A and B each have certain number of oranges. A says to B if you give me 10 of your oranges, I will have twice the number of oranges left with you. B replies if you give me 10 of your oranges then I will have the same number of oranges as left with you. Find the number of oranges with a and b.

Let the number of oranges with A be ‘a’ and that of with B be ‘b’

According to what A told to B remove 10 oranges from B (b – 10) give it to A (a + 10) and we have,

a + 10 = 2 × (b – 10) …(i)

according to what B told to A remove 10 oranges from A (a – 10) give it to B (b + 10) and we have

b + 10 = a – 10

b = a – 20 …(ii)

substituting b = a – 20 in (i)

⇒ a + 10 = 2 × (a – 20 – 10)

⇒ a + 10 = 2 × (a – 30)

⇒ a + 10 = 2a – 60

⇒ a = 60 + 10

⇒ a = 70

Substituting value of a in equation (ii)

⇒ b = 70 – 20

⇒ b = 50

Hence A has 70 oranges and B has 50 oranges