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12 Days of Christmas GMAT Competition 2025 - Day 5: A shopkeeper at a

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chasing725

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19 Dec 2025, 10:34

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Actual price =

25-x/x = 25/100

x = 20

(p+11) ------------- 5 -------- 20 ------------------- 6------------------ p

20-p-11/(p-20) = 5/6

120-6p-66 = 5p-100
11p - 154
p = 14

p+11 = Price of almonds = 25

Option C

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Imo. answer is C
Assuming cost of almonds as $A/Pound i.e. Cost of Pistachios as $P /pound = A-11
Setup equation for total cost, where Almonds are 6x pounds and Pistachios are 5x pounds
6xA + 5x(A-11) = 25/1.25 * (11x); the X's cancel out and you get A=$25

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19 Dec 2025, 11:02

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price of pesta be p, so almond is p+11
pesta=5n, almond = 6n
C.P=5np+6n(p+11)

S.P = 11n*25

profit=(11n*25)-(11np+66n)
=209n-11np

%profit=(209n-11np)/(11np+66n)=0.25
p=14
almond price=14+11 = 25

Ans 25

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Pistachios= X per pound
Almonds= X+11 per pound
Selling price= $25 per pound
Profit= 25% so Cost price of the mixture = 25/1.25=20 dollars
so 6(X+11)+5X/6+5
6X+66+5X/11=20
(11X+66)(11)=20 = 11(X+6) (11)=20
SO X+6=20
X=14
Cost of Almonds will be X+11= 14+11=25
The answer is 25

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Given that selling price is $25 which is at a 25% profit then buying price can be found by 100/125x25 =$20
Ratio of A;P = 6:5 Let cost of P be c meaning cost of A will be c+11
Average cost of the mixture is 6(c+11) + 5c/11=20
The above equation gives c as 14 and therefore price of almonds is c+11 or 14+11= 25
Ans 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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Natansha

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19 Dec 2025, 11:27

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a weighted average ques

firstly since the SP per pound is 25$ with 25% profit, then CP is

5/4 CP = 25
CP = 20

Now let pistachio cost x per pound, then almonds cost x + 11 per pound, we basically have the individual costs, the average cost of mixture and the ratio in which they are mixed, making it a weighted avg ques

A: P = 6:5

We have (x+11) 6 + 5x /11 = 20
6x + 66 + 5x = 220
Simplifying x = 14, giving us x + 11 = 25

Ans (C) 25

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19 Dec 2025, 11:28

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Bunuel

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Let weight of almonds be 6k and that of pistachios be 5k. Total weight will be 11k.
Now Profit = 0.25 i.e (SP-CP)/CP = 1/4 => SP=CP*5/4. But SP is also 25*11k, thus we get CP= 220k
let almond price be x, CP= 6k*x +5k*(x-11)=> CP= 11k*x-55k
Thus 220k =11k*x - 55k or x =25.

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19 Dec 2025, 11:52

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Bunuel

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The almond and pistachios are mixed in the ratio 6:5 by weight.

The mixture is sold at $25 per pound, earns a profit of 25%.

Cost price * (5/4) = $25

Thus, cost price is ($25*4)/5 = $20 per pound.

Let the cost of Pistachios = $x

Then, the cost of almonds = $ x+11

Using alligations: we get

x ——————-20————————(x+11)

5. 6

[5x + 6*(x+11)]/ 11 = 20

5x + 6x + 66 = 220

x = 14

The cost of almond = $ x+11 = 14+11 = $25

Option C

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Almonds:
Quantity=6n
Cost per pound: x
Cost: 6n*x

Pistachios:
Quantity=5n
Cost per pound: x-11
Cost: 5n * (x-11)

Mix:
Quantity=6n+5n= 11n
Cost per pound: 20
Cost: 11n * 20 = 220n

Mix price per pound = Mix cost per pound * (1+25%)
25 = Mix cost per pound * 1.25
Mix cost per pound= 20

Cost for 11n Mix= 6n * x + 5n * (x - 11)
220 = 6x + 5x - 55
x = 25
Answer C

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19 Dec 2025, 12:31

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almon to pistachios is 6:5 so we will take them in kgs so 6kg to 5 kg = 11kg

sp is $25 -25% profit = $20 CP

so for 11 kg mix total CP is $220

Cp of Almond is $11 more than pistachios
we have 6 kg of almond so the total excess in 6 kg is $66

220-66= 154 is the cp for both minus all the excess amount of $11/kg
154/11= $14/kg the price of pistachios
11+14=25/kg is the price of almonds.

