Question

Succesive discounts of $10\%$ and $50\%$ are equivalent to a single discount of___

• A. $60\%$
• B. $500\%$
• C. $55\%$
• D. $40\%$

Answer 1

The correct option is C $55\%$

Let the original price of any product is $\$100.$

Given, successive percentage of discounts are $10\%$ and $50\%.$

First discount amount $=\text{10\% of original price}$
$=10\%\text{of}\$100$
$=\frac{10}{100}\times \$100$
$=\frac{10}{10\times 10}\times \$100$
$=\frac{1}{10}\times \$100$
$=\$10$

$\text{Price after first discount = Original price - First discount amount}$
$=\$100-\$10=\$90$

Second discount amount $=\text{50\% of price after first discount}$
$=50\%\text{of}\$90$
$=\frac{50}{100}\times \$90$
$=\frac{50}{50\times 2}\times \$90$
$=\frac{1}{2}\times \$90$
$=\$45$

$\text{Total discount amount = First discount amount + second discount amount}$
$=\$10+\$45$
$=\$55$

$\text{Net discount percentage}=\frac{\text{Total discount amount}}{\text{Original price}}\times 100\%$
$=\frac{55}{100}\times 100\%$
$=55\%$

Hence, succesive discounts of $10\%$ and $50\%$ are equivalent to a single discount of $55\%.$