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A man purchases 2 watches for $ 560. He sells one at 15% profit and th

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aayushagrawal
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A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   08 Jun 2016, 11:29
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A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :

A) $ 260 and $ 300
B) $210 and $ 350
C) $224 and $336
D) $560 and $560
E) $224 and $ 350
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C
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   08 Jun 2016, 11:43
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x + y = 560 --- (1)
1.15x + 0.9y = 560 --- (2)

(2) - (1) --> 0.15x - 0.1y = 0
15x = 10y
x/y = 2/3 = (2*112)/(3*112) = 224/336

Answer: C
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   08 Jun 2016, 18:58
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0.15xCP1 =0.10xCP2

CP1 / CP2 = 2/3 and CP1 + CP2 = 560 (Given)

So, CP1 = 224 and CP2 = 336.
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   08 Jun 2016, 19:09
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aayushagrawal wrote:
A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :

A) $ 260 and $ 300
B) $210 and $ 350
C) $224 and $336
D) $560 and $560
E) $224 and $ 350



Hi,

Another way from choices-

firstly the sum of price of two watches = 560....
so our answer should also add up to 560... D and E can be eliminated..

Work on the remaining choices to see if 15% of lower price is equal to 10% of higher price..
A) $ 260 and $ 300.....10% of 300 = 30, but clearly 15% of 260 is not 30... Eliminate
B) $210 and $ 350.........10% of 350 = 35, but clearly 15% of 210 will be in decimal... Eliminate
C) $224 and $336...............10% of 336 = 33.6, and 15% of 224 is .15*224 = 33.6... CORRECT
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   08 Jun 2016, 21:51
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aayushagrawal wrote:
A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :

A) $ 260 and $ 300
B) $210 and $ 350
C) $224 and $336
D) $560 and $560
E) $224 and $ 350


Use weighted averages:

CPl/CPp = (15 - 0)/(0 - (-10)) = 3/2

Total cost price is $560 and cost price of the two watches are in the ratio 3:2. On the ratio scale 5 is equivalent to actual 560. So cost prices are $336 and $224.

Answer (C)
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   08 Jun 2016, 21:59
aayushagrawal wrote:
A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :

A) $ 260 and $ 300
B) $210 and $ 350
C) $224 and $336
D) $560 and $560
E) $224 and $ 350


Let initial costs are c1 and c2. Then;

c1+c2 = 560

When he sells.

1.5c1+0.9c2 = 560

c1+c2 = 1.5c1+0.9c2

0.15c1 = 0.10c2

\(\frac{c1}{c2}\) = \(\frac{10}{15}\) = \(\frac{2}{3}\)
c1+c2 = 560
Then
(2/3)c2+c2 = 560.

c2 = 336; c1 = 224.

C is the answer.
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A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   09 Jun 2016, 00:12
15% profit is nullified by 10% loss that means cost of watch with 15% profit is lower than that of cost of other watch with 10% loss, and both the values should be same.
net profit = profit gained - loss incurred
0 = Profit - Loss --> Profit = Loss

so apply 15% to smaller number and 10% to lower number and check both the values are same.

A- 2.6*15 , 30 (not equal)
B- 2.1*15 , 35 (not equal)
C- 2.24*15, 33.6 (equal, I personally converted 15% to 3/20 for easy calculation as I was doing only mind calc)

Answer - C
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   09 Jun 2016, 08:22
aayushagrawal wrote:
A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :

A) $ 260 and $ 300
B) $210 and $ 350
C) $224 and $336
D) $560 and $560
E) $224 and $ 350

Suppose price of one watch =x
then price of another watch=560-x
As per question one at 15% profit and the other at a loss of 10%
x(1+15/100)+ (560-x)(1-10/100)=560(as no profit ,no loss).
115x/100+9*560/10-9X/10=560
25x=5600
x=224
so another =560-224=336
Ans C
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   09 Jun 2016, 09:02
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aayushagrawal wrote:
A man purchases 2 watches for $ 560. He sells one at 15% profit and the other at a loss of 10%. He neither gains nor loses on the whole. Thus, the cost price of two watches are :

A) $ 260 and $ 300
B) $210 and $ 350
C) $224 and $336
D) $560 and $560
E) $224 and $ 350


x+y= 560

1.15 x+ .90y= 560
x+y = 1.15x + .90y
.1y=.15x

y=1.5x

2.5x= 560
x= 224
y=336

C is the answer
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink] New post   10 Jun 2023, 01:19
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Re: A man purchases 2 watches for $ 560. He sells one at 15% profit and th [#permalink]
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