Bunuel

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19 Dec 2025, 13:03

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x+ 25% of x = 25
Solving for x, x = 20
CP = $20 per pound
Let cost of almonds be x, then cost of pistachios is x-11.

6*x+5*(x-11) = 11*20
Solving for x, x = 25

(C) is the answer

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19 Dec 2025, 13:22

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shopkeeper mixes by weight A:P=6:5
SP=$25, Profit%=25%
so CP=25/1.25=$20 cost price of the total mixture
given that cost(A)=$11+ cost(P) all given in cost per pound
cost(A) can't exceed $20
so $14 is the best choice
A

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19 Dec 2025, 14:07

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Bunuel

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25=cp x 125/100

cp = 20.

We have weights of mixture and avg cost price..if we plug in weighted average formula

6 x (price of almonds ) + 5 x (price of pistachios) / 5+6 = 20.

20 x 11 = 6a+5p. ( we know a = 11+p).

hence 20x11= 6(11+p) + 5p

20x11= 66+ 11p.

220-66=11p.

solve for p and will get p as 14

if p is 14, a is 11+14=25.

price of almonds is 25

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19 Dec 2025, 14:19

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almond = 6x , sp = 11+ p
pista= 5x, sp= p

now sold at 25%, 25= 5/4 (a)
a= 20= cost price
(6x)(11+p) + (5x)(p) / 11x = 20
66+ 11p = 220
11p = 154
p= 14
almond price- 25

Bunuel

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19 Dec 2025, 14:35

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Bunuel

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let price of pistachio per kg=x
almond= x+11
cost of mixture of ratio6:5=25
so 6kg almond mixed with 5kg pistachio selling price= 11x25
cost price= 6(x+11)+ 5x
but selling price = 125% of cost price
so
11x25= 125% of [ 6(x+11) + 5x]
x=14
almond price per kg = x+11=25
Ans-C

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19 Dec 2025, 14:50

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$\frac{A}{P} = \frac{6}{5}$

s.p = 25$

cp(1.25) = s.p
cp = 4/5 * 25
= 20$

cost of almonds be x
cost of pistachios will be x-11

weighted average price:
$\frac{(x *6 + (x-11) * 5)}{11} = 20$

6x + 5x - 55 = 220
11x = 275
x= 25$

Ans: C

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19 Dec 2025, 20:14

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Let the weight of almonds in the mixture be 6x , weight of pistachios be 5x. Total weight of the mixture will be 11x. If the mixture is sold at $25 per pound , then total sale price of mixture will be 25*11x = $275x/pound. The mixture is sold at 25% profit. So Cost price of mixture will be (275x)/(5/4) = $220x/pound. Now , let cost price of almonds be A , and cost price of Pistachios be P.

A*6x +P*5x = 220x

Also we know that A = P+11 ,

6x(P+11) +P*5x =220x

From here P = $14/pound

Almond = 14+11 = $25/pound

Bunuel

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19 Dec 2025, 21:12

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A = 11 + P;

Removing 25% profit, the actual cost is 20.

6A + 5(A-11) = 20*11
=> A = 25

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let almond cost -> a $/pound and pistachio -> a - 11 $/pound
mixed in ratio 6:5 -> final cost $25 with 25% profit, hence before profit the cost = $20 (25% of 20 = 5 which adds on to 20 to give 25)

acc to question: 20 = [6a + 5(a-11)]/11 => a = 25

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19 Dec 2025, 21:45

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Let CP of Pistachio be: $p
then, CP of Almond: $p + 11

CP= SP / Profit % = 25/1.25 =20
Ratio by weight of Almond : Pistachio = 6 : 5
So, Weighted average for the total mixture--> [6(p+11) + 5p] / 11 = 20
--> 6p + 66 + 5p = 220
--> 11p = 11(20-6)
--> p= 14
So, CP of Almond = 14 + 11 = $25 (C)