Milk is sold at Rs `16 3/4` per litre. Find the cost of `6 2/5` litres of milk

Answer

To solve the problem, we need to find the cost of `6 2/5` litres of milk when the cost of 1 litre is `16 3/4` rupees. Let's break it down step by step.

### Step 1: Convert the mixed numbers to improper fractions
First, we convert `16 3/4` and `6 2/5` into improper fractions.

For `16 3/4`:
- Multiply the whole number (16) by the denominator (4):
\( 16 \times 4 = 64 \)
- Add the numerator (3):
\( 64 + 3 = 67 \)
- Therefore,
\[ 16 \frac{3}{4} = \frac{67}{4} \]

For `6 2/5`:
- Multiply the whole number (6) by the denominator (5):
\( 6 \times 5 = 30 \)
- Add the numerator (2):
\( 30 + 2 = 32 \)
- Therefore,
\[ 6 \frac{2}{5} = \frac{32}{5} \]

### Step 2: Calculate the cost for `6 2/5` litres
Now, we need to find the cost of `6 2/5` litres of milk. We can do this by multiplying the cost of 1 litre by the number of litres.

The cost of `6 2/5` litres is given by:
\[ \text{Cost} = \text{Cost per litre} \times \text{Number of litres} \]
Substituting the values we have:
\[ \text{Cost} = \frac{67}{4} \times \frac{32}{5} \]

### Step 3: Multiply the fractions
To multiply the fractions, we multiply the numerators together and the denominators together:
\[ \text{Cost} = \frac{67 \times 32}{4 \times 5} \]

Calculating the numerator:
\[ 67 \times 32 = 2144 \]

Calculating the denominator:
\[ 4 \times 5 = 20 \]

So we have:
\[ \text{Cost} = \frac{2144}{20} \]

### Step 4: Simplify the fraction
Now, we simplify \(\frac{2144}{20}\):
- Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 4:
\[ \frac{2144 \div 4}{20 \div 4} = \frac{536}{5} \]

### Step 5: Convert the improper fraction to a mixed number
Now we convert \(\frac{536}{5}\) into a mixed number:
- Divide 536 by 5:
\[ 536 \div 5 = 107 \quad \text{(whole number)} \]
- The remainder is:
\[ 536 - (107 \times 5) = 536 - 535 = 1 \]
Thus,
\[ \frac{536}{5} = 107 \frac{1}{5} \]

### Final Answer
The cost of `6 2/5` litres of milk is \(107 \frac{1}{5}\) rupees.

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