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

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Bunuel

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19 Dec 2025, 10:00

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Bunuel

GMAT Club Official Explanation:

Assume the total weight of the mixture is 11 pounds. This simplifies the math because the total weight (11 pounds) matches the sum of the ratio (6 parts almonds + 5 parts pistachios).

Almonds: 6 parts of the 11-pound mixture = 6 pounds of almonds.
Pistachios: 5 parts of the 11-pound mixture = 5 pounds of pistachios.

Let the cost of pistachios per pound be p. Then, the cost of almonds per pound is p + 11.

Thus, the total cost of the 11-pound mixture is:

6(p + 11) + 5p

The selling price of the mixture is 25 dollars per pound, and the shopkeeper earns a 25% profit. So the cost price of the mixture is 25/1.25 = 20 dollars per pound, and 20 * 11 for 11 pounds.

So, we get:

6(p + 11) + 5p = 20 * 11
p = 14

So, the cost of pistachios is 14 dollars per pound, and the cost of almonds is p + 11 = 14 + 11 = 25 dollars per pound.

Answer: C.

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19 Dec 2025, 09:05

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Selling price is 25 with 25% profit,
so CP of mixture = 25/1.25
=> 20

Let pistachios cost = x per pound,
then almond cost = x+11

Average cost using ratio 6:5:

(6(x+11) + 5x )/ 11 = 20
6x+66+5x = 220
11x=154
x = 14
So almond cost = 14+11
=>25

Answer: C

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19 Dec 2025, 09:08

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let take a mix with 6pound almond, 5 pound pistachio
total cost = 11 * 25 = 275
profit is 25% so cost price is 275/1.25 = 220
let cost of pista be x per pound
total cost
220 = 6* ( 11 + x) + 5x
solvong for x we get x = 14
so cost of almond = x + 11 = 25

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19 Dec 2025, 09:09

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let price of almond be A

[6A +5(A-11)]/11 = 20
=6A + 5A - 55 = 220
= 11A = 275
A = 25

Answer C

Bunuel

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19 Dec 2025, 09:12

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Bunuel

Let the cost price per pound of pistachio=x
Let the cost price per pound of almonds=x+11
SP=$25; Profit=25%
CP of mixture: 25/1.25=20
The average cost of the mixture is $20 per pound.
Using WA: Almond:Pistachio = 6:5
(6(x+11)+5x)/11=20
11x=154
x=14
Cost of almonds=14+11=$25 (OPTION C)

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19 Dec 2025, 09:17

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let price per pound of almonds be x
price per pound of pistachios = x-11

[(25*11k) - (6x+5(x-11))]/(6x + 5(x-11)) = 1/4
on solving x = 25
So, answer = C

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19 Dec 2025, 09:19

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Pistachio price=x per pound
Almond price=x+11 per pound

ratio=6:5 almond:pistachio
mix= 11p

total cost=6(x+11)+5x
=6x+66+5x=11x+66

cost per pound
(11x+66)/11=x+6
selling per pound=25
profit=25%
cost price per pound
cost=25/1.25=20

x+6=20
x=14
pistachio=14$
almond=x+11=25$

=25$

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19 Dec 2025, 09:22

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Let's assume taking 6 pounds of almonds $X + 11 per pound & 5 pounds of pistachios $ X per pound.
Sold for $ 25 making 25% profit. Hence cost per pound of mixture is $20.
For 11 pounds mixture
220= 6X + 66 + 5X
X =.14
Price of almonds per pound= X +11=25

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19 Dec 2025, 09:22

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Let the cost price of almonds be $x per pound.
The Cost price of pistachio = $x - $11 per pound

The Cost price of 1 pound of mixture = [6*x + 5(x-11)]/(6+5) = (11x - 55)/11 = x - 5

The Sales price of 1 pound of mixture = (x-5)*1.25 = 25
x-5 = 25/1.25 = 20
x = $25

Th Cost pride of almonds per pound = $25

IMO C

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19 Dec 2025, 09:22

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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

ratio of A : P = 6:5
cost of mixture is $25 sold at 25% profit
exact cost is 25/1.25 = 20
cost of P = x
cost of A =y
y=11+x

