Question

Two successive discounts of 10% and 5% are equal to a single discount of
A. $15\%$
B. \[7\dfrac{1}{2}\% \]
C. $12\%$
D. \[14\dfrac{1}{2}\% \]

Answer 1

Hint: In this problem, we will proceed to the solution by knowing the concept that if \[x\% \] discount is given on \[y\] amount then the discount amount will be expressed as \[\dfrac{{x \times y}}{{100}}\]. So, use this concept to reach the solution to the given problem.

Complete step-by-step solution:
Let total amount = Rs 100
After 10% discount the amount will be = 100 – 10% of 100
                                                                      \[
   = 100 - \dfrac{{10 \times 100}}{{100}} \\
   = 100 - 10 \\
   = 90 \\
\]
So, after the first discount of $10\%$, the remaining amount is $Rs.90$
Now, amount after $5\%$ of discount to the remaining amount = $90 – 5\% of 90$
                                                                                                             \[
   = 90 - \dfrac{{5 \times 90}}{{100}} \\
   = 90 - 4.5 \\
   = 85.5 \\
\]
So, the amount after two successive discounts of $10\%$ and $5\%$ is Rs.85.5
The total discount amount of the two successive discounts = $100 – 85.5 = Rs.14.5$
Thus, the single discount percent = \[\dfrac{{14.5}}{{100}} \times 100 = 14.5\% \]
Hence, the correct option is A. $15\%$

Note: This problem can also be solved by considering the initial amount of the money as some unknown variable and the final discount percent would have been found out in terms of the same variable. In order to solve such problems, never try to add the discount. Just separately find out the discount and finally the discount percent.