Peter bought an item from a manufacturer for $C with the intention of

Question

Peter bought an item from a manufacturer for $C with the intention of selling the item for $S in a nearby market. However, he decided to offer a discount of 20% on $S and he sold the item at this discounted price for a profit of 10%. If $S is 65% greater than the manufacturer's cost of the item, then what is the profit percentage earned by the manufacturer?

A)10.0%

B)12.8%

C)15.0%

D)16.6%

E)20.0%

(A) 10.0%
(B) 12.8%
(C) 15.0%
(D) 16.6%
(E) 20.0%

CrackverbalGMAT · Answer

For the manufacturer, C is the selling price.

For Peter, C is the Cost price and S is the Marked Price

On this Marked Price he gives a discount of 20%. Therefore the SP = 80% of MP = 0.8S ... (!)

Now he makes a 10% profit on C, therefore SP = 1.1C ... (2)

Equating 1 and 2, we get 1.1C = 0.8S or C =  \frac{8}{11}S  (This is the manufacturers SP)

We are also given that S is 65% more than the manufacturers CP.

Let the manufacturers CP = M

Then S = 1.65M

or M =  \frac{S}{1.65} = \frac{100}{165}S = \frac{20}{33}S

Profit % =  \frac{SP - CP}{CP} * 100 = \frac{\frac{8}{11} - \frac{20}{33}}{\frac{20}{33}} * 100= \frac{\frac{24 - 20}{33}}{\frac{20}{33}} * 100 = \frac{4}{20} * 100 = 20 %

Option E

Arun Kumar

imeanup · Answer

C*\frac{110}{100}=\frac{80}{100}*S

\frac{C}{S}=\frac{8}{11}

or,  \frac{C}{S}=\frac{8}{11}*\frac{3}{3}=\frac{24}{33}

Also, given that;
 S=\frac{165}{100}*C

\frac{S}{C} = \frac{33}{20}

\frac{C}{S}=\frac{20}{33}

Profit %  = \frac{24-20}{20} *100= \frac{4}{20}*100=20  %

Ans E

FazliddinKD · Answer

Let's assume:
Price = 100$
Intended price = 100$*x
Discounted price = 100$*x - 20% = Sale price 
Sale price = 110$ (110$/100$=10%)

Intended price:
100$*x - (100$*x - 100$*x*20% = 110$
100$*x - 100$*x + 80$*x = 110$
80$*x=110$
X=1.375 or 37.5% profit
Intended price = 1.375*100$ = 137.5$

Cost of manufacturer:
Cost of manufacturer 137.5$/Y=1.65%
Y = 83.33$

Profit of manufacturer: 
100$/83.3$=1.20%

Profit percentage earned by the manufacturer – 20%

loki14 · Answer

1.Let the price for manufacturer be 'M'

2.manufacturer sold it to peter for 'C'

3.Profit to manufacturer is =  *100 --> EQ:1

4.Peter wanted to sell that for S but at the end gave a discount of 20%

5.So Peter's final selling price is '0.8S'

6.Which gives 10% profit to Peter i.e. 1.1C
So 1.1C=0.8S --> S=c*(1.1/0.8)
--> Given S= 1.65M (65% more than M)
 c*(1.1/0.8)= 1.65M
 C = 1.65M* (0.8/1.1)
Substituting this in EQ:1 gives profit percentage as 20%

PrateekShawarma · Answer

CP for Peter= $c
SP for peter= $s
but sold at discount of 20% = s(1-20/100) = $0.80s
Profit he made =10% --> 0.80s=c(1+10/100) => 0.80s =1.1c ---- (1)

Let CP for Manufacturer be X
S=X(1+65/100) = 1.65X (Given 65% greater)

Profit percentage =   / c = (  / (0.80/1.1) ) * 100

Solving it
165*4/33 =20%

Peter bought an item from a manufacturer for $C with the intention of

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