20 = 6*(x+11)+ 5x / 11
220 = 11x+66
154=11x
x= 14
y= 25
option C ; $25 is correct

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19 Dec 2025, 09:28

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SP=CP(1+Profit %)
25= CP(1+0.25)
CP= 25/1.25=20
Cost price of mixture = $20 per pound

Mixture has almonds and pistachios in 6:5 by weight
Let, cost of pistachios = x and cost of almonds = x+11
(6(x+11)+5x)/(6+5) = 20
x=14

Cost of almonds = x+11 = 14+11=25

C

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19 Dec 2025, 09:32

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25% profit means 1.25*cost=sale Price=25. so, cost =20.
ratio of mixing is 6:5, so if K is per pound cost of pistachio. the almond Price K+11, Mixture price (6*(K+11) +5k)/11=20, So, K =14, pistacchio price 14+11=25.

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19 Dec 2025, 09:37

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Let the cost of a pound of Pistachio be P
Cost of a pound of Almond will be (P + 11)

The mixture is sold at a profit of 25% at $25 / pound
Cost price of mixture = 25 x 100 / 125 = $20 per pound

Almond and Pistachio are mixed in the ratio of 6:5.
If we take 6kg almond and 5kg pistachio, total of 11 kg mixture will be prepared with the cost price of 11 x 20 = $220

Also, total cost of almond + total cost of pistachio = total cost of mixture
6(P + 11) + 5P = 220
=> 11P + 66 = 220
=> P = 14

If cost of Pistachio (P) is $14 / pound, cost of almond (P + 11) = $25 per pound.

Hence, Option C

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19 Dec 2025, 09:50

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Bunuel

The ratio of almonds:pistachio is = 6:5
almonds = 6lb
pistachio = 5lb

Total cost = 6(p+11) + 5p = 6p + 66 + 5p = 11p + 66
Cost per lb of mixture = 11p + 66/11

mixture = 1.25 x cost per lb = 5 => cost per lb = 25/1.25 = 20

p + 6 = 20 => p = 14
p + 11 = 14 + 11 = 25

Cost of almonds per lb is $25
Option C

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19 Dec 2025, 09:53

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Let the weight of almonds and pistachios be $6x$ and $5x$ respectively. Total weight $= 11x$.

Cost price per pound $= C$

Selling price per pound $= $25 = 1.25C$
$=> C = $20$

$=>$ $\frac{total cost}{total weight}$ $= $20$

$=>$ total cost $= 20*11x = 220x$

Let the cost per pound of pistachios be $p$. Then cost per pound of almonds is $11+p$

$=> 6x (p+11) + 5xp = 220x$

$=> 11xp + 66x = 220x$

$=> 11xp = 154x$

$=> p = \frac{154}{11} = 14$

$=>$ cost of almonds per pound $= p + 11 = 14 + 11 = 25$

Answer is C.

Bunuel

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19 Dec 2025, 10:07

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Let the price of Pista be P
Let the price of Almonds be P+11

A: P = 6:5 by wt

hence avg cost = 6x(P+11) + 5P/11
avg cost=11P+66/11=>P+6

selling price= 1.25 x Cost price
25=1.25x CP
CP= 25/1.25=20

equating CP and Avg cost (as it is derived from cost price and NOT selling price)

20=p+6
p=14
a=14+11=25

Answer is 25

Bunuel

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19 Dec 2025, 10:09

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Let pistachios be x and almonds x+11

6(x+11)5x/6+5
11x+66/11=x+6

now, mixture is sold at 25 pwr pound with a 25% profit

25/1.25=20
x+6=20
x=14

14+11=25

Bunuel

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19 Dec 2025, 10:21

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Given:
ratio of almond and pistachio by weight = 6:5
price of almond=p+11
per pound cost= 25, profit 25%

Let cost price be x then,
$25=1.25x
x=20

from the weighted average cost, we can find the cost price of almond
6(x+11) / 11 + 5(x)/11 = 20
(6x +66+5x)/11=20
11x+66=220
11x=154
x=14
almond = 14+11=25
Option c

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19 Dec 2025, 10:30

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Bunuel