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605-655 Level|   Mixture Problems|         
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GMAT Club Olympics 2025 (Day 9): A specialty fertilizer blend contains 10 Jul 2025, 08:00
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A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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D
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GMAT Club Olympics 2025 (Day 9): A specialty fertilizer blend contains 10 Jul 2025, 08:30
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Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8
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­

GMAT Club Official Explanation:



Let the amount of the first blend be x kg, so the second blend is 24 - x kg.

The first blend is 40% nitrogen, so it contributes 0.4x kg of nitrogen.
The second blend is 20% nitrogen, so it contributes 0.2(24 - x) kg of nitrogen.
The total nitrogen in the final mixture is 35% of 24, which is 8.4 kg.

Set up the equation:
0.4x + 0.2(24 - x) = 8.4
x = 18

That means 18 kg of the first blend and 6 kg of the second. Only the second blend has phosphorus, and it's 80% of that 6 kg. So, phosphorus = 0.8 * 6 = 4.8 kg

Answer: D.
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Mixture 1 be x 40 percent nitrogen and 60 percent potassium by weight
mixture 2 be y 20 percent nitrogen and 80 percent phosphorus
final mixture is 24 kgs , 35 % N2 = .84

x+y=24

.4x+.2y = .84

x=24-y

.4*(24-y)+.2y= .84
solve for y
y=6 , is the second mixture weight

Phosphorous will be 6*.8 = 4.8 kgs

OPTION D

Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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GMAT Club Olympics 2025 (Day 9): A specialty fertilizer blend contains 10 Jul 2025, 08:24
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Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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Given: fertiliser A with 0.4 nitrogen and fertiliser B with 0.2 nitrogen by weight.
The final mixture contains 0.35 nitrogen by weight so using
0.4. 0.2

0.35

15 : 5
3 : 1
So the final ratio of A and B is 3:1 and we given total weight of the final mixture as 24 kg. Hence the weight of fertiliser A = 18Kg and B = 6Kg
And the weight of phosphorus comes from fertiliser B = 0.8 * 6kg = 4.8kg Hence the answer is option D
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Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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nitrogen to potassium is 40% to 60%, nitrogen to phosphorus is 20% to 80%, nitrogen is 35% in the mixture.(2:3)+(1:4) Implies 2/5+1/4=35 %ie 13/20 therefore 4/5+0=16/20 16/20*35*20/13*24/100=
10.8
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Carefully reading the question pays off, especially in questions like these, waste 2 minutes as I read potassium as phosphorus.

Anyhow, coming to the solution, first we would need to calculate the weight of each blend. Let x' be the weight of first blend, then

40% of x + 20% of (24-x) = 35% of 24, solving for x we get, x= 18 kg, also then the eight of second bag would be 24-18 = 6 kg

Hence, weight of phosphorus = 80% of 6 = 4.8 kg

hence option D
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Let x be weight of blend A.
Let y be weight of blend B

x+y=24
Nitrogen in the mixture 0.35⋅24=8.4 kg

0.40x+0.20y=8.4

y=24-x(from eq 1)

0.40x+0.20(24−x)=8.4
0.20x=3.6
x=18 y=6

Phosphorous in blend B is 0.8*6=4.8

Hence answer is D 4.8

Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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Blend A = 40 percent nitrogen and 60 percent potassium by weight = x
Blend B = 20 percent nitrogen and 80 percent phosphorus = y
Also, x+y = 24 kg ,..............(1)

40% Nitrogen in A + 20% Nitrogen in B = 35% in 24 kg
0.40x +0.20 y= 0.35*24=8.4
2x+y= 42...........(2)

Solve (1)&(2)
2x+y-x-y= 42-24
x= 18 and y=24-18=6

Phosphorus= 80% *6 =4.8 kg

D
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Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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This is a typical mixture question

A is 40 percent nitrogen and 60 percent potassium
B is 20 percent nitrogen and 80 percent phosphorus

When mixed the final will have nitrogen between 20 ............40 This will be divided in the ratio by which the mixture is mixed.

20..............35...........40 => A:B is 3:1

Hence, B will be of 6KG by weight. Now of this 6 Kgs 80 percent is phosphorus. => 4.8kgs

Hence, total phosphorus is 4.8kgs. IMO D
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let mix a & b
0.4a+0.2b=0.35a+0.35b
a=3b

a+b=24

a=18, b=6

phosphorous=0.8*6=4.8

Ans D
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Using weighted averages on nitrogen present in each
Blend 1: 40 percent nitrogen, Blend 2: 20 percent nitrogen, Final Mixture: 35 percent nitrogen.

20 40
35
5 15
(1:3) OR
Blend 1: Blend 2 = 3:1 in the final mixture of 24kg

Hence Blend 2 is 1/4 *24 = 6kg in the final mixture
Amount of phosphorus = 8/10 *6 = 4.8kg

Ans D
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My Answer is 4.8. Option D

Let us consider W1 is the weight of the 1st fertilizer solution and W2 is the weight of the 2nd fertilizer solution.
We are given the following information:
Solution 1:
Nitrogen : 40%=0.4
Potassium: 60%=0.6
Solution 2:
Nitrogen: 20%=0.2
Phosphorus:80%=0.8
Final Mixture:
Total weight = 24 kg
Nitrogen (N): 35%=0.35

The total weight of the final mixture is the sum of the weights of the two blends: W1+W2=24...........(1)

For the nitrogen weight in each solution, we can take

Nitrogen in solution 1 = 40% of W1=0.40W1
Nitrogen in solution 2 = 20% of W2=0.20W2

Total Nitrogen in the final mixture = 35% of 24 kg = 0.35×24 kg=8.4 kgs

We can equate for nitrogen 0.40W1+0.20W2=8.4...............(2)


From Equation 1, we can take W1=24−W2

Let's substitute in equation2: 0.40(24−W2)+0.20W2=8.4 0.40×24−0.40W2+0.20W2=8.4 9.6−0.20W2=8.4

Now on solving, we will get W1= 18kgs and W2=6Kgs

In the question it is given Solution 2 has 80% of the phosphorus.

