Let, the age of three persons is 27, 3x, 4x years respectively (where x be the common term)
After 5 years, their age will be 2x + 5, 3x + 5, 4x + 5 years respectively
According to the question,
(2x + 5) : (3x + 5) : (4x + 5) = 5 : 7 : 8 ………………(i)
Now, from (i) we can write
$\frac{2x+5}{3x+5}$ = $\frac{5}{7}$
=> 15x+25=14x+35
x = 10
The age of the younger person = 2 x 10 == 20 years
It will take 3.43 days to finish the work if they work together.
As Mr. X can finish a work in 6 days
Mr. X can do $\frac{1}{6}$ part of the work in 1 day
Again, Mr. Y can finish the same work in 8 days
Mr Y can do $\frac{1}{8}$ part of the work in 1 day
If they work together, they can do = ($\frac{1}{6}+\frac{1}{8}$) = $\frac{7}{24}$ part of the work in 1 day
They can do $\frac{7}{24}$ part of the work in 1 day
They can do 1 or total part of the work in $\frac{24}{7}$ = 3.43 days
The purchase price of the shirt is Tk. 90.
Let, the purchase price is Tk. x
Here, the gain = x of x% =x $\times$$\frac{x}{100}$=$\frac{x^{2}}{100}$ Tk
According to the question,
$\frac{x^{2}}{100}$ + x = 171
=> x$^{2}$ + 1OOx— 17100 = 0
=> x$^{2}$ + 190x – 90x – 17100 = 0
=> x(x + 190) – 90(x + 190) = 0
=> (x+190) (x-90) = 0
So, x = 90
Therefore, the purchase price is Tk. 9O
The value is 1.
x+$\frac{1}{x}$ = 2
=> $\frac{x^{2}+1}{x}$ = 2
=> $x^{2}$+1=2x
=> $x^{2}$-2x+1=0
=> $x^{2}$-2x$\times 1+1^{2}$ = 0
=> (x-1)$^{2}$ = 0
=> x-1=0
x=1
$\frac{x}{x^{2}+1-1}$
= $\frac{1}{1^{2}+1-1} $
= $\frac{1}{1}$
= 1
