Question

What is the percent decrease in length if $6$ feet is cut from $10$ foot board?
1). $40\% $
2). $60\% $
3). $50\% $
4). None

Answer 1

Hint: First, we need to know about the concepts of the percentage, so that we are able to solve the given problem easily. The percentage is the mathematical concept which is to measure the proportion of the given values in any term of the original value. The percentage is a relative value that indicates the hundredth parts of any quantity.
Formula used: To find the change in percentage we will make use of the formula that $P = \dfrac{{O - N}}{O} \times 100$ where O is the old value from the given and N is the new value.

Complete step-by-step solution:
Since from the given that we need to find the percentage of the decrease in length if $6$ feet are cut from $10$ footboard.
Since the old value is $10$ footboard and to find the new value we need to find its difference and thus we have $10 - 6 = 4$ (by subtraction) which is the new value.
Hence the old value is $10$ footboard and the new value is $4$ footboard.
Thus, substituting the values in the above-given formula, we have $P = \dfrac{{O - N}}{O} \times 100 $
$= \dfrac{{10 - 4}}{{10}} \times 100$
Further solving we have $P = \dfrac{{10 - 4}}{{10}} \times 100 $
$= \dfrac{6}{{10}} \times 100$ (by subtraction operation)
$P = \dfrac{6}{{10}} \times 100 = 6 \times 10$ by division operation
$P = 60\% $ by multiplication operation.
Hence option 2. $60\% $ is correct.

Note: The mathematical operation which we used in the given problem is Addition, subtraction, multiplication, and division.
Since multiplicand refers to the number multiplied. Also, a multiplier refers to the number that multiplies the first number. Have a look at an example; while multiplying $5 \times 7$ the number $5$ is called the multiplicand and the number $7$ is called the multiplier.
The process of the inverse of the multiplication method is called division. Like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. We usually need to memorize the multiplication tables in childhood so it will help to do mathematics.
Also, the other two operations, Addition is the summing of two or more than two numbers, or values, or variables, and in addition, if we sum the two or more numbers a new frame of the number will be found, also in subtraction which is the minus of two or more than two numbers or values example $2 - 3 = - 1$ (larger number signs stays constant)