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655-705 (Hard)|   Mixture Problems|         
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 19 Dec 2025, 22:06
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The cost of the mixture = 25/1.25 = $20
In one pound: the weight of almonds and pistachios is 6/11 and 5/11 respectively.
Lets say the cost of almonds/pound is a.
a*6/11 + (a-11)*5/11 = 20 => a = 25

Answer: C
Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 19 Dec 2025, 22:06
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Let 11x be total weight in pounds
Almonds weight= 6x/11*11x=6x
Pista weight=5x
Selling price with profit= 11x*25=275x
Cost Price= 275x-275x/5=220x
Let a be CP of almond & b be CP of Pista
220x=6xa+5xb
a=11+b
Solving a=25, b=14, CP of Almond is 25$
Answer is C
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 19 Dec 2025, 22:39
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AlmondPistachios
Quantity6x5x
CostP+11P
Total Cost6x*(P+11)5x*(P)
Total Cost = Selling Cost/(1+profit/100)
= (6x+5x)/(1.25)=220x
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 19 Dec 2025, 23:05
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Ratio 6:5 means toatl weight => 11x

Rvenue = 25(11)(x) = 1.25CP

CP = Weight of each * cost of each
=> 6x(cost of A) + 5x(cost of A +11)
=> (11xc + 55x)

25(11)(x) = 1.25(11xc + 55x)
solving gives us:

c=15
cost of almonds = 26
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 19 Dec 2025, 23:25
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Almonds are 6/11 of the mixture and pistachios having a share of 5/11

If selling at 25 gives 25% profit, then the CP is 20

Let cost of pistachio be x and almond x+11. Therefore,

6(x+11)/11 +5x/11 = 20

6x+66+5x =220

x = 14 and x+11= 25

Therefore, Option C
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 00:12
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SP = $25 Per pound
Profit = 25 %
So CP of the Mixture is , CP = 25/1.25=20
Mixture costs $20 per pound .
Almond:pistachios = 6:5
Pistachios cost = x
Almond cost = x+11
Weighted avg cost = 6(x+11) +5x/11=20
Since Almonds are more expensive , Mixture (20) , must lie closer to pistachios because pistachios have less weight compared to almonds.
Trying few options
B : If almond = $20 ❌
Pistachios = $9
avg lower than 20
C : Pis = 14
Almond = 25
Weighted avg = 6(25) +5(14)/11= 20 ✅
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 00:52
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Let's assume that the weight of the almonds is 6 pounds and that of the pistachios is 5 pounds in the mixture (as the ratio given is 6:5)

Let the cost price of the pistachios be $x per pound, therefore, the cost price of the almonds would be $(11+x) per pound.

Net Cost Price = $(66+11x)

Since the mixture is sold at $25 per pound, the total Selling Price of the mixture = $275 ($25/pound * 11 pounds)

As the profit earned is 25%:

(1.25)*Total CP = Total SP

1.25*(66+11x) = 275

Thus, the value of x = 14. Since the question specifically asks about the cost price of the almonds per pound, the required value = $(11+x) = $25
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 00:56
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Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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So Almonds and pistachios ratio is 6k:5k

It's sold at 25 per pound, which is selling price, and the cost which shopkeeper have to pay = 125x/100 = 25 ; x = 20

y+11 --- cost of almonds
Y ----- cost of pistachios

((Y+11) * 6k + (Y) * 5k)/(11k) = 20

Y = 14
So almond price is Y + 11 = 25

Answer is C
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 03:51
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Price => A = P+11
Weight => A : P = 6x : 5x
Let's take the mixture to have 11 pounds => 6pounds of A and 5 pounds of P
1.25C = 25 $/pound
C = 20 $/pound

6A + 5(A-11) = 11*20 ; A-> Cost of almonds per pound
A = 25
Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 03:57
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Is it just me or are the questions getting tougher every? :P

Either way, we're given that a shopkeeper at a movie theater concession stand mixes almond and pistachio at a 6:5 ratio, and then sells it at $25 per pound, earning a 25% profit.

The easiest thing to find here is the cost price: 1.25x = 25, hence, x = 20 or $20 per pound is the cost price.

We can also rewrite how much almond and pistachio each pound will contain. 5/11 pistachio per pound, 6/11 almond (something like 0.45 pounds and 0.55 pounds respectively - just "decimalizing" this for my own understand, as I tend to read them more clearly than fractions).

Now, an entire pound of almond is $11 more per pound than pistachio is. For instance, if pistachio is $5 per pound, almond is $16.

We can take pistachio's per pound rate to be x, and almond's x + 11.

this x when multiplied by 5/11 of a pound, and then added to (x + 11 multiplied by 5/11 of a pound), which are their respective ratios, will equal $20 per pound, which can help us set a simple equation.

5/11*x + 6/11*(x+11) = 5x / 11 + (6x + 66 whole divided by 11).

That's 5x + 6x + 66, whole divided by 11.

