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

Question

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

sashiim20 · Accepted Answer

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)...

KarishmaB · Answer

$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)

pushpitkc · Answer

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)

Luckisnoexcuse · Answer

The question is 0.9x + 200 = 1.06x

On solving x is 1250
Hence C

Sent from my iPhone using GMAT Club Forum

profileusername · Answer

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.

KarishmaB · Answer

Profit( or Loss) = Selling Price - Cost Price

Profit (or Loss) % =   * 100

verydisco · Answer

Hi, could you please tell me how you arrived at the 16% value?

aishu0091 · Answer

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

aishu0091 · Answer

<-----|----------|-------|-----> 
 -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!

CrackverbalGMAT · Answer

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

bumpbot · Answer

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

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

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