Question

Jane invites 19 of her friends to her birthday party. The cake shown in the given image has to be divided among all of them in equal cubical pieces such that the height of each piece is equal to the height of the whole cake. However, 5 more friends show up at the party. By how much should the area of each piece of cake reduce so that everyone gets a piece of cake?

• A. 40 sq in
• B. 25 sq in
• C. 20 sq in
• D. 5 sq in

Answer 1

The correct option is C 20 sq in

Area of the cake = length $\times$ width
$=50\times 40$
$=2000\text{sq in}$
If we divide the cake into 20 equal pieces of the same height (Jane + 19 of her friends), we get:
Area of each piece of cake $=\frac{2000}{20}=100\text{sq in}$
If we divide the cake into 25 equal pieces, we get:
Area of each piece of cake $=\frac{2000}{25}=80\text{sq in}$
The area of each piece needs to be reduced by 100 - 80 = 20 sq in so that everyone gets a piece of cake.