# A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes,

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

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.