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Rani bought more apples than oranges. She sells apples at ₹23 apiece a

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Rani bought more apples than oranges. She sells apples at ₹23 apiece a  [#permalink]

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New post 15 Apr 2016, 06:49
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A
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Difficulty:

  95% (hard)

Question Stats:

54% (03:29) correct 46% (03:47) wrong based on 70 sessions

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Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage.

A. 16.8%
B. 17.4%
C. 17.9%
D. 18.5%
E. 19.1%
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Re: Rani bought more apples than oranges. She sells apples at ₹23 apiece a  [#permalink]

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New post 15 Apr 2016, 07:37
1
Given: Selling price of an Apple = 23 --> Cost price = 23/1.15 = 20
Selling price of an orange = 10 --> Cost price = 10/1.25 = 8
A > O
23*(A) + 10*(O) = 653

653 - 23*(A) has to be divisible by 10 --> Units digit has to be 0
Values of A can be 1, 11, 21, 31, .... --> 1 cannot be the value
Between 11 and 21, If A = 11, O = 30 --> Not possible
If A = 21, O = 17 --> Possible

Cost price = 20*21 + 8*17 = 420 + 136 = 556

Profit = 653 - 556 = 97
Profit% = (97/556)*100 = 17.4%

Answer: B

P.S: This problem is very calculation intensive as the options are very close. I would guess and move on if I do not arrive at the answer in the stipulated time.
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Re: Rani bought more apples than oranges. She sells apples at ₹23 apiece a  [#permalink]

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New post 15 Apr 2016, 07:54
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1
anceer wrote:
Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage.

A. 16.8%
B. 17.4%
C. 17.9%
D. 18.5%
E. 19.1%


Hi,

Pl share the source

just few points on the Q..
1) Ofcourse 700 level, but the calculations are too complex for a GMAT Q..
2) The method can be tested but may be with numbers that are less calculation intensive
3) Rather it consists of 3 STEPS, which can itself be two-three Qs..



Solution:-



1) first step--


find the number of apples and oranges..
23a + 10b =653, where a>b
10b=653-23a..
so 23a should have units digit as 3 to ensure div by 10b..
so a can be 1,11,21,31..
since a>b, ONLY 21 fits in and b = 17 from equation..

2) second step--


find the CP
apples SP = 23*21= 483.
CP = 483/1.15 = 420

oranges SP = 170
CP = 170/1.25 = 136

total CP= 420+136 = 556

3) Third step


find the Profit %..
By allegation or straight \(\frac{(653-556)}{556} = \frac{97}{556}= 17.44%\)
B
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Re: Rani bought more apples than oranges. She sells apples at ₹23 apiece a  [#permalink]

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New post 17 Apr 2017, 18:38
strange, I thought percentage of profit should be calculated by using gross profit over revenue.

Can SB helps me?
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Rani bought more apples than oranges. She sells apples at ₹23 apiece a  [#permalink]

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New post 17 Apr 2017, 20:57
anceer wrote:
Rani bought more apples than oranges. She sells apples at ₹23 apiece and makes 15% profit. She sells oranges at ₹10 apiece and makes 25% profit. If she gets ₹653 after selling all the apples and oranges, find her profit percentage.

A. 16.8%
B. 17.4%
C. 17.9%
D. 18.5%
E. 19.1%


another approach to finding number of apples and oranges
price of apple-orange pair=23+10=33
653-19*33=26 no
653-18*33=59 no
653-17*33=92 yes
92=4*23, adding 4 apples to
the 17 apple-orange pairs,
for a total of 21 apples and 17 oranges
21*20+17*8=556=total cost
21*3+17*2=97=total markup
97/556=17.4% total profit
B
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Re: Rani bought more apples than oranges. She sells apples at ₹23 apiece a  [#permalink]

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New post 28 Nov 2018, 11:20
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Re: Rani bought more apples than oranges. She sells apples at ₹23 apiece a   [#permalink] 28 Nov 2018, 11:20
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