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?

A. 50, 20

B. 70, 50

C. 20, 50

D. 50, 70

Answer: Option B

Solution(By Examveda Team)

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