There was an equal number of desks and benches in the morning. At 2 p.m., some desks were added and some benches were removed, resulting in the number of desks being increased by 20% while the number of benches decreased by 20%. At 10 p.m. the number of desks increased by 50%. If a total of 48 desks were added during the day, how many more desks than benches were there in the end?

At 2 p.m.	Desks	Benches
Before	1 u	1 u
Change	+ 0.2 u	- 0.2 u
After	1.2 u	0.8 u

At 10 p.m.	Desks	Benches
Before	1.2 u	0.8 u
Change	+ 0.6 u	No change
After	1.8 u	0.8 u

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

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

Number of desks increased by desks at 10 p.m.
= 50% x 1.2 u
= ⁵⁰₁₀₀ x 1.2 u
= 0.6 u

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

0.8 u = 48

1 u = 48 ÷ 0.8 = 60

Number of more desks than benches in the end
= 1.8 u - 0.8 u
= 1 u
= 1 x 60
= 60

Answer(s): 60