Diana, Nicole and Anna had 810 pens. Nicole won some of the pens from Diana and as a result, Nicole's pens increased by 25%. Anna then won some pens from Nicole and Anna's pens increased by 50%. Finally, Anna lost some of her pens to Diana and Diana's pens increased by 20%. In the end, they realised that they each had an equal number of pens. How many percent less did Diana have in the end than what she had at first? Correct your answer to 1 decimal place.

Diana	Nicole	Anna
810
	4 u
- 1 u	+ 1 u
	5 u
		2 p
	- 1 p	+ 1 p
		3 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

25% = ²⁵₁₀₀ = ¹₄
50% = ⁵⁰₁₀₀ = ¹₂
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 810

1 group = 810 ÷ 3 = 270

1 group = 6 boxes
6 boxes = 270

1 box = 270 ÷ 6 = 45

1 group + 1 box = 3 p
270 + 45 = 3 p
3 p = 315

1 p = 315 ÷ 3 = 105

1 p = 1 x 105 = 105

1 group + 1 p = 5 u
270 + 105 = 5 u
5 u = 375

1 u = 375 ÷ 5 = 75

Number of pens that Diana had at first
= 5 boxes + 1 u
= (5 x 45) + 75
= 225 + 75
= 300

Percent that Diana had less in the end than at first
= ^{300 - 270}₃₀₀ x 100%
≈ 10.0%

Answer(s): 10.0%