Question

Two sweaters are originally the same price. Both are discounted 10%. Then one of the sweaters is discounted an additional 10%. By approximately what percent would the price of the cheaper of the two sweaters have to be increased so that the sweaters once again sell for the same price?​

Answer 1

Answer:

Let price of both sweaters = 100

As both are discounted 10%, hence price of sweaters will be:-

100-10\%\ of 100=100-\frac{10}{100} \times100=100-10=90100−10% of100=100−

100

10

×100=100−10=90

But additional 10% discount given to the cheaper sweater, hence the price of cheaper sweater will be:-90-10\%\ of\ 90=90-\frac{10}{100} \times90=90-9=8190−10% of 90=90−

100

10

×90=90−9=81

Now, to find the percent price of the cheaper sweater to be increased so that the sweaters once again sell for the same price:-

Discount amount of cheaper sweater = 100 - 81 = 19

Price of cheaper sweater after additional discount = 81

Percent price to be increased to make the sweaters once again sell for the same price = \frac{19}{81}\times100=\frac{1900}{81} =23.45\%

81

19

×100=

81

1900

=23.45%

Thus, 23.45% price would be increased to make the sweaters once again sell for the same price.