Nathu and Buchku each have certain number of oranges. Nathu says to Buckhu, "If you give me 10 of your oranges, I will have twice the number of oranges left with you". Buckhu replies, "If you give me 10 of your oranges, I will have the same number of oranges as left with you." What is the number of oranges with Nathu and Buckhu, respectively?

Let the number of oranges with Nathu be x
Number of oranges with Buchku = y
Case I,
x + 10 = 2(y - 10)
⇒ x + 10 = 2y - 20
⇒ 2y - x = 20 + 10 = 30 . . . . . . (i)
Case II,
y + 10 = x - 10
⇒ x - y = 10 + 10 = 20 . . . . . . (ii)
On adding equations (i) and (ii)
2y - x + x - y = 30 + 20
⇒ y = 50
From equation (ii),
x - 50 = 20
⇒ x = 50 + 20 = 70