I bought fruits worth Rs. `27""3/4` and vegetables worth Rs. `10""1/2`. If I gave a fifty-rupee note to the shopkeeper, how much will I get back ?

Answer

To solve the problem step by step, let's break down the costs of fruits and vegetables, find the total cost, and then calculate how much change you will receive from the shopkeeper.

### Step 1: Convert the mixed fractions to improper fractions.
- The cost of fruits is Rs. 27 3/4.
- To convert this to an improper fraction:
- Multiply the whole number (27) by the denominator (4) and add the numerator (3).
- \( 27 \times 4 + 3 = 108 + 3 = 111 \)
- So, Rs. 27 3/4 = Rs. \( \frac{111}{4} \).

- The cost of vegetables is Rs. 10 1/2.
- To convert this to an improper fraction:
- Multiply the whole number (10) by the denominator (2) and add the numerator (1).
- \( 10 \times 2 + 1 = 20 + 1 = 21 \)
- So, Rs. 10 1/2 = Rs. \( \frac{21}{2} \).

### Step 2: Find a common denominator to add the two costs.
- The denominators are 4 and 2. The least common multiple (LCM) of 4 and 2 is 4.
- Convert Rs. \( \frac{21}{2} \) to have a denominator of 4:
- \( \frac{21}{2} = \frac{21 \times 2}{2 \times 2} = \frac{42}{4} \).

### Step 3: Add the costs of fruits and vegetables.
- Now we can add the two fractions:
- \( \frac{111}{4} + \frac{42}{4} = \frac{111 + 42}{4} = \frac{153}{4} \).

### Step 4: Calculate how much change you will receive.
- You paid Rs. 50, which can be expressed as \( \frac{200}{4} \) (to have the same denominator).
- Now subtract the total cost from the amount paid:
- \( \frac{200}{4} - \frac{153}{4} = \frac{200 - 153}{4} = \frac{47}{4} \).

### Step 5: Convert the improper fraction back to a mixed number.
- To convert \( \frac{47}{4} \) to a mixed number:
- Divide 47 by 4, which gives 11 with a remainder of 3.
- So, \( \frac{47}{4} = 11 \frac{3}{4} \).

### Final Answer:
You will receive Rs. 11 3/4 as change from the shopkeeper.

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