-54 = 31 

players Do not score a goal or don't receive yellow card or do not do either = 43 +31-5=69

Number of players who scored a goal and received a yellow end = 85 - 69 = 16

Required fraction = 16/85 ans.