Question

Find the successive discount equivalent to $10\%$ and $5\%$.

Answer 1

Step 1: Calculate the final amount after the first discount:

Let the initial amount of the product be $a$.

The first discount is $10\%$.

In $100$, the amount reduced is $10$.

$\therefore$In $1$, the amount reduced is $\frac{10}{100}$.

$\therefore$In $a$, the amount reduced is $\frac{10\times a}{100}=\frac{a}{10}=0.1a$.

Thus, the final amount after the first discount is $\left(a-0.1a\right)=0.9a$.

Step 2: Find the final amount after the second discount:

Now, the initial amount is $0.9a$.

The second discount is $5\%$.

In $100$, the amount reduced is $5$.

$\therefore$In $1$, the amount reduced is $\frac{5}{100}$.

$\therefore$In $0.9a$, the amount reduced is $\frac{5\times 0.9a}{100}=\frac{4.5a}{100}=0.045a$.

Thus, the final amount after the second discount is $\left(0.9a-0.045a\right)=0.855a$.

Hence, the equivalent discount is $\frac{\left(a-0.855a\right)}{a}\times 100\%=14.5\%$.

Therefore, the equivalent discount is $14.5\%$.