A grocer buys two kinds of rice at $1.80 and $1.20 per kg. In what pro

Question

A grocer buys two kinds of rice at $1.80 and $1.20 per kg. In what proportion should these be mixed, so that by selling the mixture at $1.75 per kg 25% profit is made ?

A. 2 : 1
B. 3 : 2
C. 3 : 4
D. 1 : 2
E. 1 : 4

GMATWhizTeam · Accepted Answer

Solution:  
 • Selling price of mixture = $ 1.75 per kg
• Profit = 25%
• Cost price of mixture =  \frac{4}{5}*1.75 = $ 1.4  per kg 
Now, we will use allegation to find the ratio.
 https://www.dropbox.com/s/i7mmdbki8jw3kxj/34.jpg?dl=1 
 • Ratio of rice =  \frac{(1.40-1.20)}{(1.80-1.40)}=1: 2  
Hence, the correct answer is  Option D.

priyachandank · Answer

could you explain this part please?
.
.
.

how did we get 4/5 there?

Harsh9676 · Answer

priyachandank ,

So the Selling Price = Cost Price * (1+Profit %)
 
Therefore 1.75 = CP * (125/100)

CP = 1.4

Hope this helps.

Kudos if you like the explanation

CEdward · Answer

Rice A - 1.80/kg
Rice B - 1.20/kg

1.75 / 1.25 = 1.40

1.8A + 1.2B / A + B = 1.40
A/B = 1/2

Harsh9676  I understand how to figure this out mathematically, but can you explain to me how you know it's 1:2 vs 2:1? Which part of the ratio comes first? I always get that confused.

Harsh9676 · Answer

In the allegations diagram , it's always average - lowest value : Greatest value - Average. You learn the diagram approach you will never go wrong. It's used in so many other concepts as well. Check the below link. https://m.youtube.com/watch?v=SExmttNK5Mg Posted from my mobile device

Ashok.Battula · Answer

SP = 1.75 / KG

so CP = 1.75*100/125 = 1.4 / KG

assume x kilos of Rice A and Y kilos of Rice B

equation of Cost price is 1.8x +1.2Y =1.4 * (X+Y)

0.4x = 0.2 Y

X/Y= 1/2.

Abhishek009 · Answer

CP of rice at $1.75 per kg 25% profit = 1.4 (ie 1.75/125*100)

1.80______________________1.20

____________1.40_____________

0.20______________________0.40

Ie, 0.20 : 0.40 = 1 : 2 , Answer must be (D)

Phuong1632 · Answer

I thought that 25% of profit means 75% is cost and 25% is profit. Therefore, the cost should be 21/16.
I can't get the logic when other members say that the profit is 25% and cost is 100%

Bunuel · Answer

Profit percentage is calculated based on cost price:

Profit Percentage = (Profit / Cost Price) * 100

Phuong1632 · Answer

Thank you Bunuel, I got it

A grocer buys two kinds of rice at $1.80 and $1.20 per kg. In what pro

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A grocer buys two kinds of rice at $1.80 and $1.20 per kg. In what pro

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards