Three students A, B and C hired a computer for a month. A runs 27 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 Rs. 23700, how much ought to be paid by each ?

Answer

To solve the problem step by step, we need to calculate the contribution of each student A, B, and C based on the number of discs they ran and the days they used the computer. Then, we will find out how much each student should pay from the total rent of Rs. 23,700.

### Step 1: Calculate the contribution of each student
The contribution of each student can be calculated by multiplying the number of discs they ran by the number of days they used the computer.

- **For Student A:**
\[ \text{Contribution of A} = 27 \text{ discs} \times 19 \text{ days} = 513 \]

- **For Student B:**
\[ \text{Contribution of B} = 21 \text{ discs} \times 17 \text{ days} = 357 \]

- **For Student C:**
\[ \text{Contribution of C} = 24 \text{ discs} \times 23 \text{ days} = 552 \]

### Step 2: Find the total contribution
Now, we need to find the total contribution of all three students.

\[ \text{Total Contribution} = \text{Contribution of A} + \text{Contribution of B} + \text{Contribution of C} \]
\[ = 513 + 357 + 552 = 1422 \]

### Step 3: Calculate the ratio of contributions
Next, we will find the ratio of their contributions.

- The ratio of contributions is:
\[ A : B : C = 513 : 357 : 552 \]

To simplify this ratio, we can divide each term by the greatest common divisor (GCD) of the three numbers. However, for simplicity, we can also use the numbers as they are for the next calculations.

### Step 4: Calculate the share of each student
Now, we can find out how much each student should pay based on their contribution ratio.

- **Total Rent:** Rs. 23,700

- **Share of A:**
\[ \text{Share of A} = \left(\frac{513}{1422}\right) \times 23700 \]
\[ = \frac{513 \times 23700}{1422} \approx 8490 \]

- **Share of B:**
\[ \text{Share of B} = \left(\frac{357}{1422}\right) \times 23700 \]
\[ = \frac{357 \times 23700}{1422} \approx 5700 \]

- **Share of C:**
\[ \text{Share of C} = \left(\frac{552}{1422}\right) \times 23700 \]
\[ = \frac{552 \times 23700}{1422} \approx 10510 \]

### Final Shares
- Student A should pay approximately Rs. 8490.
- Student B should pay approximately Rs. 5700.
- Student C should pay approximately Rs. 10510.