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Both boxes had 300/2 = 150 oranges in the end. 

Before that, 1/3 of Box B went into Box A. So before this transfer,  Box B had 150 * 3/2 = 225 oranges and Box A had 300-225 = 75 oranges. 

In the beginning, 1/4 of Box A went into Box B. So Box A had 75 *4/3 = 100 oranges  and Box B had 300 – 100 = 200 oranges in the beginning. 

0 Replies 2 Likes ✔Accepted Answer

Box A has u oranges at first.
So Box B must have (300 – u) oranges at first.

(1/4)u was moved from Box A to Box B.
So Box B must have (300 – u) + (1/4)u
= 300 – (3/4)u

Now 1/3 of oranges is moved from Box B to Box A.
So Box A must have  (3/4)u + 1/3( 300 – (3/4)u)
= (3/4)u – (1/4)u + 100
= (1/2)u + 100
Box B must have 2/3(300 – (3/4)u)
= 200 – (1/2)u

Since they both have the same number of oranges in the end,
(1/2)u + 100 = 200 – (1/2)u
u = 100

So Box A has u = 100 oranges at first.
Box B has (300 – u) = 200 oranges at first.

0 Replies 2 Likes