That's 11x + 66, divided by 11 = 20 (the required rate)

We can take the denominator to the RHS, and have it divide that side, making this 11x + 66 = 20*11 = 220

11x = 220 - 66

11x = 154

x = 14

We now know that x, or the pistachio, is for $14 / pound. Naturally, the almond will be for $14 + $11 = $25 / pound. The answer here is will be C.
Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 04:53
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Almonds = 6x
Pistachios = 5x
Total Mixture = 11x
Rate = $25 per pound

Sale price = $25*11x = $275x

Let,
Cost of almonds = $(11 + a) per pound
Cost of pistachios = $a per pound

Now we know that
275x = [$a*5x + $(11+a)*6x]*1.25
220 = 5a + 6a + 66
154 = 11a
=> a = 14

Cost of almonds per pound = 14 + 11 = $25

Option C

Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 05:48
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A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

Let the cost of pistachios= x
the cost of almonds= x+11
The mixture is sold at $25 per pound with a 25% profit, so CP of mixture = 25/1.25= 20

The mixing ratio of almonds and pistachios is 6:5
Average cost = (6(x+11)+5x)/(11) = 20
(6x+66+5x)= 11*20
11x=220-66
x=154/11= 14

Cost price of almonds per pound = x+11 = 14+11 = 25
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 05:59
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Answer C

almonds to Pistachios equals 6:5 equals x: x -11

Sold for $25 with 25% profit meaning cost is y x 1.25 equals $25
y equals $20

so
6x + 5 (x-11) / 11= $20
6x + 5x - 55 / 11= 20
11x - 55 / 11= 20
x-5 =20
x = 25

Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 06:23
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A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

weight -> A : P = 6:5
Let's consider of cost almonds and pistachios as x & x - 11 respectively.

Mixture --- > Selling price = $25, Cost = $ 25/1.25 ( 25% profit ) = 100/5 = 20$ = cost.

Cost of mixture can also be determined as = (6x+5x - 55)/11 = (11x -55)/11

on comparing = > 11x/11 - 5 = 20 --> x = 25 $ C Answer.
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 06:41
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We know that,

Selling price of mixture = $25
Profit = 25%
=> Cost Price = Selling price / 1.25 = 25 / 1.25 = 20

Let,
Cost of pistachios = p
=> Cost of almonds = p + 11

Now we know that,
Almonds : Pistachios = 6:5
So lets take 11 pounds of mixture which would mean we have 6pounds of almonds and 5 pounds of pistachios

Total cost of the mixture = 6*(p+11) + 5p = 11p + 66
Average cost per pound = 11p+66 / 11 = p+6

We also know that cost per pound = 20
=> p+6 = 20
=> p = 14

Therefore, cost of almonds = p+11 = 14 + 11 = 25

C. $25
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 06:46
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A: P = 6:5
SP = 1.25CP = 25 => CP = 20

Cost of Pistachios = x per pound
Cost of Almonds = CA = x+11 per pound

So, 6 parts of Almonds and 5 parts of Pistachios cost $20

6/11(x+11) + 5/11(x) = 20
6x+5x+66 = 220
11x = 154
x=14

CA = 14+11 = $25

Bunuel
A shopkeeper at a movie theater concession stand mixes almonds and pistachios in a ratio of 6:5 by weight. The mixture is then sold at $25 per pound, earning a 25% profit. If the cost of almonds for the shopkeeper is $11 more per pound than the cost of pistachios, what is the cost price of almonds per pound?

A. $14
B. $20
C. $25
D. $26
E. $29

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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 07:04
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Let, Cost per pound of pistachios = x
Cost per pound of almonds = x+11

Cost of 11 pounds of the mixture = 6(x+11) + 5x => 11x+66
Cost per pound = 11x+66/11 = x+6

Using selling price and profit => Cost per pound = 25/1.25 = 20
x+6 = 20 => x=14

Cost of almonds = x+11= 25 => C
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 07:11
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Let's start by computing the Cost of 1 kg of mix. (25% profit with a revenue of 25$)

1.25 C = 25 ==> C = 20 $ /kg

Trick to use the ratio 6:5 is to take something divisible by 11:

let's take 1.1 kg of mix ( which costs 1.1*20 = 22 $) of which 0.6 kg are A and 0.5 kg are P

Hence we just have to solve the following:

22 = 0.6*A + 0.5*P (But the text says the cost of the A = P + 11)
Hence substituting we get:

22 = 0.6*A + 0.5*A - 5.5 ==> A = 27.5/11 * 10 = 275/11 = 25 $

IMO C!
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 07:16
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Let x = CP of pistachios
x+11 = cost of almonds


Selling price is 25$ per pound with 25% profit. Hence CP of mixture is 20$ per pound.

Given ratio is 6:5.
So , 6(x+11)+5x / 11 = 20
Therefore x = 14.

Hence , CP of almonds = 14 + 11 = 25$ per pound.

So Option C.
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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a 20 Dec 2025, 07:18
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a: almonds
p: pistachios = a-11

25% profit -> multiply by 1.25

(6a + 5(a-11))/(6+5) * 1.25 = 25
(6a + 5a - 55)/11 * 5/4 = 25
(11a - 55)/11 = 20
a - 5 = 20
a = 25

IMO C
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