How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix

Question

How many kgs of Basmati rice costing $42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing $24 per kg so that he makes a profit of 25% on selling the mixture at $40/kg?

A. 12.5 kgs
B. 16.0 kgs
C. 20.0 kgs
D. 200.0 kgs
E. 205.0 kgs

bobnil · Answer

Let Cost price of mixed rice =x
Then, 40= x(1+1/4)
 X=32
Using scale method (weighted avg), 
24----32----42
 8 : 10
 4 : 5

Ordinary rice / basmati rice = 5/4
25/ B = 5/4
B= 20
ANS C

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otautahi · Answer

Let X the kgs of Basmati rice, and we sold it with 25% profit. So-

1.25 (42X + 25*24) = (X+25) * 40
Here- 1.25 = 125/100 = 5/4

5/4 (42X + 25*24) = (X+25) * 40
42X + 25*24 = (X+25) * 160/5 = (X+25) * 32
42X - 32X = 32*25 - 24*25 = 8*25
10X = 200
X = 20

Answer: B

LukaT022 · Answer

Could you please explain how you got to 8:10 and 4:5?

Ulki201 · Answer

8:10 is the distance from each price to the mixed rice price: 32-24=8 and 42-32=10. He simplified it to 4:5 (by dividing by 2) Here's an explanation of the scaling method: https://gmatclub.com/forum/weighted-ave ... 06999.html

Ghoskrp3 · Answer

Easiest Explanation:

Since 25% profit is to be made, that means 125% of rice should cost 40$/KG, then that means, actually 100% rice should just be mixed so that it costs around 32$/KG

Now let's just substitute to get it:

(42$ rice * xKgs + 24$ rice * 25 Kgs) / (25 + x)Kgs = 32$ rice
Solving this gets 10x = 200 => x = 20Kgs

uCS2020 · Answer

How many kgs of Basmati rice costing $42/kg should a shopkeeper mix with 25 kgs of ordinary rice costing $24 per kg so that he makes a profit of 25% on selling the mixture at $40/kg?

A. 12.5 kgs
B. 16.0 kgs
C. 20.0 kgs
D. 200.0 kgs
E. 205.0 kgs

One way to solve this:

Make an equation,

Let’s say that the total Kgs of Basmati Rice the shopkeeper mixes with the normal rice is X.

The total money of selling that mixture will be : (42 * X) + (24 * 25) 
Now this isn’t an equation, so how could we make an equation with this information?

Since we know that the total weight of the mixture will be X + 25 Kgs , and each Kg will be sold for 40 $ then that means that the total cost after the shopkeeper mixes the two rices will be : (X + 25) * 40

We know that (X + 25) * 40 Is 25% more than (42 * X) + (24 * 25) then that means to equalise both expressions, we multiply the latter by 1.25 ( since 25% more means to multiply by 1.25)

1.25 ( 42X + 600) = 40X + 1000
52.50X + 750 = 40X + 1000

In the end we get : X = 20 Kgs

Meaning that the answer = C

Lorenzini · Answer

For me the trickiest thing here is realizing you mean 25% profit margin on cost.
If not, you could easily assume its SalePrice - Cost = Profit where SalePrice = 40; Profit = 40*25%=10 (margin of 25% on revenue) giving a Cost = 30 and Answer choice "A" as the correct one.

How can I be sure this is always the right connotation for "Profit of 25% on cost"?

Bunuel · Answer

Profit and profit margin are different:

•  Profit percentage  is calculated based on  cost price :
Profit Percentage = (Profit / Cost Price) * 100

•  Profit margin  is calculated based on  selling price (revenue) :
Profit Margin = (Profit / Revenue) * 100

egmat · Answer

Hi Lorenzini,  there's a firm convention that settles it every time.

The rule:  when a problem says "profit of 25%" (or "25% profit"), the base is  always the cost price  - unless it explicitly says otherwise. Profit is defined as how much you  gained relative to what you spent . So:

- Profit % = (Selling Price - Cost) /  Cost  ×  100

That's why the posted solutions write `40 = Cost × 1.25`, giving Cost =  $32/kg . The selling price is  25%  above  cost.

Your alternate reading  (Profit =  25%  of Selling Price =  $10 , so Cost =  $30 ) is the  margin on revenue  idea. That's a real business concept, but on the GMAT it is  never  the default. Test-writers will name it directly - they'll say "profit margin" or "25% of revenue" or "25% of the selling price." If the sentence just says "profit of 25%," read it as  25%on cost .

So the quick decision rule:

- "Profit of X%" / "X% profit" / "profit of X% on cost" - base =  cost .
- Only switch to selling price if the words  explicitly  point there ("margin," "of the selling price," "of revenue").

How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix

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How many kgs of Basmati rice costing Rs.42/kg should a shopkeeper mix

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