Question

Two shopkeepers announced the same price of Rs. 20000 for an article. The first one offers two successive discounts of $20%$ and $5%$, while the second one offers two successive discounts of $15%$ and $10%$. What is the difference between the effective values of discounts offered by the two shopkeepers?

Answer 1

Hint: Two shopkeepers offer two different sets of discounts. So, we calculate those two sets of discounts on the total price. We apply the formula of percentage on the price of the article successively to find out the discounted price for both cases. After that we find out the effective discount in both cases from the final price and decide their difference.

Complete step-by-step answer:
We know that if the primary balance be x and discount percentage be m, then the discounted price will be $x\left( 1-\dfrac{m}{100} \right)$ and if the marked piece and selling price be x and y respectively then the effective discount percentage be $\dfrac{x-y}{x}\times 100$.
Two shopkeepers announced the same price of Rs. 20000 for an article.
The first shopkeeper offers two successive discounts of $20%$ and $5%$.
So, for the first discount of $20%$ the discounted price will be Rs. $20000\left( 1-\dfrac{20}{100} \right)$.
The first discounted price is $20000\left( 1-\dfrac{20}{100} \right)=\dfrac{20000\times 80}{100}=200\times 80=16000$.
For the second discount of $5%$ the discounted price will be Rs. $16000\left( 1-\dfrac{5}{100} \right)$.
The first discounted price is $16000\left( 1-\dfrac{5}{100} \right)=\dfrac{16000\times 95}{100}=160\times 95=15200$.
So, the effective discount percentage be $\dfrac{20000-15200}{20000}\times 100=\dfrac{4800}{200}=24$.
Now we determine for the second shopkeeper who offers two successive discounts of $15%$ and $10%$.
So, for the first discount of $15%$ the discounted price will be Rs. $20000\left( 1-\dfrac{15}{100} \right)$.
The first discounted price is $20000\left( 1-\dfrac{15}{100} \right)=\dfrac{20000\times 85}{100}=200\times 85=17000$.
For the second discount of $10%$ the discounted price will be Rs. $17000\left( 1-\dfrac{10}{100} \right)$.
The first discounted price is $17000\left( 1-\dfrac{10}{100} \right)=\dfrac{17000\times 90}{100}=170\times 90=15300$.
So, the effective discount percentage be $\dfrac{20000-15300}{20000}\times 100=\dfrac{4700}{200}=23.5$.
It means the difference between the effective values of discounts offered by the two shopkeepers is $24-23.5=0.5$.

Note: We can also use the formula of effective discount which is more of a direct method. So, if two successive discounts k and l are applied then the effective discount is $\left( k+l-\dfrac{kl}{100} \right)$. So, for the first shopkeeper who gave two successive discounts of 20 and 5, the effective discount is $\left( 20+5-\dfrac{20\times 5}{100} \right)=25-1=24$. For the second shopkeeper who gave two successive discounts of 15 and 10, the effective discount is $\left( 15+10-\dfrac{15\times 10}{100} \right)=25-1.5=23.5$.
The difference between the effective values of discounts offered by the two shopkeepers is $24-23.5=0.5$.
This is another way to solve the problem.