Four milkmen rented a pasture. A put to graze 16 cows for 3 months, B 20 cows for 4 months, C 18 cows for 6 months and D 42 cows for 2 months/ If A's share of rent be ₹ 2400, the rent paid by C is:

Options

A. ₹ 3200
B. ₹ 4200
C. ₹ 4000
D. ₹ 5400

Answer

To solve the problem, we need to determine the rent paid by C based on the number of cows grazed and the duration of grazing by each milkman. Here's a step-by-step solution:

### Step 1: Calculate the total grazing months for each milkman
We calculate the total grazing months for each milkman by multiplying the number of cows by the number of months they grazed.

- **A:** 16 cows for 3 months = 16 * 3 = 48 cow-months
- **B:** 20 cows for 4 months = 20 * 4 = 80 cow-months
- **C:** 18 cows for 6 months = 18 * 6 = 108 cow-months
- **D:** 42 cows for 2 months = 42 * 2 = 84 cow-months

### Step 2: Find the total cow-months
Now, we add up all the cow-months calculated in Step 1.

Total cow-months = 48 (A) + 80 (B) + 108 (C) + 84 (D) = 320 cow-months

### Step 3: Determine the ratio of cow-months for each milkman
Next, we find the ratio of cow-months for each milkman compared to the total cow-months.

- **A's share:** 48 cow-months
- **B's share:** 80 cow-months
- **C's share:** 108 cow-months
- **D's share:** 84 cow-months

### Step 4: Calculate the rent share for each milkman
Since A's share of the rent is ₹2400, we can find the rent per cow-month.

Rent per cow-month = Total rent paid by A / A's cow-months
Rent per cow-month = ₹2400 / 48 = ₹50

### Step 5: Calculate the rent paid by C
Now, we can calculate the rent paid by C using the number of cow-months C has.

Rent paid by C = C's cow-months * Rent per cow-month
Rent paid by C = 108 * ₹50 = ₹5400

### Final Answer
The rent paid by C is ₹5400.

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