A and B each have a 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, I will have the same number of oranges left with you.” Find the number of oranges that A has.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 70.
Let A and B each have a certain number of oranges be X and Y
Given that
Case 1 : B gave 10 oranges to A, then A have twice the number of oranges left with B
Case 2 : A gave 10 oranges to B, then B have the same number of oranges left with A
According to the question
Case 1 :
⇒ 2(Y - 10) = (X + 10)
⇒ 2Y - 20 = X + 10
⇒ 2Y - X = 30 .......(1
Case 2 :
⇒ X - 10 = Y + 10
⇒ X - Y = 20 .........(2
Equation 1 + Equation 2
Y = 50
From Equation 2
X = 50 + 20 = 70