There was an equal number of benches and chairs in the morning. At 3 p.m., some benches were added and some chairs were removed, resulting in the number of benches being increased by 20% while the number of chairs decreased by 20%. At 9 p.m. the number of benches increased by 50%. If a total of 36 benches were added during the day, how many more benches than chairs were there in the end?

At 3 p.m.	Benches	Chairs
Before	1 u	1 u
Change	+ 0.2 u	- 0.2 u
After	1.2 u	0.8 u

At 9 p.m.	Benches	Chairs
Before	1.2 u	0.8 u
Change	+ 0.6 u	No change
After	1.8 u	0.8 u

Number of benches added
= 20% x 1 u
= ²⁰₁₀₀ x 1 u
= 0.2 u

Number of chairs removed
= 20% x 1 u 
= ²⁰₁₀₀ x 1 u
= 0.2 u

Number of benches increased by benches at 9 p.m.
= 50% x 1.2 u
= ⁵⁰₁₀₀ x 1.2 u
= 0.6 u

Number of benches added during the day
= 1.8 u - 1 u
= 0.8 u

0.8 u = 36

1 u = 36 ÷ 0.8 = 45

Number of more benches than chairs in the end
= 1.8 u - 0.8 u
= 1 u
= 1 x 45
= 45

Answer(s): 45