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30 Sep 2018, 06:34
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A shopkeeper mixes three varieties of rice costing $10,$12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at$15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these
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Joined: 02 Aug 2009
Posts: 6958

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30 Sep 2018, 07:56
Sriharsh wrote:
A shopkeeper mixes three varieties of rice costing $10,$12, $17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at$15.60 per kg?

(A) 9:14:36
(B) 11:14:25
(C) 14:36:43
(D) 2:6:3
(E) None of these

(10x + 12y + 17z)/ x+y+z = CP ........ (A)

profit % = (SP-CP)/CP

From above formula CP = 13
Putting the value of 13 in equation A , we get
4z =3x+y

Only option D satisfy this equation, Hence correct answer is Option D
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Joined: 21 Nov 2016
Posts: 37
Re: A shopkeeper mixes three varieties of rice costing $10,$12, $17 per [#permalink] Show Tags 30 Sep 2018, 18:52 We have 3 varieties of rice each costing$10, $12, and$17.
The shopkeeper mixes these three varieties and sells the mixture at $15.6 which gets him a profit of 20%. Now, CP +CP(20/100) = 15.6 Implies, CP =$13.0

So we have x grams of $10 rice, + y grams of$12 rice + z grams of $17 rice, all mixed together to form 1 kg of rice with a cost price of$13.0
Implies , 10x+12y+17z = 13(x+y+z)
Implies, 4z = 3x + y

The above equation shows us that z has to me minimum of all three.
By seeing the options only D has z being minimum.
So lets check for D.
4z = 3x + y
Implies, 4(3) = 3(2)+6
Implies , 12 = 12

So option D is the correct answer.
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Re: A shopkeeper mixes three varieties of rice costing $10,$12, $17 per [#permalink] Show Tags 05 Oct 2018, 03:42 chetan2u wrote: Sriharsh wrote: A shopkeeper mixes three varieties of rice costing$10, $12,$17 per kg. Which of the following can represent a possible ratio in which the three varieties are mixed, if the trader makes a profit of 20% by selling the mixture at $15.60 per kg? (A) 9:14:36 (B) 11:14:25 (C) 14:36:43 (D) 2:6:3 (E) None of these Now the profit is 20%, so let us find the average price the price at which there is no profit and no loss... 15.60=120x/100......x=15.6×100/120=13 So prices are 10:12:17 and average 13.. Let us how far the numbers are from average price.. (13-10):(13-12):(17-13).....3:1:6... So the ratio *the difference of the price on either side of average price should be equal.. So let us check the choices.. (A) 9:14:36..........so $$9*(13-10)+14*(13-12)=36*(17-13)...9*3+14*1=36*4$$.....no (B) 11:14:25......so $$11*(13-10)+14*(13-12)=25*(17-13)...11*3+14*1=25*4$$.....no (C) 14:36:43......so $$14*(13-10)+36*(13-12)=43*(17-13)...14*3+36*1=43*4$$.....no (D) 2:6:3......so $$2*(13-10)+6*(13-12)=3*(17-13)...2*3+6*1=3*4.....12=12$$...yes (E) None of these D Hi chetan2u! I think you made a small mistake with the marked ratio! Shouldn't it be 3:1:4? Cheers _________________ Quantitative Megathread:https://gmatclub.com/forum/ultimate-gmat-quantitative-megathread-244512.html Verbal Megathread:https://gmatclub.com/forum/all-you-need-for-gmat-verbal-164070.html Flashcards Quant + Verbal:https://gmatclub.com/forum/gmat-flashcards-108651.html Thursdays with Ron:https://gmatclub.com/forum/manhattan-s-thursdays-with-ron-consolidated-video-index-223612.html#p2138753 Re: A shopkeeper mixes three varieties of rice costing$10, $12,$17 per &nbs [#permalink] 05 Oct 2018, 03:42
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