She buys cakes in groups of 2 and muffins in groups of 3. Therefore, in order to have the same amount of cakes and muffins in the end, the ratio of the number of groups of cakes to the number of groups of muffins she bought must be 3 : 2.

Since we know she spent $55 more on cakes than muffins,

27 units – 16 units = 55
11 units = 55
1 unit = 5

3 units = 15 (No. of groups of 2 cakes)
Total no. of cakes = 15 × 2
= 30

Since no. of cakes and muffins bought is the same,

Total no. of cakes and muffins = 30 × 2
= 60

Dear Adwin

Many thanks for your prompt answer.

May i clarify

the ratio of the number of groups of cakes to the number of groups of muffins she bought must be 3 : 2

So that 2 cakes x 3 units = 6

3 muffins x 2 units =6

in order to derive the same number of units purchase?

Yes. That is correct.

Adwin, Many thanks.  Sincerely appreciate.