If 15 oxen or 20 cows can eat the grass of a field in 80 days, then in how…
2023
If 15 oxen or 20 cows can eat the grass of a field in 80 days, then in how many days will 6 oxen and 2 cows eat the same grass?
- A.
300
- B.
104
- C.
160
- D.
120
Attempted by 51 students.
Show answer & explanation
Correct answer: C
Concept: When two different kinds of workers (here, oxen and cows) each need a different but known time to finish the SAME job alone, first find how long each portion of the mixed team would take alone by direct inverse proportion, then combine those two times using the standard "working together" rule: 1/T = 1/T1 + 1/T2, where T1 and T2 are the alone-times of the two portions.
Applying it here:
15 oxen alone finish the field in 80 days, so by inverse proportion 6 oxen alone would finish it in (15 × 80) ÷ 6 = 200 days.
20 cows alone finish the field in 80 days, so by inverse proportion 2 cows alone would finish it in (20 × 80) ÷ 2 = 800 days.
Combine the two rates (not the two times): 1/T = 1/200 + 1/800 = 4/800 + 1/800 = 5/800 = 1/160.
So T = 160 days.
Cross-check: Since 15 oxen and 20 cows both clear the same field in 80 days, one ox eats at 20/15 = 4/3 the rate of one cow. So 6 oxen are worth 6 × 4/3 = 8 cow-equivalents, and the full team of 6 oxen + 2 cows is worth 8 + 2 = 10 cow-equivalents. The whole field equals 20 cows × 80 days = 1600 cow-days of eating, so the mixed team finishes it in 1600 ÷ 10 = 160 days — the same result.