Three students A, B and C hired a computer for a month. A runs 27 floppy discs for 19 days, B runs 21 for 17 days and C runs 24 for 23 days. If at the end of the month, the rent amounts to Rs23700, how much ought to be paid by A?

Options

A. Rs 8550
B. Rs 5950
C. Rs 9200
D. Rs 6750

Answer

To determine how much A ought to pay, we will calculate the total usage of the computer by each student and then find A's share of the total rent.

### Step 1: Calculate the total usage for each student
- **A's usage:**
\[ \text{Usage by A} = \text{Number of floppy disks} \times \text{Number of days} = 27 \times 19 \]
\[ \text{Usage by A} = 513 \]

- **B's usage:**
\[ \text{Usage by B} = \text{Number of floppy disks} \times \text{Number of days} = 21 \times 17 \]
\[ \text{Usage by B} = 357 \]

- **C's usage:**
\[ \text{Usage by C} = \text{Number of floppy disks} \times \text{Number of days} = 24 \times 23 \]
\[ \text{Usage by C} = 552 \]

### Step 2: Calculate the total usage
Now, we will sum up the total usage by all three students:
\[ \text{Total usage} = \text{Usage by A} + \text{Usage by B} + \text{Usage by C} \]
\[ \text{Total usage} = 513 + 357 + 552 = 1422 \]

### Step 3: Calculate the cost per unit of usage
The total rent for the month is Rs 23,700. We can find the cost per unit of usage:
\[ \text{Cost per unit} = \frac{\text{Total rent}}{\text{Total usage}} = \frac{23700}{1422} \]
Calculating this gives:
\[ \text{Cost per unit} \approx 16.66 \]

### Step 4: Calculate A's share of the rent
Now, we will calculate how much A needs to pay based on their usage:
\[ \text{A's share} = \text{Usage by A} \times \text{Cost per unit} = 513 \times 16.66 \]
Calculating this gives:
\[ \text{A's share} \approx 8547.78 \]

### Step 5: Round to the nearest whole number
Since currency is usually rounded to the nearest whole number, we can round A's share:
\[ \text{A's share} \approx 8548 \]

### Final Answer
A ought to pay Rs 8548.

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