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# Answer

Original unshaded : now unshaded : “missing” area due to shading : shaded of A : shaded of B : shaded overlapped area

= 23 : 17 : 23-17 : 6/2 : 3 : 3

= 23 : 17 : 6 : 3 : 3 : 3

answer is 3:23

Actually I disagree with all the answers above.

- The question states that “the ratio of the unshaded area to the total area of square A and rectangle B before the overlapping is 17:23″.
- It then asks the “the ratio of the shaded area to the total area of square A and rectangle B before the overlapping“.

Both the above are “before the overlapping”.

So if the unshaded area is 17 parts before the overlapping, then the shaded area must be 6 parts, if there are 23 parts in total.

The argument that the shaded area is 3 parts only works if the first part of the question is reworded to “the ratio of the unshaded area to the total area of square A and rectangle B after the overlapping is 17:23″.

unshaded area : total area of A and B

17 : 23

This means,

unshaded area = 17 units

total area of A and B = 23 units

Therefore,**total area of A and B – unshaded area** will give you **2 times of the shaded area**. *(this is because the shaded area is currently being overlapped by part of A and part of B)*

23 units – 17 units = 6 units

We now only need to find 1 times of shaded area, so 1 times of shaded area = 6/2 = 3 units

Therefore, the ratio of shaded area : total area of A and B is 3 : 23

Ans : 3 : 23.

Note :

23 – 17 = 6 (shaded area of Square A + shaded area of Rectangle B)

6/2 = 3 (overlapping shaded area as shown in the figure)

shaded area : total area of Square A and Rectangle B before the overlapping

3 : 23

Hope this answers your question.

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