Natalie, Usha and Cathy had 1350 pens. Usha won some of the pens from Natalie and as a result, Usha's pens increased by 50%. Cathy then won some pens from Usha and Cathy's pens increased by 40%. Finally, Cathy lost some of her pens to Natalie and Natalie's pens increased by 20%. In the end, they realised that they each had an equal number of pens. How many percent less did Natalie have in the end than what she had at first? Correct your answer to 1 decimal place.

Natalie	Usha	Cathy
1350
	2 u
- 1 u	+ 1 u
	3 u
		5 p
	- 2 p	+ 2 p
		7 p
5 boxes
+ 1 box		- 1 box
6 boxes
1 group	1 group	1 group

50% = ⁵⁰₁₀₀ = ¹₂
40% = ⁴⁰₁₀₀ = ²₅
20% = ²⁰₁₀₀ = ¹₅

Working backwards.

3 groups = 1350

1 group = 1350 ÷ 3 = 450

1 group = 6 boxes
6 boxes = 450

1 box = 450 ÷ 6 = 75

1 group + 1 box = 7 p
450 + 75 = 7 p
7 p = 525

1 p = 525 ÷ 7 = 75

2 p = 2 x 75 = 150

1 group + 2 p = 3 u
450 + 150 = 3 u
3 u = 600

1 u = 600 ÷ 3 = 200

Number of pens that Natalie had at first
= 5 boxes + 1 u
= (5 x 75) + 200
= 375 + 200
= 575

Percent that Natalie had less in the end than at first
= ^{575 - 450}₅₇₅ x 100%
≈ 21.7%

Answer(s): 21.7%