Pubali Bank Ltd - Junior Officer (Cash) - 17.05.2013/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ If $x^2$+$y^{}$=4 and $x^{}$-$y^{}$=- then $x^{}$+$y^4$ is

বর্ণনাঃ

$$\begin{gathered} x^4+y^4=\frac{(x^2+y^2{)}^2+(x^2-y^2{)}^2}{2} \\ =\frac{(4{)}^2+(-4{)}^2}{2} \\ =\frac{16+16}{2} \\ =16 \end{gathered}$$

প্রশ্নঃ If product of 3 consecutive integers is 120, then the sum of the integers is--

বর্ণনাঃ

সহজ উপায় হচ্ছে Answer এ দেয়া Number  গুলো observe কর
6x7x8=336;5x9x7=210 and 4x5x6=120; So, the sum of the integers is 4+5+6=15   

প্রশ্নঃ There are 900 students in a school . 4% of them left the school and 50% of the remaining are girls. How many girls remained?

বর্ণনাঃ

900 জন এর 4%=900 x .04=36
36জন চলে যাওয়ায় বাকি থাকে =900-36=864
এবং বাকি 864এর 50% girls =864 x .50=432 

প্রশ্নঃ The minimum value of 2x2 +8x -5 is

বর্ণনাঃ

$2x^2+8x-5=2(x^2+2.x.2+2^2)-8-5=2(x+2{)}^{{}^2-13}$
যখন X+2=0,তখন $2x^2+8x-5$  এর value সবনিন্ম, যা -13

প্রশ্নঃ If the market price is Tk 25, the revenue of selling five units in Taka is --

বর্ণনাঃ

Here, revenue is equal to selling price.
So,If 1 Unit selling price/revenue is 25tk.
So, 5    "      "          "            =25x5=125 tk

প্রশ্নঃ There are 12 more apples than oranges in a basket of 36 apples and oranges. How many apples are in the basket?

বর্ণনাঃ

Let, oranges =x and Apples=x+12
So, x+(x+12)=36
or,2x =24
So,x=12 
So, Apples=12+12=24

প্রশ্নঃ Bina is 10 years older than Mim . In 7 years time. Bina will be twice as old as Mim.

বর্ণনাঃ

Let,Mim's present age=x 
and Bina's present age=x+10 
According to question,
x+10+7=(x+7)x2
So, x=3
So, Bina's Present age=3+10=13

প্রশ্নঃ If product of 3 consecutive integers is 120, then the sum of the integers is--

বর্ণনাঃ

সহজ উপায় হচ্ছে Answer এ দেয়া Number  গুলো observe কর
6x7x8=336;5x9x7=210 and 4x5x6=120; So, the sum of the integers is 4+5+6=15   

প্রশ্নঃ If 15 is the fifth number in a series of 5 consecutive odd numbers, what is the third number in the series?

বর্ণনাঃ

series টি হচ্ছে 7, 9, 11, 13, 15

প্রশ্নঃ The difference of two numbers is 7 and their product is 60 , then one of the two numbers must be -

বর্ণনাঃ

x-y=7; x=(y+7)
xy=60
or,(y+7).y=60
or,$$\begin{gathered} y^2+7y-60=0 \\ (y+12) (y-5)=0 \\ So,Y=-12,5 \\ So,the two number is 12 and 5 \end{gathered}$$

প্রশ্নঃ A woman had 50 ducks . All but 8 died. How many ducks are still alive?

বর্ণনাঃ

All but 8 মানে ৮টি বাদে বাকি সব।

প্রশ্নঃ Reza's average in four tests is 80% . what marks does he need in his fifth test to raise his average to 84% .

বর্ণনাঃ

ধরি, প্রথম 4টি exam এর যোগফল x 
এবং 5th exam এ পাওয়া marks y $$\begin{gathered} \frac{x}{y}=80 \\ x=4x80 \\ and,\frac{x+y}{5}=84 \\ So,Y=5x84-x \end{gathered}$$ অথাৎ 100% 

প্রশ্নঃ Which fraction is the largest?

বর্ণনাঃ

Generally উপরে নিচের Difference যত less হয় fraction তত large । তবে পার্থক্য একই হলে, যে ক্ষেত্রে ব্যবহৃত সংখ্যা বড় সেই fraction বড়। যেমন 4/5 ও 9/10 এর মধ্যে 9/10>4/5।

প্রশ্নঃ A 5% monthly salary increase resulted in a salary increase of TK. 6,000 per year for an employee. What was his monthly salary before the increase?

