X and Y take a grass ground on lease for 300 for grazing their animals. If X grazes 10 animals for 5 weeks and Y grazes 15 animals for 7 weeks. The ratio in which they should divide the rent is:
अपने पशुओं को चराने के लिए x और Y ने एक घास के मैदान को ₹ 300 पट्टे (किराये) पर लिया। यदि x ने 10 पशुओं को 5 सप्ताह चराया तथा Y ने 15 पशुओं को 7 सप्ताह तक चराया, तो उन्हें आपस में किस अनुपात में किराया बाँटना चाहिए ?

Options

A. 1:2
B. 10 : 21
C. 11: 20
D. 2:1

Explanation

To find the ratio in which X and Y should divide the rent for grazing their animals, we need to calculate the total grazing effort contributed by each person. The grazing effort can be calculated by multiplying the number of animals grazed by the number of weeks they were grazed.

### Step 1: Calculate the grazing effort for X
- X grazes 10 animals for 5 weeks.
- Grazing effort by X = Number of animals × Number of weeks = 10 animals × 5 weeks = 50 animal-weeks.

### Step 2: Calculate the grazing effort for Y
- Y grazes 15 animals for 7 weeks.
- Grazing effort by Y = Number of animals × Number of weeks = 15 animals × 7 weeks = 105 animal-weeks.

### Step 3: Find the total grazing effort
- Total grazing effort = Grazing effort by X + Grazing effort by Y = 50 animal-weeks + 105 animal-weeks = 155 animal-weeks.

### Step 4: Determine the ratio of grazing efforts
- The ratio of grazing efforts of X to Y = Grazing effort by X : Grazing effort by Y = 50 : 105.

### Step 5: Simplify the ratio
- To simplify the ratio 50 : 105, we can divide both numbers by their greatest common divisor (GCD), which is 5.
- 50 ÷ 5 = 10 and 105 ÷ 5 = 21.
- Therefore, the simplified ratio is 10 : 21.

### Step 6: Conclusion
- The rent should be divided in the ratio of 10 : 21.