Anna, Barbara and Diana had 1260 marbles. Barbara won some of the marbles from Anna and as a result, Barbara's marbles increased by 50%. Diana then won some marbles from Barbara and Diana's marbles increased by 75%. Finally, Diana lost some of her marbles to Anna and Anna's marbles increased by 20%. In the end, they realised that they each had an equal number of marbles. How many percent less did Anna have in the end than what she had at first? Correct your answer to 1 decimal place.

Anna	Barbara	Diana
1260
	2 u
- 1 u	+ 1 u
	3 u
		4 p
	- 3 p	+ 3 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
75% = ⁷⁵₁₀₀ = ³₄
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1260

1 group = 1260 ÷ 3 = 420

1 group = 6 boxes
6 boxes = 420

1 box = 420 ÷ 6 = 70

1 group + 1 box = 7 p
420 + 70 = 7 p
7 p = 490

1 p = 490 ÷ 7 = 70

3 p = 3 x 70 = 210

1 group + 3 p = 3 u
420 + 210 = 3 u
3 u = 630

1 u = 630 ÷ 3 = 210

Number of marbles that Anna had at first
= 5 boxes + 1 u
= (5 x 70) + 210
= 350 + 210
= 560

Percent that Anna had less in the end than at first
= ^{560 - 420}₅₆₀ x 100%
≈ 25.0%

Answer(s): 25.0%