Annie purchased 10 bicycles in 2017, all at the same price. She sold

Question

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Annie purchased 10 bicycles in 2017, all at the same price. She sold six of these at a profit of 25% and the remaining four at a loss of 25%. If she made a total profit of $2000, then what was her purchase price of a bicycle, in $?

A. 8000
B. 6000
C. 4000
D. 3000
E. 2000

6*1.25p + 4*0.75p - 10p = 2000
0.5p = 2000
p = 4000

Answer C.

A. 8000
B. 6000
C. 4000
D. 3000
E. 2000

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GMATWhizTeam · Answer

Solution:  
Let the price of one bicycle be x.
 • The profit and loss is 25%, which is with respect to cost price
• Thus, 25% of CP =  \frac{x}{4} 
 o Profit on 6 bicycles = \frac{6x}{4} 
o Loss on 4 bicycles =  \frac{4x}{4}  
• Overall profit = profit – loss
 o  2000 = \frac{6x}{4} – \frac{4x}{4} 
o  8000 = 2x 
o  x = 4000    
Hence, the correct answer is  Option C.

freedom128 · Answer

10 bicycles were bought at price P each 
---> Cost= 10P

6 bicycles are sold at priced at 1.25P each, while 4 other bicycles are sold at priced at 0.75P each. 
---> Total sell = 6*1.25P + 4*0.75P = 10.5P.

Profit = 2000 = 10.5P -10P = 0.5P. 
So, purchase price of a bicycle is: P=2000/0.5=4000

FINAL ANSWER IS (C)

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monikakumar · Answer

Annie purchased 10 bicycles in 2017, all at the same price. She sold six of these at a profit of 25% and the remaining four at a loss of 25%. If she made a total profit of $2000, then what was her purchase price of a bicycle, in $?

A. 8000
B. 6000
C. 4000
D. 3000
E. 2000

6*1.25p + 4*0.75p - 10p = 2000
0.5p = 2000
p = 4000

Answer C.

A. 8000
B. 6000
C. 4000
D. 3000
E. 2000

6(5/4)x+4(3/4)x=10x+2000,
on solving, x=4000
C

unraveled · Answer

Annie purchased 10 bicycles in 2017, all at the same price. She sold six of these at a profit of 25% and the remaining four at a loss of 25%. If she made a total profit of $2000, then what was her purchase price of a bicycle, in $?

A. 8000
B. 6000
C. 4000
D. 3000
E. 2000

6*1.25p + 4*0.75p - 10p = 2000
0.5p = 2000
p = 4000

Answer C.

A. 8000
B. 6000
C. 4000
D. 3000
E. 2000

6*1.25p + 4*0.75p - 10p = 2000
0.5p = 2000
p = 4000

Answer C.

GMATGuruNY · Answer

Average profit per bicycle  = \frac{2000}{10} =  $200

Since 6 bicycles earn a 25% profit, while 4 suffer a 25% loss, the average profit percentage for all 10 bicycles =  \frac{6*25 - 4*25}{10} =   5%

Thus, $200 in profit must represent 5% of the purchase price:
 200 = \frac{5}{100}x 
 x = 4000

C

GMATGuruNY · Answer

An alternate approach is to PLUG IN THE ANSWERS, which represent the purchase price for each bicycle.
When the correct answer is plugged in, the total profit = 2000

B: 6000
25% of 6000 = 1500
Since 6 bicycles earn a 25% profit, while 4 suffer a 25% loss, the total profit  = 6*1500 - 4*1500 = 2*1500 = 3000 
The result is too HIGH.

D: 3000
Since the purchase price here is 1/2 the purchase price in B, the total profit here will be half the total profit yielded by B:
 \frac{1}{2}*3000 = 1500 
The result is too LOW.

Since B yields a result that is too HIGH, while D yields a result that is too LOW, the correct answer must be BETWEEN B AND D.

C

MrSengupta · Answer

The answer is (C) .

Let the cost price of a cycle is b .

Therefore (1.25b*6+0.75b*4)-(10b)=2000
 => b=4000

exc4libur · Answer

2000+10x=6(5/4x)+4(3/4x)
2000=7.5x+3x-10x
2000=0.5x
x=4000

Ans (C)

madgmat2019 · Answer

Let the CP of each bicycle be x.....then for 10 its 10x

SP of 6 cycles each is 1.25x........for all 6 its 7.5x
SP of 4 cycles each is 0.75x........for all 4 its 3x

total SP of 10 is 10.5x

Profit = 10.5x-10x= 0.5x = 2000

x=4000

OA:C

yashikaaggarwal · Answer

Let price of one cycle be x and he bought 10 cycles so 10x
6 sold at 25% profit so SP is 6*1.25x=7.5x
4 sold at 25% loss so SP is 4*0.75x=3x
Total revenue generated is 7.5x+3x=10.5x
Profit=10.5x-10x=0.5x=2000
x=4000
So OA is C

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Annie purchased 10 bicycles in 2017, all at the same price. She sold

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Annie purchased 10 bicycles in 2017, all at the same price. She sold

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