Four milkmen rented a pasture. M put to graze 16 cows for 3 months and N 42 cows for 4 months, O 18 cows for 6 months and P 42 cows for 2 months. If M's share of rent be Rs. 2400, the rent paid by O is.-

Answer

To solve the problem, we need to calculate the contribution of each milkman in terms of cow-months and then determine the rent paid by O based on M's share of rent.

### Step 1: Calculate cow-months for each milkman
Cow-months are calculated by multiplying the number of cows by the number of months they were grazed.

- For M:
\[ \text{Cow-months} = 16 \text{ cows} \times 3 \text{ months} = 48 \text{ cow-months} \]

- For N:
\[ \text{Cow-months} = 42 \text{ cows} \times 4 \text{ months} = 168 \text{ cow-months} \]

- For O:
\[ \text{Cow-months} = 18 \text{ cows} \times 6 \text{ months} = 108 \text{ cow-months} \]

- For P:
\[ \text{Cow-months} = 42 \text{ cows} \times 2 \text{ months} = 84 \text{ cow-months} \]

### Step 2: Find the total cow-months
Now, we will sum up all the cow-months calculated above:
\[ \text{Total cow-months} = 48 + 168 + 108 + 84 = 408 \text{ cow-months} \]

### Step 3: Calculate the rent per cow-month
Since M's share of the rent is Rs. 2400 for his 48 cow-months, we can find the rent per cow-month:
\[ \text{Rent per cow-month} = \frac{2400}{48} = 50 \text{ Rs. per cow-month} \]

### Step 4: Calculate the rent paid by O
Now, we can calculate the rent paid by O based on his cow-months:
\[ \text{Rent paid by O} = \text{Cow-months by O} \times \text{Rent per cow-month} = 108 \times 50 = 5400 \text{ Rs.} \]

### Final Answer
The rent paid by O is Rs. 5400.

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