সহকারী ব্যবস্থাপক ১২.০৭.২০১৯/গণিত এর প্রশ্ন পরুন ।

প্রশ্নঃ By selling a bicycle for TK. 2,850,a shopkeeper gains 14% . If the profit is reduced to 8% ,then the selling price will be

বর্ণনাঃ

ATQ,
114% = 2850 Tk
.'. 108% $=\frac{2850}{114}\times 108=Tk.2700$

প্রশ্নঃ In recent survey of the student of a public university . It is found that 65% students are good in Mathematics and 45% students are good in Mathematics and 45% students are good in Statistics. How many students are good in both Mathematics and statistics of the public university?

বর্ণনাঃ

Students good in
both mathematics 
and statisties 
=(65 +45)% -100%
=110% -100% =10%

প্রশ্নঃ Naizel is twenty years older than Nekata . In three years Naizel will be twice as old as Neketa will be. How old is Neketa now?

বর্ণনাঃ

Let, Neketa's age x
.'. Naizel's  age x +20 
ATQ, 
2(x+3) =x +23
বা,  x=23 -6=17

প্রশ্নঃ A wall 8m long, 6 m high and 22.5 cm thick is made up of bricks, each measuring 25 cm $\times$ 6 cm The number of bricks required is

বর্ণনাঃ Volume of wall =$$\begin{gathered} (8\times 100)\times (6\times 100)\times 22.5 \\ =10800000 \\ Volume of bricks =25\times 11.25\times 6 \\ =1687.5 \\ .\text{'}. The number of bricks =\frac{10800000}{1687.5} \\ =6400 \end{gathered}$$

প্রশ্নঃ The length of a rectangle is increased by 25% .By what percentage should the width be decreased so that the area of the rectangle remains unchanged?

বর্ণনাঃ

Let,
Length 100
Width 100
So, area = $$\begin{gathered} 100\times 100=10,000 \\ Increased length =100\times \frac{125}{100}=125 \\ Let, New width = x \\ ATQ, \\ 125\times x =10,000 \\ \Rightarrow x=\frac{10000}{125}=80 \\ So, percentage decreased \\ =\frac{100-80}{100}\times 100 \\ =20\% \end{gathered}$$

প্রশ্নঃ The average age of 12 children is 15 years. If another child comes the average age comes to 13. what is the age of the new child?

বর্ণনাঃ

Total age of 12 children 
=$$\begin{gathered} 15\times 12=180 \\ " " " " 13 " \\ =13\times 13=169 \\ .\text{'}. New child age =180-169 \\ =11 \end{gathered}$$

প্রশ্নঃ A train 150 meter long and running at a speed of 60 km per hour takes 30 seconds to cross a bridge. What is a length of the bridge?

বর্ণনাঃ

Let, length of bridge be
=x 
Speed =60 kmph 
=$$\begin{gathered} 60\times \frac{5}{18} \\ We know, Length \\ = Speed \times time \end{gathered}$$
$$\begin{gathered} \Rightarrow 150 +x = 60\times \frac{5}{18}\times 30 \\ \Rightarrow x=500 - 150 =350 \end{gathered}$$

প্রশ্নঃ Find the vlue of n if 27 $n\frac{-1}{3}=243$

বর্ণনাঃ

$$\begin{gathered} {27}^n\frac{-1}{3}=243 \\ \Rightarrow (3^3{)}^{\frac{-n}{3}}=3^5 \\ \Rightarrow 3\frac{-3n}{3}=3^5 \\ \Rightarrow 3^{-n}=3^5 \\ \Rightarrow n=-5 \end{gathered}$$

প্রশ্নঃ $5^{-3}+5^{-3}+5^{-3}+5^{-3}+5^{-3}=?$

বর্ণনাঃ

$$\begin{gathered} 5^{-3} +5^{-3}+5^{-3} \\ +5^{-3}+5^{-3}=5.5^{-3} \\ =5^{1-3} \\ =5^{-2} \end{gathered}$$

প্রশ্নঃ If the difference between the circumference and diameter of a circle is 60 cm. then the radius of the circle is

বর্ণনাঃ

ATQ,
$$\begin{gathered} 2\mathrm{\pi r} -2\mathrm{r}= 60 \\ \Rightarrow 2\mathrm{r} (\mathrm{\pi }-1) =60 \\ \Rightarrow \mathrm{r}=\frac{30}{\mathrm{\pi }-1}=\frac{30}{{\displaystyle \frac{22}{7}}-1} \\ =\frac{30}{{\displaystyle \frac{22-7}{7}}}=\frac{30}{{\displaystyle \frac{15}{7}}} \\ =\frac{30}{15}\times 7 \\ =14 \end{gathered}$$