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

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

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

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)

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!

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 \(CP =\frac{\frac{20}{11x}-\frac{5}{11x}}{\frac{20}{11x}}\times 100=\frac{20-5}{20}\times 100=75\%\)

Hence the right answer is Option C

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