Amount of Phosphorus 0.80×6 kg Amount of Phosphorus = 4.8 kg
And, the final mixture contains 4.8 kilograms of phosphorus

Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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Assume:
Formula X contains 40g nitrogen and 60g potassium per 100g.
Formula Y contains 20g nitrogen and 80g phosphorus per 100g.

Given the equation:
(40X + 20Y) / (100X + 100Y) = 35/100

Solving yields:
1500Y = 500X
X:Y = 3:1

This implies:
In every 100g,
Nitrogen: (40 3/4) + (20 1/4) = 35g
Potassium: 60 3/4 = 45g
Phosphorus: 80 1/4 = 20g

The ratio is:
35:45:20

For 24kg, the phosphorus content is:
24kg * 20/100 = 4.8kg
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Two fertilizer blends are combined to create a 24-kilogram mixture that contains 35 percent nitrogen. The first blend is made up of 40 percent nitrogen and 60 percent potassium, while the second blend contains 20 percent nitrogen and 80 percent phosphorus. To find how much phosphorus is in the final mixture, consider how the nitrogen levels combine. Since the final blend is 35 percent nitrogen, or 8.4 kilograms, and the first blend has more nitrogen than the second, more of it must be used. By determining the proper ratio that results in 8.4 kilograms of nitrogen, it turns out that 18 kilograms of the first blend and 6 kilograms of the second are mixed. Only the second blend contains phosphorus, and since it is 80 percent phosphorus, 80 percent of the 6 kilograms—or 4.8 kilograms—is phosphorus. Therefore, the final mixture contains 4.8 kilograms of phosphorus.
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Fertilizer A : 40% (Nitrogen) & 60% (Potassium)
Fertilizer B : 20% (Nitrogen) & 80% (Phosphorus)
Let x be the % of Fertilizer A in final mixture
so the nitrogen content in final mixture could be written as:
0.4x+0.2(1-x)=0.35 .....(35% given)
so, x=4/5
Fertilizer A : Fertilizer B = 4:1
Phosphorus content = 0.80 X 1/5 X 24kgs
Answer = 4.8kgs Option D
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40 ___35__________20

(40-35)/(35-20) = 1/3

40% N blend is 3 times the 20% N blend
Let the weight of these belnds be 3x and x respectively
3x+x=24
x=6

kilograms of phosphorus = 6*0.8=4.8
Bunuel
A specialty fertilizer blend contains 40 percent nitrogen and 60 percent potassium by weight. A different blend contains 20 percent nitrogen and 80 percent phosphorus. When these two blends are combined to create a final mixture, the result contains 35 percent nitrogen. If the final mixture weighs 24 kilograms, how many kilograms of phosphorus does it contain?

A. 3.2
B. 3.6
C. 4
D. 4.8
E. 10.8


 


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Here's a step-by-step solution to this mixture problem:

1. Define Variables:

Let Blend 1 be the first fertilizer blend.

Let Blend 2 be the second fertilizer blend.

Let x be the weight (in kg) of Blend 1 in the final mixture.

Let y be the weight (in kg) of Blend 2 in the final mixture.

2. Set Up Equations Based on Total Weight and Nitrogen Content:

Total Weight: The final mixture weighs 24 kg.
x+y=24 (Equation 1)

Nitrogen Content:

Blend 1: 40% nitrogen = 0.40x kg of nitrogen

Blend 2: 20% nitrogen = 0.20y kg of nitrogen

Final Mixture: 35% nitrogen of 24 kg = 0.35∗24 kg of nitrogen

So, 0.40x+0.20y=0.35∗24
0.40x+0.20y=8.4 (Equation 2)

3. Solve the System of Equations:

From Equation 1, we can express y in terms of x:
y=24−x

Substitute this into Equation 2:
0.40x+0.20(24−x)=8.4
0.40x+4.8−0.20x=8.4
0.20x=8.4−4.8
0.20x=3.6
x=3.6/0.20
x=18 kg

Now find y:
y=24−x=24−18=6 kg

So, the final mixture contains 18 kg of Blend 1 and 6 kg of Blend 2.

4. Calculate Phosphorus Content:

Phosphorus is only present in Blend 2, and Blend 2 contains 80% phosphorus.
Amount of phosphorus = 80% of y
Amount of phosphorus = 0.80∗6 kg
Amount of phosphorus = 4.8 kg

The final answer is 4.8
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GMAT Club Olympics 2025 (Day 9): A specialty fertilizer blend contains 10 Jul 2025, 09:39
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Blend A: 40% nitrogen, 60% potassium
Blend B: 20% nitrogen, 80% phosphorus
Final mixture: 35% nitrogen, total weight = 24 kg

a + b = 24
0.4a + 0.2b = 0.35 * 24 = 8.4

Solving for a and b,
4*(24 - b) + 2b = 84
96 - 4b + 2b = 84
96 - 2b = 84
2b = 12
b = 6 --> a = 18

Phosphorus = 0.8 * b = 0.8 * 6 = 4.8 kg
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M1 contains :
N = 40%
K = 60%

M2 contains :
N = 20%
P = 80%

Using alligation method,
We get M1 : M2 = 3:1

Thus M2 is 1/4 th of the Total Mixture
So M2 = 6kg
Thus P is :
6*0.8 = 4.8 kg

Thus Answer is D
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