A and B both have some pencils. If A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A, then they will have the same number of pencils. How many pencils does each have ?

Let A have x pencils and B have y pencils.

Given,

If A gives 10 pencils to B, then B will have twice as many as A.

∴ 2(x - 10) = y + 10

⇒ 2x - 20 = y + 10

⇒ 2x - y = 10 + 20

⇒ 2x - y = 30 ………(1)

Given,

If B gives 10 pencils to A, then they will have the same number of pencils.

∴ x + 10 = y - 10

⇒ x - y = -10 - 10

⇒ x - y = -20 ……….(2)

Subtracting equation (2) from (1), we get :

⇒ 2x - y - (x - y) = 30 - (-20)

⇒ 2x - x - y + y = 30 + 20

⇒ x = 50

Substituting value of x in equation (1), we get :

⇒ 2(50) - y = 30

⇒ 100 - y = 30

⇒ y = 100 - 30 = 70.

Hence, A has 50 pencils and B has 70 pencils.