Final answer:
After increasing Lotty's initial share by 30%, the new ratio for sharing the money between Lotty and Rafael, after simplification, is 13:15.
Step-by-step explanation:
Lotty and Rafael initially agree to share any winnings in the ratio 2:3 respectively. After winning a total of £2000, they reconsider and decide that Lotty's share should be increased by 30%. To find the new sharing ratio, we first compute Lotty's initial share which is (2/5) of £2000, giving £800. Now increasing £800 by 30% we get £1040. Rafael's share remains the same, that is, (3/5) of £2000, which is £1200.
The new ratio of their shares is £1040 (Lotty) to £1200 (Rafael). To simplify this ratio, we need to find a common factor. The greatest common divisor of 1040 and 1200 is 40. Dividing both numbers by 40 gives us a simplified ratio of 26:30. However, both 26 and 30 are still divisible by 2, which further simplifies the ratio to 13:15.