বর্ণনাঃ

6000 Tk per year increase হলে প্রতি মাসে income =$\frac{6000}{12}=500 tk$ 
অথাৎ তার প্রতি মাসের Salary  এর 5% হচ্ছে 500 tk.
monthly salary x 5% =500
So,monthly salary=$=\frac{500\times 100}{5}=10000$  

প্রশ্নঃ If the sum of the 3 consecutive integers is 240 , then the sum of the two larger integers is:

বর্ণনাঃ

ধরি, প্রথম integer টি x 
so, x+x+1+x+2=240
or,3x+3=240
or,3x=237
so, x=79 
এবং larger integer  দুটির যোগফল =80+81=161 

প্রশ্নঃ Rice is now being sold at Taka 20 a kg. During last month its rate was Taka 16 per kg . By how much percent should a family reduce its consumption so as to keep the expenditure fixed?

বর্ণনাঃ

ধরি, L এবং T যথাক্রমে Last month এবং This month  এর চালের পরিমাণ
So, cost last month =16L; this month =20T  
যেহেতু cost একই রাখা হয়েছে,এই দুটি same 
so, 16L=20T or, T=.8L  
অথাৎ This month  তারা rice consume করবে, 8 times of last month or 80% 
So,reduction in consumption =(100-80)%=20%  

প্রশ্নঃ A person walking 5/6 of his usual rate is 40 minutes late. What is his usual time?

বর্ণনাঃ

Let, usual time is t and usual rate is 1 unit.
According to Question
⸫ 1×t=5/6 (t+40)
⇒6t=5(t+40)
⇒t=200 minutes.
⸫ 3 hrs 20 minutes.

প্রশ্নঃ One dog tells the other that there are two dogs in front of me. The other one also shouts that he too had two behind him. How many are they?

বর্ণনাঃ

The number of Dog are three (3)

প্রশ্নঃ what is the number of integers between 101 and 199 which exactly divisible by 5 or 7?

বর্ণনাঃ

There ae 19 divisible by 5 and 14 divisible by 7
এদের মধ্যে 3টি both 5 এবং 7 দ্বারা divisible 
So,Total integers =19+14-3=30

প্রশ্নঃ If selling price is doubled, the profit triples, Find the profit percent,

বর্ণনাঃ

ধরি, উৎপাদন খরচ x এবং selling price y 
তাহলে 3(y-x)=(2Y-x)
or,y=2x
এবং profit=(Y-x)=(2x-x)=x  
So,the percent of profit x=$(\frac{x}{x}\times 100\%)=100\%$

প্রশ্নঃ The average weight of 8 persons increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg . What might be the weight of the new person?

বর্ণনাঃ

Total weight increased =(8x2.5)kg=20kg
so,Weight of new person=(65+20)=85kg

প্রশ্নঃ 3 pumps , working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

বর্ণনাঃ

ধরা যাক, প্রতিদিনের Working hour  'x'
বেশি পাম্প, কম working hour per day 
কম দিন,বেশি      "        "    "    "
$$\begin{gathered} \frac{pumps 4:3}{Days 1:2}: : 8:x \\ So,4\times 1\times x=3\times 2\times 8 \\ or,x=\frac{3\times 2\times 8}{4}=12 \end{gathered}$$      

প্রশ্নঃ Running at the same constant rate 6 identical machines can produce a total of 270 bottles per minute . At this rate, how many bottles could 10 such machines produce in 4 minutes?

বর্ণনাঃ

ধরা যাক,  required bottle সংখ্যা 'x'
বেশি বেশি machine, বেশি bottle 
 "     "    minute,  "   bottle  
$$\begin{gathered} \frac{pumps 4:3}{Days 1:2}: : 8:x \\ So,4\times 1\times x=3\times 2\times 8 \\ or,x=\frac{3\times 2\times 8}{4}=12 \end{gathered}$$ 

প্রশ্নঃ what least number must be added to 1056 , so that the sum is completely divisible by 23?

বর্ণনাঃ

$\begin{array}{c}23\left|1056\right|45\\ \begin{array}{c}95\\ \begin{array}{c}-\\ \begin{array}{c}136\\ \begin{array}{c}116\\ \begin{array}{c}-\\ 21\end{array}\end{array}\end{array}\end{array}\end{array}\end{array}$

⸫ প্রয়োজনীয় least number= (23-21)=2

প্রশ্নঃ Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. what is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

বর্ণনাঃ

S= [1,2,3,4, ------19,20]
ধরি, E=event of 3 অথবা 5 এর multiple পাবার সম্ভাব্যতা =[3,6,9,12,15,18,5,10,20]
⸫ P(E)=n(E)/n(S)= 9/20