ans: 34.
Givenx = 3+$\sqrt{8}$……………(i)
=> $\frac{1}{x}$ = $\frac{1}{3+\sqrt{8}}$
=> $\frac{1}{x}$ =$\frac{3-\sqrt{8}}{(1+\sqrt{8})(3-\sqrt{8})}$
=> $\frac{1}{x}$ = $\frac{3-\sqrt{8}}{(3)^{2}-(\sqrt{8})^{2}}$
=> $\frac{1}{x}$ = $\frac{3-\sqrt{8}}{9-8}$
=> $\frac{1}{x}$ = $\frac{3-\sqrt{8}}{1}$
$\frac{1}{x}$ = (3-$\sqrt{8}$)……………………….(ii)
অতএব, (i) + (ii) হতে পাই
=> x+$\frac{1}{x}$ = (3+$(3+\sqrt{8)+(3-\sqrt{8})}$
=> x $\frac{1}{x}$ = 3+$\sqrt{8+3-\sqrt{8}}$
=> x $\frac{1}{x}$ = 6………………………………….(iii)
এখন, $x^{2}+\frac{1}{x^{2}}=(x+\frac{1}{x})^{2}-2x\times \frac{1}{x}$
= 6$^{2}$-2
= 36 -2
34
ans: The number of children is 100 and amount of money 450 Tk.
Let, the number of children = x
and the amount of money each gets = y Tk.
The total amount of money distributed = xy Tk.
so, According to question (x – 25) (y + 1.5) = xy……………………….. (i)
And (x+50) (y- l.5) =xy………………………… (ii)
We get from equation (i)
(x – 25) (y + 1.5) =xy
=> xy+ 1.5x – 25y-37.5 =xy
=> 1.5x – 25y = 37.5
=> 3x – 50y = 75 …………………(iii)
We get from equation (ii)
(x + 50) (y- l.5) =xy
=> xy-1.5x+50y-75 =xy
=> -1.5x + 50y = 75……………………….. (iv)
adding equation (iii) & (iv), we get
3x – 50y = 75
-1.5x + 50y = 75
1.5x =150
x = $\frac{150}{1.5}$ = 100
Putting the value of x in eqution (iii), we get
3x — 50y = 75
=> (3 x 100)-50y= 75
=> 300 – 50y = 75
=> – 50y = 75 – 300
=> – 50y = – 225
=> y=$\frac{-225}{-50}$
y = 4.5
Now putting the value of y in (iii)
=> 3x-50y = 75
=> 3x- (50) x (4.5) = 75
=>3x-225=75
=> 3x = 75 + 225
=> 3x = 300
=> x=$\frac{300}{3}$
x = 100
The number of children = x = 100 and
The total amount of money distributed = x $\times$ y = 4.5 x 100 = 450 Tk.
ans: Loss 40,000 Tk.
As the distributor gives 500 copy free, the remaining number of copy = (3,500 -500) = 3,000.
Total cost of the distributor = 4,00,000 Tk.
Now, at 25% discount if market price is 100 Tk. the selling price is (100 -25) Tk. = 75 Tk.
When, market price is 100 Tk. then selling price = 75 Tk.
When, market price is 1 Tk. then selling price =$\frac{75}{100}$ Tk.
When, market price is 160 Tk. then selling price = $\frac{75×160}{100}$ = 120 Tk.
Revenue from 3,000 copy = (3,000 x 120) = 3,60,000 Tk.
But, the cost price = 4,00,000 Tk.
Loss = (4,00,000 -3,60,000) Tk. = 40,000 Tk.
