In a hospital there is a consumption of 1350 litres of milk for 70 patients for 30 days. How many patients will consume 1710 litres of milk in 28 days ?

Options

A. 59
B. 85
C. 95
D. 105

Answer

To solve the problem step by step, we will use the concept of direct variation. The amount of milk consumed is directly proportional to the number of patients and the number of days.

### Step 1: Understand the given data
We have:
- Consumption of milk (M1) = 1350 litres
- Number of patients (P1) = 70
- Number of days (D1) = 30

We need to find out how many patients (P2) will consume 1710 litres of milk (M2) in 28 days (D2).

### Step 2: Set up the relationship using the formula
We can set up the relationship as:
\[ \frac{M1}{P1 \times D1} = \frac{M2}{P2 \times D2} \]

### Step 3: Substitute the known values into the equation
Substituting the known values:
\[ \frac{1350}{70 \times 30} = \frac{1710}{P2 \times 28} \]

### Step 4: Calculate the left side of the equation
Calculating the left side:
\[ 70 \times 30 = 2100 \]
So,
\[ \frac{1350}{2100} \]

### Step 5: Simplify the left side
Now simplify:
\[ \frac{1350 \div 105}{2100 \div 105} = \frac{12.857}{20} \approx 0.64285 \]

### Step 6: Set up the equation for P2
Now we can set up the equation:
\[ \frac{1350}{2100} = \frac{1710}{P2 \times 28} \]

Cross-multiplying gives:
\[ 1350 \times (P2 \times 28) = 1710 \times 2100 \]

### Step 7: Calculate the right side
Calculating the right side:
\[ 1710 \times 2100 = 3591000 \]

### Step 8: Solve for P2
Now we have:
\[ 1350 \times 28 \times P2 = 3591000 \]
Calculating \(1350 \times 28\):
\[ 1350 \times 28 = 37800 \]
So,
\[ 37800 \times P2 = 3591000 \]
Now, divide both sides by 37800:
\[ P2 = \frac{3591000}{37800} \]

### Step 9: Calculate P2
Calculating \(P2\):
\[ P2 = 95 \]

### Conclusion
Thus, the number of patients that will consume 1710 litres of milk in 28 days is **95**.