An unknown compound displays singlets at δ 2.1 ppm and 2.56 ppm in the ratio of 3: 2. what is the structure of the compound?

1) As can be seen from any 1H NMR chemical shift ppm tables, hydrogens which have δ values from 2ppm to 2.3ppm are hydrogens from carbon which is bonded to a carbonyl group. From this, we can conclude that our hydrogens belong to the type, but from 2 different alkyl groups because of 2 different signals.

2) So, one alkyl group is CH3 and second one can be CH or CH2.

3) If we know that ratio between two types of hydrogens is 3:2, it can be concluded that second alkyl group is CH2. 

4) Finally, we don't have any other signals and it indicates that part of the compound which continues on CH2 is exactly the same as the first part.

The ratio remains the same, 3:2 ie 6:4