16:25 is actually the ratio of the areas.
The area of the rectangle is 32*24=768 sq cm.
If we increase the length by the ratio 5:4 we get 32*5/4=40 cm.
And the width=24*5/4=30 cm. The area of the enlarged rectangle is 40*30=1200 sq cm.
The ratio of the areas is 768/1200=16*48/(25*48)=16/25=16:25.