The faster pump has exactly double the flow rate of the slower pump.
Let us say he uses the fast pump to fill the larger container first and the slow pump to fill the smaller container.
Let us say it takes 10 minutes (you can use any time as volume of containers is not specified) to fill the smaller container with half its volume. In 10 minutes smaller container will be filled with 60 litres (6 litres per minute) whilst the larger container will be filled with 120 litres (12 litres per minute). Using this assumption, smaller container must have a volume of 120 litres in total.
Now the containers are swapped with each other. The fast pump fills the smaller container and the slow pump fills the larger container. Both of them are filled at the same time. We have assumed that smaller container has a volume of 120 litres. Now that the faster pump is being used to fill the remaining 60 litres of the small container, it takes 5 minutes to fill the remaining 60 litres. Total time taken to fill smaller container = 15 minutes.
Slower pump is being used to fill the remaining volume of larger container. It already has 120 litres and it takes 15 minutes in total to fill the larger container.
In the remaining 5 minutes, the larger container will be filled with 6 x 5 = 30 litres.
Total volume of larger container = 120 + 30 = 150 litres.
Extra volume of larger container = 150 – 120 = 30 litres
Percentage larger = (30 ÷ 120) x 100 = 25%