Question

Four sheep farmers rented a pasture, Anil grazed his 24 sheep for 3 months, Bimal 10 sheep for 5 months, Champak 35 sheep for 4 months and Damodar 21 sheep for 3 months,. If Anil’s share of rent is Rs. 720, find the total rent of the pasture:

• A. Rs.3,200
• B. Rs.3,250
• C. Rs.2,300
• D. Rs.4,000

Answer 1

The Correct Option is B

To find the total rent of the pasture, we need to calculate the contribution of each farmer based on the number of sheep and months they grazed, and then determine their share of rent proportionally.

1. Determine the rate at which the rent is shared among the farmers. Each farmer's share of the rent is proportional to the product of the number of sheep and the duration (in months) those sheep grazed.
2. Calculate the grazing units (sheep-months) for each farmer:
   1. Anil: \(24 \text{ sheep} \times 3 \text{ months} = 72 \text{ sheep-months}\)
   2. Bimal: \(10 \text{ sheep} \times 5 \text{ months} = 50 \text{ sheep-months}\) 
   3. Champak: \(35 \text{ sheep} \times 4 \text{ months} = 140 \text{ sheep-months}\)
   4. Damodar: \(21 \text{ sheep} \times 3 \text{ months} = 63 \text{ sheep-months}\)
3. Sum the total grazing units: \(72 + 50 + 140 + 63 = 325 \text{ sheep-months}\)
4. Let the total rent be \(R\).
5. According to the problem, Anil's share is Rs. 720. Anil's share formula: \(\frac{72}{325} \times R = 720\)
6. Solve for \(R\): \(R = \frac{720 \times 325}{72} = 3250\)
7. Thus, the total rent of the pasture is Rs. 3,250.

By following these calculations, we can confirm that the total rent for the pasture is indeed Rs. 3,250, making this the correct answer.