Question

Successive discount of \[10\% \] , \[12\% \] and \[15\% \] amount to a single discount of:
(A) \[32.68\% \]
(B) \[35.28\% \]
(C) \[36.68\% \]
(D) None of these

Answer 1

Hint: According to the question, firstly we will assume any number on which we can three successive discounts that is \[10\% \] , \[12\% \] and \[15\% \] .So, here we will take a number that is 100 and we will calculate all the three discount values differently by using the formula that is \[\left( {n - discount\,\% \,n} \right)\] here n is the number which is assumed that is 100 and the value we get after calculating that will be our next number which is to be used to calculate discount. Hence, we get a required answer.

Formula used:
 Here, we use the formula for the calculation of discount is \[\left( {n - discount\,\% \,n} \right)\]

Complete step-by-step answer:
Let us assume the number to be 100.
Firstly, we will calculate a discount on \[10\% \] by using the formula that is \[\left( {n - discount\,\%\, n} \right)\] and here n is assumed to be 100.
On substituting the given values we get,
\[ \Rightarrow 100 - \left( {10\% \times 100} \right)\]
Here, we will write \[10\% \] as \[\dfrac{{10}}{{100}}\] we get,
\[ \Rightarrow 100 - \left( {\dfrac{{10}}{{100}} \times 100} \right)\]
After simplifying we get,
\[ \Rightarrow 90\]
Secondly, we will calculate a discount on \[12\% \] by using the formula that is \[\left( {n - discount\,\%\, n} \right)\] and here n is calculated to be 90.
On substituting the given values we get,
\[ \Rightarrow 90 - \left( {12\% \times 100} \right)\]
Here, we will write \[12\% \] as \[\dfrac{{12}}{{100}}\] we get,
\[ \Rightarrow 90 - \left( {\dfrac{{12}}{{100}} \times 90} \right)\]
After simplifying we get,
\[ \Rightarrow 79.2\]
At last, we will calculate a discount on \[15\% \] by using the formula that is \[\left( {n - discount\,\% \,n} \right)\] and here n is assumed to be \[79.2\] .
On substituting the given values we get,
\[ \Rightarrow 79.2 - \left( {15\% \times 79.2} \right)\]
Here, we will write \[15\% \] as \[\dfrac{{15}}{{100}}\] we get,
\[ \Rightarrow 79.2 - \left( {\dfrac{{15}}{{100}} \times 79.2} \right)\]
After simplifying we get,
\[ \Rightarrow 67.32\]
Now, we will calculate that how much of 100 is equal to \[67.32\] and we will use the above formula \[\left( {n - discount \,\%\, n} \right)\] to calculate the \[discount\% \]
So, after substituting the values we get,
$\Rightarrow$ \[100 - \left( {\dfrac{{discount}}{{100}} \times 100} \right) = 67.32\]
Canalling 100 on numerator and denominator in left side we get,
$\Rightarrow$ \[100 - 67.32 = discount\]
After simplifying we get,
$\Rightarrow$ \[discount = 32.68\]
Hence, the correct option is (A) \[32.68\% \]

Note: To solve these types of questions you can also verify the result by using a simplifying and basic calculation method of percentage. Just according to the given question, put the values of \[10\% \] , \[12\% \] and \[15\% \] of 100 respectively. Therefore, we get \[\left( {\dfrac{{90}}{{100}} \times \dfrac{{88}}{{100}} \times \dfrac{{85}}{{100}}} \right)\% = 32.68\% \]