If the cost of `5 2/5` litres of milk is Rs `236 1/4`, find its cost per litre

Answer

To find the cost per litre of milk, we need to follow these steps:

### Step 1: Convert the mixed numbers to improper fractions
1. Convert `5 2/5` litres to an improper fraction.
- \( 5 = \frac{5 \times 5}{5} = \frac{25}{5} \)
- Adding the fraction: \( \frac{25}{5} + \frac{2}{5} = \frac{27}{5} \)
- So, \( 5 \frac{2}{5} = \frac{27}{5} \) litres.

2. Convert `236 1/4` to an improper fraction.
- \( 236 = \frac{236 \times 4}{4} = \frac{944}{4} \)
- Adding the fraction: \( \frac{944}{4} + \frac{1}{4} = \frac{945}{4} \)
- So, \( 236 \frac{1}{4} = \frac{945}{4} \) Rs.

### Step 2: Set up the equation for cost per litre
To find the cost per litre, we divide the total cost by the total litres:
\[ \text{Cost per litre} = \frac{\text{Total Cost}}{\text{Total Litres}} = \frac{\frac{945}{4}}{\frac{27}{5}} \]

### Step 3: Simplify the division of fractions
When dividing fractions, we multiply by the reciprocal:
\[ \frac{945}{4} \div \frac{27}{5} = \frac{945}{4} \times \frac{5}{27} \]

### Step 4: Multiply the fractions
Multiply the numerators and the denominators:
\[ \frac{945 \times 5}{4 \times 27} = \frac{4725}{108} \]

### Step 5: Simplify the fraction
Now, we simplify \( \frac{4725}{108} \):
- Find the GCD (Greatest Common Divisor) of 4725 and 108, which is 9.
- Divide both the numerator and the denominator by 9:
\[ \frac{4725 \div 9}{108 \div 9} = \frac{525}{12} \]

### Step 6: Convert to mixed number
To convert \( \frac{525}{12} \) to a mixed number:
- Divide 525 by 12:
- 12 goes into 525, 43 times (since \( 12 \times 43 = 516 \)).
- The remainder is \( 525 - 516 = 9 \).
- So, \( \frac{525}{12} = 43 \frac{9}{12} \).

### Step 7: Simplify the fraction part
The fraction \( \frac{9}{12} \) can be simplified:
- Divide both numerator and denominator by 3:
\[ \frac{9 \div 3}{12 \div 3} = \frac{3}{4} \]

### Final Answer
Thus, the cost per litre of milk is:
\[ 43 \frac{3}{4} \text{ Rs.} \]

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