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# A couple who own an appliance store discover that if they advertise a

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Math Expert
Joined: 02 Sep 2009
Posts: 60772
A couple who own an appliance store discover that if they advertise a  [#permalink]

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02 Feb 2016, 02:00
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Difficulty:

5% (low)

Question Stats:

97% (01:26) correct 3% (00:27) wrong based on 48 sessions

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A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent?

A. 2%
B. 4%
C. 5%
D. 8%
E. 12%

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Re: A couple who own an appliance store discover that if they advertise a  [#permalink]

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02 Feb 2016, 02:17
Let List price of an item = 100
Discount on each item = 10%
Discounted price of an item = .9*100 = 90
If they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%
Originally if 10 items were sold in a month , with the new discount 12 items will be sold
Original revenue = No of items* Price of an item = 10 * 100 = 1000
New revenue = 12 * 90 = 1080
Increase in gross income = 1080 - 1000 = 80
% increase in gross revenue = 80/1000 * 100% = 8%
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02 Feb 2016, 11:44
Sales revenue = units sold * selling price = q*p
Units sold increased by 20% = 1.2q
Selling price decreased by 10% = (1-0.1)p = 0.9p
New sales revenue = 1.2q*0.9p = 1.08qp

Percent increase in sales revenue = $$\frac{(NewSalesRevenue - Old Sales Revenue)}{Old Sales Revenue}= \frac{1.08qp-q*p}{q*p}$$ = 0.08 = 8%

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Dave de Koos
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Re: A couple who own an appliance store discover that if they advertise a  [#permalink]

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03 Feb 2016, 21:43
Bunuel wrote:
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent?

A. 2%
B. 4%
C. 5%
D. 8%
E. 12%

Assume there are hundred items with price \$100 each
Initial sales = 100*100

Sales after discount = 90*120

Percentage increase =$$\frac{{(10800 - 10000)}}{10000}$$ *100 = 8%
Option D
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Re: A couple who own an appliance store discover that if they advertise a  [#permalink]

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04 Feb 2016, 02:31
Bunuel wrote:
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent?

A. 2%
B. 4%
C. 5%
D. 8%
E. 12%

Assume the price = 100x
Total items sold = 100y

Gross income from sales without giving away discounts = 100x*100y = 10000xy
Gross income from sales after giving discounts = 90x*120y = 10800xy

Increase in sales = $$\frac{{new sales - old sales}}{{old sales}}$$

Increase in sales % = $$\frac{{(10800xy - 10000xy)}}{10000xy}$$ * 100 = 800/100 = 8% (Option D)
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Re: A couple who own an appliance store discover that if they advertise a  [#permalink]

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04 Feb 2016, 04:06
Bunuel wrote:
A couple who own an appliance store discover that if they advertise a sales discount of 10% on every item in the store, at the end of one month the number of total items sold increases 20%. Their gross income from sales for one month increases by what percent?

A. 2%
B. 4%
C. 5%
D. 8%
E. 12%

Revenue = Price * Quantity sold

New Revenue = (9/10) * Price * (6/5) * Quantity sold = (54/50) * Original Revenue = (108/100) * Original Revenue

This is an increase of 8%.

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Re: A couple who own an appliance store discover that if they advertise a   [#permalink] 04 Feb 2016, 04:06
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