Two individuals, A and B, have rented a field. A places 21 horses in the field for 6 months and 15 cows for 2 months. B adds 15 cows for 6 months and 40 sheep for 7.5 months. If 3 horses consume the same amount of food as 5 cows, and 6 cows eat as much as 10 sheep, what portion of the rent should A cover?

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CGL MAINS 2026, SSC

Correct Answer :B - 9/17

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Detailed Text Solution

Given relations:
3 horses = 5 cows → 1 horse = 5/3 cows.

6 cows = 10 sheep → 1 cow = 10/6 = 5/3 sheep.

Convert everything to cows.

A's usage:
21 horses for 6 months.

1 horse = 5/3 cows.

21 horses = 21 × 5/3 = 35 cows.

Consumption = 35 × 6 = 210 cow-months.

15 cows for 2 months = 30 cow-months.

Total A = 240 cow-months.

B's usage:
15 cows for 6 months = 90 cow-months.

1 cow = 5/3 sheep → 1 sheep = 3/5 cow.

40 sheep = 40 × 3/5 = 24 cows.

24 cows for 7.5 months = 180 cow-months.

Total B = 270 cow-months.

Ratio A : B = 240 : 270 = 8 : 9.

A's share of rent = 8/(8+9) = 8/17.