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 ?

Let A has x number of mangoes and B has y number of mangoes.

In 1st case (if B gives 30 mangoes to A):

⇒ x + 30 = 2(y - 30)

⇒ x + 30 = 2y - 60

⇒ x = 2y - 60 - 30

⇒ x = 2y - 90 ……………(1)

In 2nd case (if A gives 10 mangoes to B):

y + 10 = 3(x - 10)

⇒ y + 10 = 3x - 30

⇒ y = 3x - 30 - 10

⇒ y = 3x - 40 ……………(2)

On solving equations (1) and (2), we get :

⇒ y = 3(2y - 90) - 40

⇒ y = 6y - 270 - 40

⇒ y = 6y - 310

⇒ 6y - y = 310

⇒ 5y = 310

⇒ y = $\dfrac{310}{5}$

⇒ y = 62

From equation (1),

⇒ x = 2 x 62 - 90

⇒ x = 124 - 90

⇒ x = 34

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