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GMAT Club Olympics 2025 (Day 9): A specialty fertilizer blend contains

1 2 3 4 5

kvaishvik24

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x kg of Blend 1 contains 40% Nitrogen and 60% Potassium
y kg of Blend 2 contains 40% Nitrogen and 60% Potassium

Total mixture : x+y =24 kg

Now, total nitrogen is 35%, so:
0.40x+0.20y=0.35(x+y)
0.40x+0.20y=0.35x + 0.35y
0.05x=0.15y
x=3y

So, total mixture is 3y+y = 24
y=6kg

We are asked kgs of phosphorus i.e.,
80% of y
0.80 * 6
4.8 Kgs

Option D

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Blend 1 ---> Nitrogen(N) : Potassium (K) = 40:60 = 2:3
Blend 2 ---> Nitrogen (N) : Phosphorus (P) = 20:80 = 1:4

Using the allegation method, we get,

After mixing blends 1 and 2, we get them in the ratio of B1:B2 = 3:1
4 units of this mixed blend are 24 Kg
1 unit of this mixed blend is 6kg

Thus, we can say that B2 is 6kg
In B2, we have N : P = 1:4

So, 5 units of B2 is 6kg
1 unit of B2 is 6/5 kg
4 units of B2 (which is nothing but P) is (6/5)*4 = 4.8 kg

Answer D.

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Solving mixture problems can be performed through setting up a matrix:

	nitrogen	Kg	Final mixture
Blend A	0.4	24-x	9.6-0.4x
Blend B	0.2	x	0.2x
Final mixture	0.35	24	8.4

From here we can set up the equation: 8.4 = 9.6 - 0.4x + 0.2x which solves to x = 6. Now that we know that the second blend will be 6 kg we can calculate the amount of phosphorus to be 0.8 * 6 = 4.8. Answer D.

Regards,
Lucas

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To reach an overall nitrogen level that sits closer to the richer blend (40% nitrogen) than to the poorer one (20% nitrogen), you must use 3 times as much of the 40/60 blend as of the 20/80 blend. In other words, for every 4 total parts of mixture, 3 parts come from the 40% nitrogen fertilizer and 1 part from the 20% nitrogen fertilizer.
Since the finished mixture weighs 24 kg, dividing it into 4 equal parts gives 6 kg per part. 3 parts (18 kg) are drawn from the 40/60 blend and one part (6 kg) from the 20/80 blend. Only the second blend contributes any phosphorus, and because that blend is 80% phosphorus, those 6kg deliver just under 5kg of phosphorus to the final batch. Also, 80% of 6 kg is 4.8 kg, so the finished 24 kg mixture contains 4.8 kg of phosphorus.

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Total quantity (Blend A + Blend B) = 24 kg
% of N= 35/100 * 24 = 42/5

Blend A
Let x be the quantity of blend A:-
N in kg = 0.4x
K in kg=0.6x

Blend b
Let (24-x) be the quantity of blend A:-
N in kg = (24-x)0.2
P in kg = (24-x)0.8

Blend A + B
N quantity:

(24-x)0.2 + 0.4x = 42/5
x=18
24-18=6 kg

kilograms of phosphorus= 6*0.8=4.8 kg
Correct answer is D

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1st blend contains 40 percent nitrogen and 60 percent potassium by weight. The 2nd 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. That means (blend 2) / (blend 1) = (40 - 35)/(35-20) = 5/15 = 1/3

Assume the weight of blend 2 = a, then the weight of blend 1 = 3a.

3a + a = 24 kg, so a = 6. Phosporus accounts for 80% of 6. Hence Phosphorus = 4.8 kgs

Answer: D

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Let the total weight of fertilizer 1= X, fertilizer 2= Y

According to the given information:
X+Y = 24
40%*X + 20%*Y = 35% *24
$\\
4*X + 2*Y = \frac{3.5}{10} *24\\
$
2X + Y =42

Solving the two equations, we get X= 18, Y= 6

Phosphorus in the mixture = 80%*Y = 80%*6 = 4.8

Answer: Option D

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Speciality Fertilizer contains 40% Nitrogen, and 60% Potassium.

A different blend contains 20% Nitrogen and 80% Phosphorus.

When we mix the two fertilisers , we get 35% of nitrogen.

40% ————— 35% ——————— 20%

15%. : 5%

The ratio of speciality fertilizer : Different blend = 3:1

The final mixture contains 24 kilograms. This 24 kilograms is split into 18 kg of Speciality Fertilizer and 6 kg of Different Blend.

