If a man sells x oranges for a dollar, he loses 45 percent. By how muc

Question

If a man sells x oranges for a dollar, he loses 45 percent. By how much percentage should the man reduce his cost to make a profit of 10 percent on selling 2x oranges in a dollar?

A. 25%
B. 50%
C. 75%
D. 150%
E. 300%

PoojanB · Accepted Answer

Given(1):
SP for x oranges = $1
Loss = 45%
Hence, CP for X oranges = 1/(0.55) = 100/55..........(1)

Given(2):
SP for 2x oranges = $1
Profit = 10%
So, CP for 2x oranges = 1/(1.1) = 100/110
Hence, CP for x oranges = 100/(110*2) = 100/220.............(2)

Therefore:
From eq 1 and 2, Reduction in CP =  /  (100/55)]  * 100 
 = 75%

Kritisood · Answer

hey, i have query, for C2. why would we take SP for 2x oranges as $1. if SP of x oranges is 1 then SP for 2x should be 2?

PoojanB · Answer

Hi  @Kritisood 
It is a given condition in the question.

Lets elaborate it more to make things clear.

Initially the question says the man sells x oranges and losses 45%. Which means at this point his SP is 0.45 times of CP.(For x oranges).We call it CP1,THis is one condition.

Now the same man wants to sell 2x oranges in 1 dollar and he wants to gain 10% profit.THis is different condition.
SO while making the equation for this condition we have to consider 2x oranges only. we are calling it CP2.

The main question asked is how much the cost priced should be reduced in order to gain 10% profit.
which nothing but percent decrease from CP1 to CP2.

Hope this make things clear

GMATinsight · Answer

Cost - Loss =$1 on selling x oranges

i.e. Cost - 0.45 Cost = 0.55* Cost = 1
i.e. Cost of x oranges = 100/55 = 20/11
 
 Selling Price of 2x Oranges required = $1
Selling Price of x Oranges required = $1/2
now, with 10% profit, 110% of new cost = 1/2
i.e. New cost of x oranges = (1/2)*(1/1.1) = 5/11

Reduction in cost required =  (20/11)  -  (5/11)  =  15/11

% reduction in cost = Reduction *100 / Previous cost = (15/11)*100 / (20/11) = 75%

Answer: Option C

Kritisood

TarPhi · Answer

PoojanB   GMATinsight   Bunuel

Can you please explain this part?

Given(2):
SP for 2x oranges = $1
Profit = 10%
 So, CP for 2x oranges = 1/(1.1) = 100/110 
Hence, CP for x oranges = 100/(110*2) = 100/220.............(2)

GMATinsight · Answer

TarPhi The question states that how much percentage should the man reduce his cost to make a profit of 10 percent on selling 2x oranges in a dollar? Profit of 10% of cost = Selling Price i.e. Cost + 10% of cost = SP i.e. CP + (10/100)*CP = SP i.e. 1.1 CP = SP i.e. CP of 2x oranges = SP of 2x oranges/1.1 I hope this helps!

SaquibHGMATWhiz · Answer

Solution:

First scenario,   SP of each orange  =\frac{1}{x}    loss percentage = 45%   We know  SP=CP(1-\frac{l}{100})    Thus, we can say  \frac{1}{x}=CP(1-\frac{45}{100})⇒CP=\frac{20}{11x}    
 Second scenario,   SP of each orange  =\frac{1}{2x}    Profit percentage = 10%   We know  SP=CP(1+\frac{p}{100})    Thus, we can say  \frac{1}{2x}=CP(1+\frac{10}{100})⇒CP=\frac{5}{11x}    
 Percenateb reduction in  CP =\frac{\frac{20}{11x}-\frac{5}{11x}}{\frac{20}{11x}}	imes 100=\frac{20-5}{20}	imes 100=75\%

Hence the right answer is    Option C

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If a man sells x oranges for a dollar, he loses 45 percent. By how muc

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If a man sells x oranges for a dollar, he loses 45 percent. By how muc

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards