Two men, M and N, rent a pasture. M uses 12 cows for 4 months and 18 goats for 5 months, while N uses 26 goats for 7 months. If 3 cows are equivalent to 7 goats, what is M's share of the rent?

The correct answer is $\frac{101}{192}$.

To find M's share of the rent, we first need to convert all animals into a common unit (either cows or goats) and calculate the total usage in terms of "animal-months" for both M and N.

Step 1: Convert all animals into goat units
We are given that 3 cows are equivalent to 7 goats.
Therefore, 1 cow is equivalent to:
$\frac{7}{3}$ goats.

Step 2: Calculate M's total consumption in terms of goat-months
M has 12 cows for 4 months and 18 goats for 5 months.
Converting 12 cows to goats:
12 cows = $12\times \frac{7}{3}=4\times 7=28$ goats.

Now, calculate M's total usage in goat-months:
Usage by 12 cows for 4 months = 28 goats × 4 months = 112 goat-months.
Usage by 18 goats for 5 months = 18 goats × 5 months = 90 goat-months.

Total usage by M:
$112+90=202$ goat-months.

Step 3: Calculate N's total consumption in terms of goat-months
N uses 26 goats for 7 months.
Total usage by N:
$26\times 7=182$ goat-months.

Step 4: Calculate the total pasture usage
Total usage by both M and N combined:
$202+182=384$ goat-months.

Step 5: Find M's fraction of the total rent
M's share of the rent is the ratio of M's usage to the total usage:
M's Share = $\frac{202}{384}$

Dividing both the numerator and the denominator by 2:
$\frac{202÷2}{384÷2}=\frac{101}{192}$

Thus, M's share of the total rent is $\frac{101}{192}$.