Carcass wrote:

A manufacturer is designing two rectangular game boards. The width of the smaller board is one-half the width of the larger board, and the length of the smaller board is one-sixth the length of the larger board. If the smaller board has area N, then what is the difference between the areas of the game boards, in terms of

N ?

A) 3N

B) 9N

C) 11N

D) 12N

E) 18N

For easy calculation at first consider-

Numerical value for wwidth and Length of the larger board and number is divisible

For larger board let us assume-

Length = 12

Width =4

therefore for smaller board

Length = \(\frac{1}{6}\) *12 = 2

Width = \(\frac{1}{2}\)* 4 = 2

(Plz note every square can be rectangle but every rectangle cannot be square and these numbers assumed

still hold valid for the statement)Therefore Area of Smaller Board= N = 4 and Area of Larger Board = 48

The difference between the areas= 48 -4 = 44

Now plug the value of N in the solution

Only option C satisfy

(Remember the we can put different value for Length and Breadth and the answer is remain the same, for easy calculation we take nos. that are divisible by 2 and 6)
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