Question

find two positive rational numbers whose sum is 1 and if the smaller is divided by the greater the result is 1 by 2

Answer 1

let the two positive rational numbers be x and yà
a.t.q.
x+y=1 eq.1
x/y=1/2
y=2x eq2
put this value of y in eq 1
x+2x=1
3x=1=
x=1/3
put x =1/3 in eq.2
y=2×1/3
y=2/3

Answer 2

two positive rational numbers whose sum is 1 and if the smaller is divided by the greater the result is 1 by 2  are $\frac{1}{3}$ and ($\frac{2}{3}$).

Let the two numbers be a and b, out of which a is the smaller number.

In the first part of the question, it is mentioned that the sum of these numbers equal to 1.

So, a + b = 1                                           ......(1)

And, in the second part of the question, it is mentioned that when the smaller number (a) is divided by the greater number (b) gives $\frac{1}{2}$

 $\frac{a}{b} = \frac{1}{2}$

or, b = 2a                                                  ......(2)

Replacing the value of b = 2a from (2) in (1), we get,

a + 2a = 1

⇒ 3a = 1

⇒ a = $\frac{1}{3}$

Putting a = $\frac{1}{3}$ in (2), we get the value of b as

b = 2($\frac{1}{3}$)

So, b = ($\frac{2}{3}$)

Thus, the smaller number, a is equal to $\frac{1}{3}$ and the larger number, b is equal to ($\frac{2}{3}$)