A merchant mixes three varieties of rice costing $20/kg, $24/kg and $3

Question

A merchant mixes three varieties of rice costing $20/kg, $24/kg and $30/kg and sells the mixture at a profit of 20% at $30/kg. How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

A. 1 kg

B. 3 kgs

C. 5 kgs

D. 6 kgs

E. 7 kgs

A. 1 kg

B. 3 kgs

C. 5 kgs

D. 6 kgs

E. 7 kgs

CrackverbalGMAT · Accepted Answer

SOLUTION:

A=20$kg, B=24$kg ,C =30$kg
Let x kg be rice A ,y kg be rice B and 2 kg be quantities of rice C
Final CP = 25

Equating the Cost Prices we have-
20x+24y+60=25(x+y+2)
=>y=10−5x
Since, y cannot be zero or negative and for any value of x above 1 we have 0 or negative y
x can only be 1 giving y=5 kg (OPTION C)

Hope this helps

Devmitra Sen(Math)

Kinshook · Answer

Given: A merchant mixes three varieties of rice costing $20/kg, $24/kg and $30/kg and sells the mixture at a profit of 20% at $30/kg. 
Asked: How many kgs of the second variety will be in the mixture if 2 kgs of the third variety is there in the mixture?

Cost price of the mixture = $30/1.2 = $25/kg

If we take 2kgs of third variety and 2 kgs of first variety

Cost price of the mixture = (20*2 + 30*2)/(2+2) = 100/4 = $25/kg

There is no need to have second variety rice in the mixture.

Bunuel 
The question needs some correction.

A. 1 kg

B. 3 kgs

C. 5 kgs

D. 6 kgs

E. 7 kgs

imeanup · Answer

The mixture is sold for a profit of $ 30/kg, the cost price of the mixture 30/1.2 = $ 25/kg
Qa-------Qc
20-------30
-----25-----
5---------5 Ratio (1:1)
Similarly, 
Qb--------Qc
24--------30
------25-----
5----------1 Ratio (5 : 1)

Now if we mix both these mixtures, we have the following quantities in the FINAL mixture.
Qa=1 kg from mixture 1 only
Qb=5 kg from mixture 2 only
Qc=1 kg from mixture 1 AND 1 kg from mixture 2

So, the ratio of the mixture added is 1 : 5 : 2 
2 kg of the 3rd variety mixture is already given in the question, so, the 2nd variety is 5 kg.
Ans C

harshchougule · Answer

How did you calculate Final CP = 25??
Can you please breakdown the solution I am really struggling in this mixture question.
Thanks

venkycs98 · Answer

The question should probably specify that (i) At least 1 KG of each variety must be included in the mixture and also (ii) Only int values are allowed in the mixture

venkycs98 · Answer

We need to make a couple of assumptions -
1. All three varieties are present in the final mixture
2. Number of KGs of each variety is an int.

With these assumptions -

Lets calculate the cost price of the rice mixture
We know that the seller makes a profit of 20% by selling the mixture at 30$
So -

=> 6/5*x = 30 
=> x = 25 (cost price)

Let number of KGs of variety 1 be x and 2 be y

the equation will be -

( 20x + 24y + 2*30 ) / (x + y + 2 ) = 25

=> 20x + 24y +60 = 25x + 25y + 50
=> 5x + y = 10
Armed with our assumptions, lets plug in values for y

A. y = 1

5x + 1 = 10 
=> 5x = 9 
x not an int, wrong answer

B. y = 3

5x + 3 = 10
5x = 7
 x not an int, wrong answer

C. y = 5

5x + 5 = 10
=> x =1
 Correct answer

ZIX · Answer

If  Qb:Qc is 5:1, then why did you change the ratio to 5:2 in the final mixture? if Qc is 2 then Qb must be 10 (5:1)

bumpbot · Answer

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A merchant mixes three varieties of rice costing $20/kg, $24/kg and $3

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A merchant mixes three varieties of rice costing $20/kg, $24/kg and $3

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