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A trader sold a cycle at a loss of 10%. If the selling price had been

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aveek86
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A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   23 Jun 2017, 13:57
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A trader sold a bike at a loss of 10%. If the selling price had been increased by $200, there would have been a gain of 6%. The cost price of the bike is

A) $1200
B) $1205
C) $1250
D) $1275
E) $1305
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C
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sashiim20
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   23 Jun 2017, 14:18
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aveek86 wrote:
A trader sold a bike at a loss of 10%. If the selling price had been increased by $200, there would have been a gain of 6%. The cost price of the bike is

A) $1200
B) $1205
C) $1250
D) $1275
E) $1305


Let Cost price of bike be \(= x\)

Selling price of bike is at loss of 10% = 90% of x \(= \frac{90}{100} * x = 0.9x\)

If selling price had been increased by $200, would gain of 6% = 106% of x \(= 0.9x + 200 ==> \frac{106}{100} * x = 0.9x + 200\)

\(1.06x = 0.9x + 200\)

\(1.06x - 0.9x = 200\)

\(0.16x = 200\)

\(x = \frac{200}{0.16} = \frac{200 * 100}{16} = $1250\) . Answer (C)...
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   23 Jun 2017, 14:18
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Went by options.

Started with C
If the price of bike is 1250$, the price after loss(10%) will be 1125$. However, if he sold the bike at 200$ more, the new price would be 1325, which is 6% of the cost (hence making it a gain)

Option C is our correct answer!

Method 2 (Algebraic method)

Let price of bike be x

.9x + 200 = 1.06x
200 = .16x
(200 * 100)/16 = x
x = 50*25 = 1250(Option C)
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   23 Jun 2017, 14:23
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The question is 0.9x + 200 = 1.06x

On solving x is 1250
Hence C


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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   10 Aug 2017, 14:07
Can someone explain the basic concept of calculating gain or loss? Although it's apparently quite easy to understand, I still had difficulty in making sense of it in this question in terms of its calculation.
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   11 Aug 2017, 00:36
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aveek86 wrote:
A trader sold a bike at a loss of 10%. If the selling price had been increased by $200, there would have been a gain of 6%. The cost price of the bike is

A) $1200
B) $1205
C) $1250
D) $1275
E) $1305


$200 is equivalent to 16% of the cost price because it converts 10% loss to 6% gain.
200 = (16/100)*Cost price
Cost price = $1250

Answer (C)
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   11 Aug 2017, 00:43
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TheMastermind wrote:
Can someone explain the basic concept of calculating gain or loss? Although it's apparently quite easy to understand, I still had difficulty in making sense of it in this question in terms of its calculation.


Profit( or Loss) = Selling Price - Cost Price

Profit (or Loss) % = [Profit (or Loss) / Cost Price] * 100
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   09 Apr 2020, 13:04
VeritasKarishma wrote:
aveek86 wrote:
A trader sold a bike at a loss of 10%. If the selling price had been increased by $200, there would have been a gain of 6%. The cost price of the bike is

A) $1200
B) $1205
C) $1250
D) $1275
E) $1305


$200 is equivalent to 16% of the cost price because it converts 10% loss to 6% gain.
200 = (16/100)*Cost price
Cost price = $1250

Answer (C)


Hi, could you please tell me how you arrived at the 16% value?
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   14 Dec 2021, 22:30
I'd appreciate if this someone can confirm if this method is correct:
A trader sold a bike at a loss of 10%. If the selling price had been increased by $200, there would have been a gain of 6%. The cost price of the bike is

loss = 10% = 1/10
Loss = CP-SP/CP = 10x-9x/10x
so taking it as a ratio, we can say
CP:SP = 10:9 ---->1

If SP was increased by $200, the profit%=6%

SP+200 ---> 9x+200

(9x+200-10x)/10x = 6/100
900x+20,000-1000x = 60x
20,000-100=60x
20,000=160x
x=20,000/160
x=125

CP=10x so 125*10=1250

Quite a long approach though
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   14 Dec 2021, 22:39
VeritasKarishma wrote:
aveek86 wrote:
A trader sold a bike at a loss of 10%. If the selling price had been increased by $200, there would have been a gain of 6%. The cost price of the bike is

A) $1200
B) $1205
C) $1250
D) $1275
E) $1305


$200 is equivalent to 16% of the cost price because it converts 10% loss to 6% gain.
200 = (16/100)*Cost price
Cost price = $1250

Answer (C)


<-----|----------|-------|----->
-10 0 6
-10 is the loss and 6 is the profit after an increase of 200$ in the selling price. so the total movement would be an increase of 16% (i.e. it would have to move by 10 points to 0 and then 6 points again)

Could someone help me out with why '$200 is equivalent to 16% of the cost price'?
why is it the cost price?

Thanks!
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Re: A trader sold a cycle at a loss of 10%. If the selling price had been [#permalink] A trader sold a cycle at a loss of 10%. If the selling price had been   15 Dec 2021, 05:22
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A trader sold a bike at a loss of 10%

Sp = 90% of CP

If the selling price had been increased by $200, there would have been a gain of 6%.

New SP = 106% of CP

New SP = SP + 200$

90% of CP + 200 = 106% of CP

16 % of CP = 200

CP = 200/16 * 100 = 1250

Option C is the answer.

Thanks,
Clifin J Francis
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