# $A$ 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

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Hint: Always start by assigning x entities to one and according to that assign the next variable if they are related and if not assign another variable.

Let us assume the number of mangoes $A$ has is $x$,

And the number of mangoes $B$ has is $y$.

Therefore, if we look at the condition given in the question, for $A$,

$30 + x = 2\left( {y - 30} \right)$ …..(1)

And for B,

$10 + y = 3\left( {x - 10} \right)$ …..(2)

Note: Make sure the equations formed are correct and satisfy the question’s conditions.

On simplification of the above two equations, we get

$x - 2y + 90 = 0$ …..(3)

And the second equation becomes,

$ - 6x + 2y + 80 = 0$…..(4)

Let us add (3) and (4),

$ - 5x + 170 = 0$

From here, we get the value of $x = 34$

Therefore, $A$ has $34$ mangoes.

Now, let us put the value of $x$ in (1),

$34 - 2y + 90 = 0$

$2y = 124$

$y = 62$

Therefore, $B$ has $62$ mangoes.

Let us assume the number of mangoes $A$ has is $x$,

And the number of mangoes $B$ has is $y$.

Therefore, if we look at the condition given in the question, for $A$,

$30 + x = 2\left( {y - 30} \right)$ …..(1)

And for B,

$10 + y = 3\left( {x - 10} \right)$ …..(2)

Note: Make sure the equations formed are correct and satisfy the question’s conditions.

On simplification of the above two equations, we get

$x - 2y + 90 = 0$ …..(3)

And the second equation becomes,

$ - 6x + 2y + 80 = 0$…..(4)

Let us add (3) and (4),

$ - 5x + 170 = 0$

From here, we get the value of $x = 34$

Therefore, $A$ has $34$ mangoes.

Now, let us put the value of $x$ in (1),

$34 - 2y + 90 = 0$

$2y = 124$

$y = 62$

Therefore, $B$ has $62$ mangoes.

Last updated date: 29th Sep 2023

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