Question

A merchant changed his trade discount from 25% to 15%. This would increase selling price by:
(a) $3\dfrac{1}{3}\%$
(b) $6\dfrac{1}{6}\%$
(c) $13\dfrac{1}{3}\%$
(d) $6\dfrac{1}{3}\%$

Answer 1

Hint: Let the list price of the item be Rs. x. Find the discounts in each case when 15% discount is given and when 25% discount is given. Find the difference between the discounts to get the difference in the two cases. Also, find the selling price when the 25% discount was given by subtracting the discount in case of 25% from x. Finally, divide the difference we got between the discounts by this SP and multiply by 100 to get the answer.

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 initial discount given is 25% of the list price was given.
$\text{discounted amount}=25\%\text{ of list price}=25\%\text{ of x}$
$\Rightarrow \text{discounted amount}=\dfrac{25}{100}\times x.$
Now it is given that the discount is decreased to 15%. In this case the discount given is:
$\text{discounted amount}=15\%\text{ of list price}=15\%\text{ of x}$
$\Rightarrow \text{discounted amount}=\dfrac{15}{100}\times x.$
Now we know that if we subtract the discount amount from the list price we get the selling price. So, we will find the selling price when a 25% discount was given.
$\therefore \text{Selling price after first discount}=\text{list price}-\text{discount amount}=x-\dfrac{25}{100}x=\dfrac{75}{100}x$
Now if we subtract the discount in case of 15% from the discount in case of 25%, we get the difference in selling price in both the cases, which is actually the increase in the price when the discount is decreased.
$\text{Selling Price increase}=\dfrac{25}{100}x-\dfrac{15}{100}x=\dfrac{10}{100}x$
Now, for finding the percentage change, we will divide the increase in selling price we got by the SP in case of 25% and multiply by 100.
$\text{Percentage increase in price}=\dfrac{\dfrac{10}{100}x}{\dfrac{75}{100}x}\times 100=\dfrac{10}{75}\times 100=\dfrac{40}{3}\%$
Now we will convert it to mixed fraction. We know that the number smaller than 40 and divisible by 3 is 39, which when divided by 3 gives quotient 13.
$\text{Percentage increase in price}=\dfrac{40}{3}\%=13\dfrac{1}{3}\%$
Hence, the answer to the above question is option (c).

Note: Remember that you need to find the increase with respect to the initial selling price and not with respect to the list price. Also, for finding the increase in price you can find the two selling price, i.e., in case of 25% discount and in case of 15% discount and get the difference, but that would be lengthier as compared to finding the difference between the discounts and we can use this because they are discounted price with respect to the same list price.