A and B each have a certain number of mangoes. A says to B “If you give me 30 of your mangoes, I will have twice as many 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?

Let A have x mangoes and B have y mangoes.

Here, after getting 30 mangoes from B, A has (x + 30) mangoes.

And the mangoes left with B = (y – 30) mangoes.

Now, according to the question:

→ x + 30 = 2(y – 30)

→ x + 30 = 2y – 60

→ x – 2y = – 60 – 30

→ x – 2y = – 90 …..(1)

Now, after getting 10 mangoes from A, B has (y + 10).

Also, mangoes remain left to A = (x – 10) mangoes.

Now, according to the question:

→ y + 10 = 3(x – 10)

→ y + 10 = 3x – 30

→ y – 3x = – 30 – 10

→ y – 3x = – 40 …………(2)

Multiplying the equation (2) with 2. We get:

→ 2y – 6x = – 80 …….. (3)

Now, by adding equation 1 and Equation 3, we get:

→ (x - 2y) + (2y - 6x) = (- 90) + (- 80)

→ x – 6x = – 90 – 80

→ – 5x = – 170

→ x = 34

Now, put the value of x in equation (2), we get:

→ y – 3x = – 40

→ y – 3(34) = – 40

→ y – 102 = – 40

→ y = 102 – 40 

→ y = 62

Hence, A has 34 mangoes and B has 62 mangoes.