Aruna cut a cake into two halves and cut one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake?

Options

A. 120 grams
B. 140 grams
C. 240 grams
D. 280 grams

Explanation

To solve the problem step by step, let's break it down:

1. **Understanding the Problem**: Aruna cuts a cake into two halves. This means she has two equal parts of the cake. One half she keeps whole, and the other half she cuts into smaller pieces.

2. **Identifying the Total Pieces**: According to the problem, Aruna has a total of 7 pieces of cake. This includes:
- 1 whole half of the cake
- 6 smaller pieces from the other half

3. **Weight of Each Small Piece**: Each of the smaller pieces weighs 20 grams. Since there are 6 smaller pieces, we can calculate the total weight of these pieces:
\[ \text{Weight of 6 pieces} = 6 \times 20 \text{ grams} = 120 \text{ grams} \]

4. **Weight of Half the Cake**: Since the 6 smaller pieces come from one half of the cake, the weight of this half is 120 grams.

5. **Finding the Original Weight of the Cake**: Since the original cake was cut into two equal halves, the other half (which is whole) must also weigh the same as the half that was cut into pieces. Therefore, the weight of the original cake is:
\[ \text{Weight of original cake} = \text{Weight of half cake} + \text{Weight of other half cake} = 120 \text{ grams} + 120 \text{ grams} = 240 \text{ grams} \]

Thus, the original weight of the cake was **240 grams**.