Question

If \[15\% \]of \[45\% \]of a number is \[105.3\]. What is \[24\% \] of that number?
A.\[385.5\]
B.\[374.4\]
C.\[390\]
D.\[375\]

Answer 1

Hint: In order to determine the percent of a given number, we can use the following formula:
\[p(\% ) = \dfrac{x}{y} \times 100\] . In the given question, we have to choose the \[24\% \] percentage of the missing number as our answer. We can form an equation with the given data and assume the unknown variable as \[x\]to solve and find the number. We will simply have to do \[24\% \] after finding out \[x\].

Complete step-by-step answer:
Calculating percentages is a simple mathematical procedure. If you need to find a ratio or a component of a quantity as a proportion of another quantity, you can express it as a percentage.
To find out the percent of a given number, we can use the following formula:
\[p(\% ) = \dfrac{x}{y} \times 100\]
Where:
\[x\]= Number for which percentage is to be found out;
\[y\]= Total or whole number of given data
We are given that \[15\% \] of \[45\% \] of a number is \[105.3\]. Let the number be \[x\]. We can form the equation as follows:
\[x \times \dfrac{{15}}{{100}} \times \dfrac{{45}}{{100}} = 105.3\]
Solving the multiplication, we get,
\[x \times \dfrac{{675}}{{10000}} = 105.3\]
Cross multiplying on the other side of equation, we get,
\[x = 105.3 \times \dfrac{{10000}}{{675}}\]
\[x = 1560\]
Hence, the missing number is \[1560\].
Now \[24\% \] of \[1560\] will be:
\[1560 \times \dfrac{{24}}{{100}} = 374.4\]
Hence Option (B) \[374.4\] is the correct answer.
So, the correct answer is “Option B”.

Note: In the given case, we have formed a simultaneous linear equation to find out the answer. A simultaneous equation is one in which two or more quantities are connected by means of two or more equations. It consists of a small number of independent equations.
Simultaneous equations are also known as systems of equations because they are made up of a finite number of equations for which a general solution is found. They are generally solved by substitution or elimination method.