Question

After successive discounts of 12% and 5% an article was sold for Rs. 209. What was the original price of the article?

Answer 1

Hint: Let the list price of the article be Rs. x. When you subtract 12% of x from x you get the price after the first discount. Then again subtract 5% of the price after first discount from the price after first discount to get the final selling price and equate it with Rs. 209. Solve the equation to get the original price x.

Complete step-by-step answer:
Let us start the solution to the above question by letting the list price, i.e., the original price be Rs. x. It is given that the discount given is 12% of the list price was given.
$\text{discounted amount}=12\%\text{ of list price}=12\%\text{ of x}$
$\Rightarrow \text{discounted amount}=\dfrac{12}{100}\times x.$
Now we know that if we subtract the discount amount from the list price it will give the price after the first discount.
$\therefore \text{Selling price after first discount}=\text{list price}-\text{discount amount}=x-\dfrac{12}{100}x=\dfrac{22}{25}x$
Now it is given that a successive discount of 5% is also given.
$\text{Selling price}=\text{first discounted price}-\dfrac{5}{100}\times \left( \text{first discounted price} \right)$
$\Rightarrow \text{Selling price}=\dfrac{22}{25}x-\dfrac{5}{100}\times \dfrac{22}{25}x$
$\Rightarrow \text{Selling price}=\dfrac{22}{25}x\left( \dfrac{95}{100} \right)$
Also, is given that the final selling price is Rs. 209. So, substituting this in our equation, we get
$209=\dfrac{22}{25}x\left( \dfrac{19}{20} \right)$
$\Rightarrow \dfrac{209\times 25\times 20}{19\times 22}=x$
$\Rightarrow 250=x$
Therefore, we can conclude that the original price of the article is Rs. 250.

Note:Remember that successive discounts of 12% and 5% are not equal to 17% of the total discount. In the case of successive discounts first the 12% is given on the list price and the extra 5% is given on the price we get on the first discounted price while direct 17% is a total of 17% on the list price.