A man sold 20 articles for $60 and gained 20%. How many

Please help me here... I get the answer 50. OA is definately correct or am i making some mistake please correct me where i am wrong.

20 articles for $60 means selling price = 3
20% profit is made so Cost Price = 2.5

Man has to incur a loss of 20% means he has to make a total loss of 20% and he sells X units in 90$

60+90 = 0.8 * (C.P. for 20+X units)
C.P. for 20+X units = 75*5/2

But the cost price for one unit is 2.5 so, 75*5/(2*2.5) = 75 = Number of units sold.
20 units were sold for 60$ so 55 units sold for 90$

Can someone explain where am i wrong here???

The loss of 20% in the second part of the question doesn't include the initial 20 items. It's just on the X number of items he needs to sell for a total of $90.
So 90=0.8(C.P of x units) So C.P of x units=$112.5 and since we know that C.P of each item is $2.5.
No of items he need to sell or x= 112.5/2.5 =45

I think my approach was somewhat different.

60 = 6/5x , so x = 50

That's total cost

So then 50/20 = 5/2 that's cost per article

Now then, 90/x = 5/2 (4/5)

x = # of articles

X = 45

A is the best answer

Cheers!
J

c=cost per item
q=quantity of items

20%gain
60/20c=1.2
c=3/1.2

20%loss
90/(3/1.2)*q=.8
90=(2.4/1.2)q
q=45

Cost price of 20 articles \(= 100 * \frac{60}{120} = 50\)

Cost price per article \(= \frac{50}{20}\)

To make a 20% loss, selling price per article \(= 80 * \frac{50}{20} * \frac{1}{100} = 2\)

Number of articles for $90 loss \(= \frac{90}{2} = 45\)

Answer = A

CP of 20 items = 50
CP of 1 item = 2.5

To sell one item at 20% loss , SP of 1 item = 2.5*8/100 = 2

We need to sell 45 items to have a SP of $90.

SP = 45

this is some weird question.
nevertheless, I got to A.

USE Percentage method:-

man sells 20 articles for 60 so per article selling price is 3 dollars-

gain is 20 above the regular price- which is 100+20=120 percent for 3 dollars

so

if for 3 dollars ---->120 percent

for x dollars -------> 80 percent (20% loss =regular price - 20%=100-20=80 %)
we will get x=2

GIVEN selling price to get 20% loss is 90 dollars
now 90/2=45 (A)

I do not really understand this question from an English standpoint, to be honest.

I went through the solutions and I get the math, but the formulation really confused me.

Lets say each article costed him x and he initially sold them for 1.2x (Because he sold for 20% profit).

so 20 * 1.2x = 60 => x = 2.5.

Cost price for article = 2.5. If it were to 20 % loss, selling price should be 80% of cost price, Selling price = 0.8 * 2.5 = 2

if he sold each item for $2, he must sell 90/2 items , that are 45 items. Hence answer is A

ok So
here are my two cents

Profit % is given so

20= ((SP-CP)/CP)* 100

20= (( 60*20 - x)/x) *100

Solving for x we get x=1000 i.e cost of 20 items is 1000

Now he is selling some articles at 90 $ and the loss % is given as 20

CP is fixed at 1000

Loss% =( (CP-SP)/CP)*100

20 = ((1000- 90 *N)/1000)*100

solving for N i get N = 80/9 and i am nowhere near any of the options so what did i do wrong here

Please explain

Sp of an article = 3

cp = 3/120 * 100 = 5/2

we want to incur loss of 20% . sp must be 80 of 5/2.

(5/2 )* 80/100 = 2.

total sp : 90

selling price : 2

90/2 = 45.

The correct answer must be A.

A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $90 to incur a loss 20%?

Profit/Loss is an application of Percentage increase/decrease concept.

Total SP = $60 and Profit % = 20 %

That means,when total CP is increased by 20 % , we will get total SP.

120% of Total CP = Total SP

120% of Total CP = 60$

\(\frac{120}{100}\) * Total CP = 60

\(\frac{6}{5}\) * Total CP = 60

Total CP = 50 $

Total Cp of 20 article = 50 $
Cp of 1 article = 50/20 = 2.5 $.

Then he sells for $90 to incur a loss 20%

Total SP = $90 and Loss % = 20%

That means, when the total CP is decreased by 20 % we will get total SP.

80% of Total CP = 90 $
\(\frac{4}{5} \)* Total CP = 90

Total CP = \(90*\frac{5}{4}\\
\)
CP of 1 article = 2.5$

No of articles he sold = 90*\(\frac{5}{4}/\)2.5= 90* 5/(4*2.5) = 90/2 = 45 articles

Option A is the answer.

Thanks,
Clifin J Francis,
GMAT SME

If selling price is 60 and there is a 20% profit, it means cost price is 50.
Alternatively,

Cost price * (6/5) = 60
Cost price = 50 (for 20 articles)
Cost price per article is $2.5

To incur a loss of 20% with selling price of 90,
cost price * (4/5) = 90
Cost price = 112.5

There must be an odd number of articles, more than 40 to give a cost price of more than 100.
Only option (A) fits.
Answer (A)

Had other options been relevant too, we would have calculated 112.5/2.5 = 45

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