Pubali Bank Ltd - Officer/Senior Officer - 11.07.2014/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ What percentage of numbers from 1 to 70 have squares that end in the digit 1 ?

বর্ণনাঃ

Squares that end in the digit 1 be number of last digit 1 & 9.
So numbers are 1, 9, 11, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
So total number is 14.
$\therefore$ Percentage = $\frac{14}{70}\times 100$ = 20

প্রশ্নঃ A number,when 35 is subtracted from it, reduces to its 80 percent. What is four-fifth of that number ?

বর্ণনাঃ

Let the number be x.
Now, According to question
x - 35 = 80% of x
$\Rightarrow$ x - 35 = $\frac{80x}{100}$
$\Rightarrow$ x - $\frac{80x}{100}$ = 35
$\Rightarrow \frac{100x-80x}{100}$ = 35
$\Rightarrow$ 20x = $35\times 100$
$\Rightarrow x=\frac{35\times 100}{20}$
$\Rightarrow$ x = 175
$\Rightarrow$ $\therefore \frac{4}{5}x=140$

প্রশ্নঃ A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are :

বর্ণনাঃ

Let the maximum marks be x.
Then, 33% of x = 125 + 40
$\Rightarrow \frac{33}{100}\times \times =165$
$\Rightarrow 33x=165\times 100$
$\Rightarrow$ x = $\frac{165\times 100}{33}$
$\therefore$ x = 500

প্রশ্নঃ If x% of y is equal to z, What percent z is x ?

বর্ণনাঃ

x% of y = z 
$\Rightarrow \frac{x}{100}y=z$
$\therefore x=\frac{z\times 100}{y}$

প্রশ্নঃ A sum of money at simple interest amounts to Tk. 815 in 3 tears and to Tk. 854 in 4 years.The sum is :

বর্ণনাঃ

Simple Internet ofr 1 year = Tk. (854-815) = Tk. 39
$$\begin{gathered} Simple Interest for 3 years = Tk. (39\times 3) = Tk. 117 \\ \therefore Principal or sum = Tk. ( 815-117) Tk. 698 \end{gathered}$$

প্রশ্নঃ The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is :

বর্ণনাঃ

Let, principal amount be x
So interest would be $$\begin{gathered} \frac{x}{2} \\ I=Pnr \\ \Rightarrow \frac{x}{2}=x \times n\times r \\ \Rightarrow \frac{1}{2}=n\times r=.05\times 6=.48 \end{gathered}$$
So, data inadequate

প্রশ্নঃ 36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?

বর্ণনাঃ

Let, the required number of days be x. Less man, More days ( Indirect Proportion)
$$\begin{gathered} \therefore 27:36::18:x \\ \Rightarrow \frac{27}{36}=\frac{18}{x} \\ \Rightarrow 27x=18\times 36 \\ \Rightarrow x = \frac{18\times 36}{27} \\ \therefore x =24 \end{gathered}$$

প্রশ্নঃ 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?

বর্ণনাঃ

Let the required number of bottles be x more weaves, more mats ( Direct Proportion), more days, more math (Direct Proportion)
$$\begin{gathered} Weavers \begin{array}{r}4\\ 4\end{array} \left.\begin{array}{r}8\\ 8\end{array}\right\}:: 4 : x \\ Days \\ \therefore 4\times 4\times x=8\times 8\times 4 \\ \Rightarrow x = \frac{8\times 8\times 4}{8\times 4} \\ \therefore x =16 \end{gathered}$$

প্রশ্নঃ If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

বর্ণনাঃ

Let the required number days be x.
Less spiders, More days (Indirect Proportion)
Less webs, Less days (Direct Proportion)
Spider 1 ; 7
Webs 7 : 1
$\therefore 1\times 7\times x=7\times 1\times 7$
$\Rightarrow x=7$

প্রশ্নঃ If 3 men or 6 boys can do a piece of work in 10 days,working 7 hours a day; how many days will it take to complete a piece of work twice as large with 6 men and 2 boys working together for 8 hours a day ?

বর্ণনাঃ

3 men = 6 boys
So (6 men + 2 boys) = (12 boys + 2 days) = 14 boys
More work, More days (direct proportion)
More boys, Less days (indirect   ")
More hours per day, less days (  "      " )
Work 1 : 2
Boys 14 : 6 : : 10 : x
Hours per day 8 : 7
$\therefore (1\times 14\times 8\times x)=\left(2\times 6\times 7\times 10\right)$
x = 840/112 = 7.5

প্রশ্নঃ The length of a rectangle is twice its breadth . If its length is decreased y 5 cm and breadth is increased by 5 cm , the area of the rectangle is increased by 75 sq. cm . Find the length of the rectangle.

