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# 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?

Given:

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."

To do:

We have to find the number of mangoes each has.

Solution:Let the number of mangoes with A and the number of mangoes with B be $x$ and $y$ respectively.

If A gets 30 mangoes from B then the number of mangoes with A is $x+30$ and the number of mangoes with B is $y-30$.

If B gets 10 mangoes from A then the number of mangoes with A is $x-10$ and the number of mangoes with B is $y+10$.

According to the question,

$x + 30 = 2(y-30)$.....(i)

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

$y+10=3x-30$

$y=3x-30-10$

$y=3x-40$.....(ii)

Substituting $y=3x-40$ in equation (i), we get,

$x+30=2(3x-40-30)$

$x+30=6x-140$

$6x-x=30+140$

$5x=170$

$x=\frac{170}{5}$

$x=34$

This implies,

$y=3(34)-40$

$y=102-40$

$y=62$

**Therefore, A has 34 mangoes and B has 62 mangoes.**