A rectangular park was redesigned and as a result of which its length increased by 50%. If the area of the park, remained unchanged, then by how much percentage had the breadth been reduced?

Let's assume the length and breadth of the rectangular park initially are 30a and 30b respectively.

Area =$$length \times breadth$$ = $$30a \times 30b$$    Eq.(i)

= 900ab

A rectangular park was redesigned and as a result of which its length increased by 50%.

Length after redesigned = 30a of (100+50)% = 30a of 150% = 45a    Eq.(ii)

If the area of the park remained unchanged.

Area after redesigned = 900ab (same as earlier.)

Let's assume the breadth after redesigned is 'y'.    Eq.(iii)

From Eq.(i), Eq.(ii) and Eq.(iii).

$$30a \times 30b = 45a \times y$$

900ab = 45ay

y = 20b

the percentage reduction in breadth = $$\frac{\left(30b-20b\right)}{30b}\times\ 100$$

= $$\frac{10b}{30b}\times\ 100$$

= 33.33%