In this type I prefer to use number; however there are other ways to solve it -

Let
B = smaller side = 3

A = Larger side = 1 + (2*3) = 7

So the total length = 10.

Put the value of L in the option and we need 7 as an answer. Only option E yields the correct answer.

It is also advisable to start substituting the number L from option C as we will come to know whether we need to proceed towards option A or to option E.
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We can let b= the length of piece B and (2b - 1) = the length of piece A and create the equation:

b + 2b - 1 = L

3b - 1 = L

3b = L + 1

b = (L + 1)/3

So the length of piece A is:

2(L + 1)/3 - 1

(2L + 2)/3 - 1

(2L + 2)/3 - 3/3 = (2L - 1)/3

Answer: E
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This problem can be solved algebraically.

The length of the board = L

It is cut into two pieces, one smaller and another larger.

Lets call the smaller piece S.

Now we know that the length of the longer piece is 2.S + 1.

But the choices are all representing the length of the longer piece in terms of L, the total length of the board.

So we need an equation relating S to L so that 2.S + 1 can be represented in terms of L, the total length, instead of the smaller piece S.

Since Length of the board = Length of the Smaller Piece + Length of the Larger Piece

L = S + 2.S + 1

L = 3.S + 1

3.S + 1 = L

3.S = L - 1

S = (L - 1)/3

Now we substitute the above equation into 2.S + 1, which is the length of the longer piece in terms of the shorter piece.

=> 2.[(L - 1)/3] + 1

= 2.[(L-1) + 3]/3

= (2.L - 2 + 3)/3

= (2.L + 1)/3

Answer is E.
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