Question

A handbag is sold at 2,150 after a 14% discount.
(a) Find the marked price of the handbag.
(b) Ifthe handbag was sold at a 10% discount and then at a further 4% discount
on the discounted price, would the selling price be the same?​

Answer 1

$\tt{Solution \: \: (a) :}$

Selling price of a handbag=2150

The percentage of discount that was added to it=14%

Which means :-

Let the marked price of the handbag be b .

Then :-

$= b - \frac{14}{100} \times b = 2150$

$= b - \frac{14 \times b}{100} = 2150$

$= \frac{b}{1} - \frac{14b}{100} = 2150$

$= \frac{100b}{100} - \frac{14b}{100} = 2150$

$= \frac{86b}{100} = 2150$

$= 86b = 2150 \times 100$

$= 86b = 215000$

$= b = \frac{215000}{86}$

$= b \bold{= 2500}$

Thus, the marked price of this handbag=2500

Now let us check whether or not we have found out the correct marked price by checking if or not a 14% discount will make the selling price as 2150:-

$= 2500 - \frac{14}{100} \times 2500 = 2150$

$= 2500 - \frac{14 \times 2500}{100} = 2150$

$= 2500 - \frac{35000}{100} = 2150$

$= 2500 - 350 = 2150$

$= 2150 = 2150$

As the marked price of the handbag after a discount of 14% results in the selling price 2150, we can conclude that we have found out the correct marked price.

Therefore, the marked price of the handbag was=2500

$\tt{Solution \: \: (b) :}$

If there were two discounts totally applied,then they would be called as successive discounts.

Thus, the successive discounts applied on the handbags are:-

$10\% \: \: and \: \: 14\%$

The final discount on the bags :-

$= 10 + 4 - \frac{10 \times 4}{100}$

$= 14 - \frac{40}{100}$

$= 14 - 0.4$

$=\bold{ 13.6 \: \: \%}$

Thus, the final discount applied will be=13.6%

Which means,the price of he handbag after a 13.6% discount:-

$= 2500 - \frac{136}{10} \times \frac{1}{100} \times 2500$

$= 2500 - \frac{136}{1000} \times 2500$

$= 2500 - \frac{136 \times 2500}{1000}$

$= 2500 - \frac{340000}{1000}$

$= 2500 - 340$

$= \bold{2160}$

Thus,the price of the handbag after successive discounts of 10% and 4% will be=2160

No, the price wont be the same if successive discounts of 10% and 4% are applied instead of a total discount of 14%.

Therefore, the selling price wont be the same if successive discounts of 10% and 4% are applied on the discounted price.The selling price when 10% and 4% discounts are applied will be=2160