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Intern
Joined: 28 Oct 2017
Posts: 7

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30 Sep 2018, 06:55
1
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
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Manager
Joined: 05 Oct 2017
Posts: 61
Location: India
Schools: GWU '21, Isenberg'21

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30 Sep 2018, 17:52
1
1
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. Manager Joined: 07 Aug 2018 Posts: 109 Location: United States (MA) GMAT 1: 560 Q39 V28 Re: A shopkeeper mixes three varieties of rice costing$10, $12,$17 per  [#permalink]

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05 Oct 2018, 02:42
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
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Senior Manager
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Posts: 252
A shopkeeper mixes three varieties of rice costing $10,$12, $17 per [#permalink] Show Tags 28 Oct 2018, 22:41 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 OA:D Let the weight of each variety in the mixture be $$x,y,$$ and $$z$$ kg Weight of the total mixture $$=x+y+z$$ Cost price + Profit = Selling price Cost price $$= 10x+12y+17z$$ Profit $$=\frac{20}{100}$$ Cost price $$= 0.2$$ Cost price Selling price $$= 15.6(x+y+z)$$ $$10x+12y+17z +0.2(10x+12y+17z)= 15.6(x+y+z)$$ $$1.2(10x+12y+17z)=15.6(x+y+z)$$ $$10x+12y+17z = 13(x+y+z)$$ $$3x+y-4z=0$$ Only Option D satisfies $$3x+y-4z=0$$ As per option D, $$x=2m,y=6m$$ and $$z=3m$$ L.H.S : $$3x+y-4z = 3*2m+6m-4*3m = 6m+6m-12m=0$$ R.H.S : $$0$$ $$L.H.S=R.H.S$$ A shopkeeper mixes three varieties of rice costing$10, $12,$17 per &nbs [#permalink] 28 Oct 2018, 22:41
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