Question:
A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?
Solution:
To find:
(1) Total mangoes of A.
(2) Total mangoes of B.
Suppose A has x mangoes and B has y mangoes,
According to the given conditions,
$x+30=2(y-30)$
$x+30=2 y-60$
$x-2 y+30+60=0$
$x-2 y+90=0$....(1)
$y+10=3(x-10)$
$y+0=3 x-30$
$y-3 x+10+30=0$
$y-3 x+40=0$.....(2)
Multiplying eq. 1 by (3),
3x + 6y + 270 = 0 …… (3) and
Now adding eq.2 and eq.3
5y = 310
$y=\frac{310}{5}$
$y=62$
$x-2 \times 62+90=0$
$x-124+90=0$
$x-34=0$
$x=34$
Hence A has 34 mangoes and B has 62 mangoes.