Question

On a chessboard percentage of black colored squares is:
A. 50%
B. 60%
C. 15%
D. 75%

Answer 1

Hint: Here, we will first define how many squares are there in a chessboard and how they are arranged. There are a total of 64 squares out of which there are equal numbers of black and white squares. Then we will assume the number of black squares to be ‘x’ which will make the number of white squares equal to x as well. Then we will keep the sum of the number of black and white boxes equal to 64 and obtain the value of x. Thus, we will then use the value of x to find the percentage of black squares. Hence, we will have an answer.

Complete step-by-step solution
Here, we have to find the percentage of black squares on a chessboard. For that, we will first have to know how many squares are there on a chessboard.
Now, we know that in a chessboard there are equal numbers of black and white squares arranged alternately. We also know that there are a total of 64 squares.
Hence, if we assume the number of black squares to be ‘x’, the number of white squares will also be ‘x’. Hence, we can say that:
\[x+x=64\]
Solving this, we get the value of x as:
$\begin{align}
  & 2x=64 \\
 & \Rightarrow x=\dfrac{64}{2} \\
 & \Rightarrow x=32 \\
\end{align}$
Thus, there are a total of 32 black squares on a chess board.
Thus, we get the percentage of black squares as:
$\begin{align}
  & \dfrac{32}{64}\times 100 \\
 & \Rightarrow \dfrac{1}{2}\times 100 \\
 & \therefore 50\% \\
\end{align}$
Thus, the percentage of black squares on a chess board is 50%. Hence, option (A) is the correct option.

Note: We already know that in a chessboard, half of the squares are black and half are white. Thus, we can straightaway mark the answer correct as 50% without any of the above-shown calculations in objective or competitive type questions. Once it comes as subjective, the whole calculation as shown should be done to obtain complete marks.