Dia and Urea are two chemical fertilizers. Dia is consists of N,P and K and Urea consists of only N and P,A mixture of Dia and Urea is prepared in which the ratio of N,P and K is `26%,68% and 6%` respectively. The ratio of N,P and K in Dia is `20%,70% and 10%` respectively. what is the ratio of N and P in the Urea?

Options

A. `27% and 63%`
B. `33% and 67%`
C. `35% and 65%`
D. `70% and 30%`

Answer

To find the ratio of Nitrogen (N) and Phosphorus (P) in Urea, we can follow these steps:

### Step 1: Understand the Composition of the Mixture
We know that the mixture of Dia and Urea has the following composition:
- Nitrogen (N): 26%
- Phosphorus (P): 68%
- Potassium (K): 6%

And the composition of Dia is:
- Nitrogen (N): 20%
- Phosphorus (P): 70%
- Potassium (K): 10%

Urea consists of only Nitrogen (N) and Phosphorus (P).

### Step 2: Set Up the Equations
Let’s denote:
- \( x \) = the fraction of Dia in the mixture
- \( y \) = the fraction of Urea in the mixture

From the information given, we know:
- \( x + y = 1 \) (since the total mixture is 100%)

The contributions to N and P from Dia and Urea can be expressed as:
- For Nitrogen:
\[ 0.20x + N_U = 0.26 \]
- For Phosphorus:
\[ 0.70x + P_U = 0.68 \]

Where \( N_U \) and \( P_U \) are the percentages of N and P in Urea.

### Step 3: Solve for \( N_U \) and \( P_U \)
From the first equation, we can express \( N_U \):
\[ N_U = 0.26 - 0.20x \]

From the second equation, we can express \( P_U \):
\[ P_U = 0.68 - 0.70x \]

### Step 4: Find the Ratio of N and P in Urea
Since Urea consists only of N and P, we need to find the ratio \( \frac{N_U}{P_U} \):
\[ \frac{N_U}{P_U} = \frac{0.26 - 0.20x}{0.68 - 0.70x} \]

### Step 5: Substitute \( x \) and Simplify
To find the values of \( x \) and \( y \), we can use the total percentage of K in the mixture:
- K in Dia = 10% and K in Urea = 0%
- The total K in the mixture is 6%, so:
\[ 10x + 0y = 0.06 \]
This implies:
\[ x = 0.06 / 0.10 = 0.6 \]
Thus, \( y = 1 - x = 0.4 \).

### Step 6: Substitute \( x \) Back
Now substituting \( x = 0.6 \) back into the equations for \( N_U \) and \( P_U \):
\[ N_U = 0.26 - 0.20(0.6) = 0.26 - 0.12 = 0.14 \]
\[ P_U = 0.68 - 0.70(0.6) = 0.68 - 0.42 = 0.26 \]

### Step 7: Calculate the Ratio
Now we can find the ratio of N to P in Urea:
\[ \frac{N_U}{P_U} = \frac{0.14}{0.26} = \frac{14}{26} = \frac{7}{13} \]

### Final Answer
The ratio of Nitrogen (N) to Phosphorus (P) in Urea is \( 7:13 \).

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