Question

A and B each have certain number of oranges. A says to B, "if you give me $10$ of your oranges, I will have twice the number of oranges left with you." B replies, "if you give me $10$ of your oranges, I will have the same number of oranges as left with you." Find the number of oranges with A and B separately.

Answer 1

Suppose A has $x$ no. of oranges and B has $y$ no. of oranges.

According to the given conditions, we have

$x+10=2(y-10)\Rightarrow x-2y+30=0$ (i)

and, $y+10=x-10\Rightarrow x-y-20=0$ ..(ii)

Substracting equation (ii) from equation (i), we get

$-y+50=0\Rightarrow y=50$

Putting $y=50$ in equation (i), we get $x=70$

Hence, A has $70$ oranges and B has $50$ oranges.