A shopkeeper mixes three varieties of rice costing $10, $12, $17 per

Question

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

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

harsha3699 · Accepted Answer

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.

chetan2u · Answer

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

soapbolt · Answer

(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

T1101 · Answer

Hi  chetan2u !

I think you made a small mistake with the marked ratio! Shouldn't it be 3:1:4?

Cheers

Bismarck · Answer

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

GMATGuruNY · Answer

Since the $15.60 selling price yields a profit of 20%, the $15.60 selling price represents 120% of the cost of the mixture:
1.2x = 15.6
12x = 156
x = 13

Since the average cost of the mixture ($13) is closer to the two lowest cost prices ($10 and $12) than to the highest cost price ($17), more than half of the mixture must be composed of the $10 and $12 varieties.
Implication:
In the correct ratio, the sum of the parts for the two lowest prices will be greater than the part for the highest price.
Of the four answer choices, only D (2:6:3) satisfies this condition:
2+6>3

D: 2:6:3
If we combine 2 kgs of the $10 rice, 6 kgs of the $12 rice, and 3 kgs of the $17 rice -- for a total of 11 kgs -- the average cost per kg  = \frac{(2*10)+(6*12)+(3*17)}{11} = \frac{143}{11} = 13 
Success!

D

kaustav04 · Answer

Hi,

Since the CP is 13 
And he has three varieties of rice, costing him 10, 12 and 17.

Why can't it be 
 /3 = 13

Meaning; all in equal proportion? ?

What am i missing here?

Posted from my mobile device

josenetofaria · Answer

It can be.

But the question asks: " Which of  the ones bellow  could be.. ".

Certainly, if the option 1:1:1 was there as well, there would be two responses.

ScottTargetTestPrep · Answer

Solution:
 
Before the shopkeeper is selling the mixture rice for a profit of 20%, the cost of the mixture is 15.6/1.2 = $13 per kg. Let’s check the answer choices, starting with the easiest one, choice D.

We need to determine:

10(2) + 12(6) + 17(3) = 13(2 + 6 + 3) ?

20 + 72 + 51 = 13(11) ?

143 = 143 ? → Yes

Therefore, the correct answer is D.

Answer: D

Abhishek009 · Answer

$  15.60  represents  120 % of CP

So, CP  = \frac{15.60}{1.20} = 13

NOw, check the options , start with easiest option (D) in this case...

\frac{10*2 + 12*6 + 17*3}{(2+6+3)} = \frac{(20 + 72 + 51)}{11} = 13 , Anwer must be (D)

DhanyaAbhirami · Answer

How to land at the answer without plugging in the choices?
Are multiple ratios possible? How to we arrive at a possible ratio?

ayushiii02 · Answer

Can we say that if we look at the choice A,B,C . It is just more of 17 dollar product which would not keep the profit to be 20% if sold at 15.6 
Hence we eliminate those

Krunaal · Answer

Your observation is reasonable: if the proportion of the $17 product is too high, it will pull the weighted average cost above $13. Since the selling price of $15.60 with a 20% profit implies a cost price of $13, choices where the $17 product dominates would indeed fail to meet the required cost price. However, as it is more intuitive and can help eliminate some options quickly, it also does not necessarily guarantee correctness. The correct method involves calculating the weighted average -   I would recommend that you use this intuitive approach to test D. directly into the equation you get using weighted averages.

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