Question

A and B rent a pasture for 10 months by contributing equal rent; A puts in 80 cows for 7 months and leaves. How many cows can B put in for the remaining 3 months, if he pays half as much rent again as A?

• A. \(250\)
• B. \(280\)
• C. \(275\)
• D. \(200\)
• E. \(120\)

Answer 1

The Correct Option is B

Concept: Rent is shared in proportion to
(number of cows × time).
Step 1: A's work.
\[ 80 \times 7 = 560 \text{ cow-months} \]
Step 2: Let B use \(x\) cows for 10 months.
\[ B = 10x \]
Step 3: Given relation.
B pays \(\frac{3}{2}\) times A: \[ \frac{10x}{560} = \frac{3}{2} \]
Step 4: Solve.
\[ 10x = 840 \Rightarrow x = 84 \]
Step 5: Remaining 3 months.
Total cows B uses: \[ = \frac{840}{3} = 280 \]
Step 6: Option analysis.

• (A) Incorrect $\times$
• (B) Correct \checkmark
• (C) Incorrect $\times$
• (D) Incorrect $\times$
• (E) Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (B).