Question
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.Solution
Suppose A has x no. of oranges and B has y no. of oranges. According to the given conditions, we have x + 10 = 2(y - 10)  x - 2y + 30 = 0 … (i) and y + 10 = x -10 x-y-20 = 0 … (ii) Subtracting equation (ii) from equation (i), we get – y + 50 = 0  Putting y = 50 in equation (i), we get x = 70 Hence, A has 70 oranges and B has 50 oranges. = 50
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