Ramesh and Ganesh had some oranges initially. If Ramesh gave 5 oranges to Ganesh, then Ganesh will have thrice as many oranges as Ramesh. Instead of that, if Ganesh was to give 5 oranges to Ramesh, then they both will have the same number of oranges. Find the ratio of oranges that were distributed between Ramesh and Ganesh?

Let the number of oranges Ramesh has be x and the number of oranges Ganesh has be y.
According to the first condition,
y + 5 = 3(x - 5)
⇒ 3x - y + 10 = 0 ...(i)
According to the second condition,
x + 5 = y - 5
⇒ x - y + 10 = 0 ...(ii)
On subtracting Eq. (ii) from Eq. (i), we get x = 15
On substituting the value of x in Eq.(ii), we get y = 25
∴ The ratio of oranges to be distributed Ramesh and Ganesh = 15:25 = 3:5