বর্ণনাঃ

Correct answer is 40 cm.
Let, breadth x cm & length 2x cm
$\therefore$ Area = $2x^2$
length decreased by 5 cm
$2x^2$ length = 2x - 5
breadth increased by 5 cm
$2x^2$ breadth = x + 5
Area increased by 75 $c{m}^2$
$\therefore (x+5)\left(2x-5\right)-2x^2=75$
$\Rightarrow 2x^{2 }-5x+10x-25-2x^2=75$
$\Rightarrow$ 5x - 25 = 75
$\Rightarrow$ 5x = 1000
$\therefore$ x = 20
breadth = 20 cm
length = $20\times 2$ cm = 40 cm.
Note : Answer is not present in options.

প্রশ্নঃ A courtyard 25 m long and 16 m broad is to be paved with bricks of dimension 20 cm by 10 cm . The total number of bricks required is :

বর্ণনাঃ

Number of bricks = $\left(\frac{Area of courtyard}{Area of 1 brick}\right)$
$=\left(\frac{2500\times 1600}{20\times 10}\right)$
= 20,000

প্রশ্নঃ The ratio between the length and the perimeter of a rectangular plot is 1 : 3 ,what is the ratio between the length and breadth of the plot?

বর্ণনাঃ

Let, length be =x
and perimeter = 3x
Then, two length is = 2x
So, two breadth is = 3x - 2x = x
i.e one breadth is = $\frac{x}{2}$
Accourding to the question,
x: $\frac{1}{2}$x
$\Rightarrow$ 2 : 1

প্রশ্নঃ The length of a rectangular plot is 60% more than its breadth . If the difference between the length and the breadth of that rectangle is 24 cm. what is the area of that rectangle ?

বর্ণনাঃ

Let the breadth of the rectrangle be x cm then length = x + 60% of x = x +0.6x = 1.6x cm
Given difference between length and breadth is 24 cm
hence 1.6x - x = 24
$\Rightarrow$ x = 40 cm
length = $1.6\times 40$ = 64 cm
Area = $length\times breath$
$64\times 40$ = 2560 s.cm.

প্রশ্নঃ A tradesman sold and article at a loss of 20% . If the selling price had been increased by Tk. 100 . there would have been a gain of 5% . what was the cost price of the article ?

বর্ণনাঃ

Let cost price be Tk.x
then, (105% of x) - (80% of x ) = 100
$\Rightarrow \frac{25x}{100}$ = 100
$\Rightarrow \frac{x}{4}=100$
$\therefore$ x = 400
So, cost price = Tk. 400

প্রশ্নঃ Peter purchased a machine for Tk. 80,000 and spent tk. 5000 on repair and Tk. 1000 on transport and sold it with 25% profit . At what price did he sell the machine?

বর্ণনাঃ

Cost Price =  Tk. (80000 + 5000 + 1000)
= Tk. 86000
Profit = 25%
Sells price = 125% of Tk. 86000
=Tk. (125/100$\times$86000)
=Tk. 107500

প্রশ্নঃ when a plot is sold for TK. 18,700 , the owner loses 15% . At what price must the plot be sold in order to gain 15% ?

বর্ণনাঃ

85 : 18700 = 115 : x
$\Rightarrow x=\left(\frac{18700\times 115}{85}\right)$
= 25300
Hence S.p.= TK. 25300

প্রশ্নঃ The percentage profit earned by selling an article for TK. 1920 is equal to the percentage loss incurred by selling the same article for TK. 1280 .At what price should the article be sold to make 25% profit?

বর্ণনাঃ

Let, Cost Price be Tk. X
Then, $\frac{1920-x}{x}\times 100=\frac{x-1280}{x}\times 10$
$\Rightarrow$ 1920 - x = x - 1280
$\Rightarrow$2x = 3200
$\Rightarrow$ x = 1600
$\therefore$ Required S.P. = 125% of Tk. 1600
=Tk. $\left(\frac{125}{100}\times 1600\right)$ = Tk. 2000

প্রশ্নঃ A can complete a journey in 10 hours. He travels first half of the journey at the rate of 21 km / hr and second half at the rate of 24 km .hr. Find the total journey in km.

বর্ণনাঃ

Let the distance be x
$$\begin{gathered} So,\frac{\left({\displaystyle \frac{1}{2}}\right)x}{21}+\frac{\left(\frac{1}{2}\right)x}{24}=10 \\ \Rightarrow \frac{x}{21}+\frac{x}{24}=20 \\ \Rightarrow 15x = 168\times 20 \\ \Rightarrow x =\frac{168\times 20}{15} \\ \therefore 224km \end{gathered}$$

প্রশ্নঃ which of the following is not a leap year ?

বর্ণনাঃ

1. Leap years are any year that can be evenly divided by 4 ( such as 2012,2016 etc)
2. Except if it can be evenly devided by 100. then it itn't leap year (such as 2100,2200, etc)
3. Except if it can be evenly divided by 400,then it is leap year (such as 2000,2400)