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?

Answer 1

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 =2y -60`

`x - 2y +30 + 60 =0`

`x - 2y =90 =0`

`y +10 =3(x -10)`

`y +0 = 3x-30`

`y -3x +10+30 =0`

`y + 3x +40 =0`

`y - 3x +10 +30 =0`

`y - 3x +40 =0`

Multiplying eq. 1 by 3

3x + 6y + 270 = 0 …… (3) and

Now adding eq.2 and eq.3

5y = 310

`y = 310 /5`

`y = 62`

`x - 2xx62+90 =0`

`x - 124 + 90 =0`

`x - 34 = 0`

`x = 34`

Hence A has 34 mangoes and B has 62 mangoes.