Percentage passing sieve no 200 = 50% , Liquid limit = 20% and Plastic limit = 5%, the classification of this soil according to the AASHTO Method is:a.Noneb.A-5c.A-6d.A-4

The AASHTO Soil Classification system classifies soils into seven primary groups, named A-1 through A-7, based on their relative expected quality for road embankments, sub-grades, sub-bases, and bases. Some of the groups are then divided into subgroups, such as A-1-a and A-1-b. Furthermore, a Group Index may be calculated to quantify a soil's expected performance within a group.

To classify the soil according to the AASHTO Method, we need to consider the percentage passing sieve no 200, the liquid limit, and the plastic limit.

Given:

• Percentage passing sieve no 200 = 50%
• Liquid limit = 20%
• Plastic limit = 5%

According to the AASHTO classification system:

• A-4 soils have 35-75% passing the No. 200 sieve.
• A-5 soils have more than 51% passing the No. 200 sieve.
• A-6 soils have 50-85% passing the No. 200 sieve and a liquid limit of 41-60% if estimated plasticity index is 10-30, or a liquid limit of 31-40% if estimated plasticity index is 31 or more.
• A-7 soils have more than 85% passing the No. 200 sieve and a liquid limit of more than 50%.

Given the provided values, the soil does not fit into the A-5, A-6, or A-7 categories due to the liquid limit and plastic limit values. However, it does fit into the A-4 category as it has 50% passing the No. 200 sieve, which falls within the 35-75% range for A-4 soils.

Therefore, the classification of this soil according to the AASHTO Method is A-4 (option d).