**CONCEPT: **The question tests on the abilities to frame and solve algebraic equations.

**SOLUTIONS:**

Let D = the number of **Democrat senators** **last year**

Then D + 20 = the number of **Republican senators** **last year,**

__As the total members remain same;__

The number of **Democrat senators this year**

=D+*2 (These are the 2 Republican Members who turned Democratic)*

Thus, the number of **Republican senators this year**

** ****=** Number of **Republican senators** **last year + 2**

** **(D + 20) - 2

= D + 18 (The two members have been moved from Republic to Democrat)

**Total Senate Members this year**

= Republic + Democrat

= (D+18) + (D+2) = 2D+20

**Thus according to question,**

(D + 18) [Republic Members this year]

= (2/3) (2D+20) [**Total Senators this year] **3(D + 18) = 2(2D + 20)

3D + 54 = 4D + 40

14 = D

Therefore, the total number of senators this year is 2(14) + 20 = 48.

**(**

**Option E)**