The phosphorus in different blend is in the ratio 1:4 = Nitrogen : Phosphorous

The different blend is 6 kg in total. And Phosphorous is (4/5)*6 = 4.8 Kg

Option D

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using shortcut formula
20 40
\ /
35
/ \
(40-35) (35-20)
5 : 15
1 : 3
We know 1x+3x = 24kg, hence x = 6kg
Only the first mixture contains phosphorus and we are adding 1x = 6kg of it
Hence the Phosphorus in it = 80% of 6kg = 4.8kg

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Bunuel

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Call: x kg = 0.4 Nitrogen + 0.6 Potassium
y kg = 0.2 Nitrogen + 0.8 Phosphorus
we have : x + y = 24 and 0.4x + 0.2y = 0.35*24=8.4
=> 0.4x + 0.2*(24 - x) = 8.4
=> 0.4x + 4.8 - 0.2x = 8.4
=> 0.2x = 3.6 => x = 18
=> Phosphorus = (24 - 18)*0.8 = 4.8kg

Answer: D.4.8

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	Nitrogen	Other substance
Mixture A	40%	60%
Mixture B	20%	80%
Final Mixture	35%	65%

Ratio of Mixtures, $\frac{A}{B}=\frac{35-20}{40-35}=\frac{3}{1}$

Out of 24 kg of final mixture, 18kg is Mixture A & 6kg is Mixture B

Mixture B has 80% of phosphorus. $0.8*6=4.8 kg$

Answer: D

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Let N be for nitrogen
K for potassium
P for phosphorus

In first blend, N:K = 2:3
In second blend N: P = 1:4

Let x and y be the respective weights
x+y=24
also it contains 35% nitrogen
=> 0.4x+0.2y = 0.35*24 = 8.4

Solving for x and y, we get x=18, y=6
Only second blend contain phosphorus, so total weight of phosphorus = 0.8*y = 0.8*6 = 4.8kg

Hence D is answer

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mixtures	N%	K%	P%	weight
I	40	60	0	24-x
II	20	0	80	x
combination I&II	35			24

let x be the weight of the second mixture in II;N-nitrogen K-potassium P-phosphorus

using law of allegation for N
40(24-x)+20x=35*24
on solving we get x=6 kg
so weight of phosphorus in the resultant mixture=80% of 6=4.8 kg

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Blend A: 40% nitrogen
Blend B: 20% nitrogen
Mixture: 35% nitrogen
With the mapping strategy, we can easily say that the ratio of A to B in the final mixture is 3:1
Or we can calculate, assuming A and B for the amount of each, we have: $\frac {40}{100}A + \frac {20}{100}B = \frac {35}{100}(A+B) $, which will give us $\frac{A}{B}=3$
Anyway, if the ratio of A to B is 3:1 in the final mixture, and the total weight of the final mixture is 24, the amounts of Blends A and B in the mixture are 18 and 6, respectively.
The question asks for the weight of phosphorus, which is 80 percent of blend B, will equal: $\frac {80}{100} * 6 =4.8$

The answer is D.

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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?

Let A = "specialty fertilizer", B = "different blend", and F = "final mixture"

Since both have Nitrogen, and is presented for us the Nitrogen concentration for the final result, I'll use Nitrogen as our baseline to perform the calculations required.

Alligation method:

20%..............35%........................40%
|____<-X->_____|______<-Y->________|
B....................F..............................A

X equals distance between 20 and 35 = 15
Y equals distance between 35 and 40 = 5

Now, we cross and find the proportion:

A:B = 15p:5p
A:B = 3p:1p

Ouw final blend have 24kg. Since our proportion is 3:1, that sums 4, our p = 24/4 = 6.

Final blend then contains 18kg of A and 6kg of B.

The component that contains phosphorus is B, in a 80% proportion. Therefore, our amount in kg of phosphorus in final mixture is equal to 6kg*0.8 = 4.8kg

Answer = D. 4.8

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Bunuel

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20 ----------- 35 ---- 40

Ratio = 15/5 = 3:1

In the 24 kgs of the final mixture only 1 part is that blend that contains phosphorus.

1/4 * 24 = 6

In the 6kgs, 80% is phosphorous.

Amount = 6 * 0.8 = 4.8

Option D

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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?

Seeing a mixture problem, first trigger is to check if we can use allegation, in the above problem we can.

Blend A = 40% nitrogen.

Blend B = 20% nitrogen.

Mixture of A and B = 35% nitrogen.

Using allegation, we get the ratio of Blend A to Blend B in the mixture to be 3:1.

So, as there are a total of 4 parts (3+1), simply adding the ratios, we get 4 parts = 24kg, so 3 parts = 18kg and 1 part = 6kg. (using unitary method)

The 1 part belongs to blend B, only blend to have phosphorus, so this 6kg has 80% of phosphorus in it.

Therefore, 6*80% = 4.8 kg.

Option D.